Fluids doi: 10.3390/fluids4030175

Authors: Dmitry Bratsun Vladimir Vyatkin

A class of closed-form exact solutions for the Navier&ndash;Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

]]>Fluids doi: 10.3390/fluids4030174

Authors: Lim Wen Zhen Quoc B. Thai Thanh X. Nguyen Duyen K. Le Jason Kai Wei Lee Yee Qing Xiang Hai M. Duong

Exercising in a tropical climate with constant high temperatures and high humidity increases the risk of heatstroke for active people who frequently train outdoors. For these active persons, a cooling source of water nearby can be essential, and this is usually carried in canteen bottles. However, commercially available water canteen bottles have limited thermal insulation capability to keep the liquid content cooled for the required period. This work proposed an engineering solution to enhance the heat insulation performance of water canteen bottles, using recycled cellulose aerogels made from paper waste for the first time as an insulating layer. Recycled cellulose aerogels wrapped around the water canteen bottle provides excellent thermal insulation performance, while not adding significant weight to the bottle. The temperature of the ice slurry in the canteen bottle was measured periodically over four hours with a mercury thermometer. The effects of the static and dynamic conditions on the temperature rate were also quantified. A 1.5 cm thickness of 1.0 wt.% recycled cellulose aerogel wrapped around the canteen bottle can provide an excellent thermal insulation performance with the lowest rise in temperature, achieving a low final temperature of the ice slurry content of 3.5 &deg;C after 4 h. This result is much better than that provided by available commercial bottles under the same conditions.

]]>Fluids doi: 10.3390/fluids4030173

Authors: Emad Jafari Nodoushan Taeil Yi Young Ju Lee Namwon Kim

While traditional oil recovery methods are limited in terms of meeting the overall oil demands, enhanced oil recovery (EOR) techniques are being continually developed to provide a principal portion of our energy demands. Chemical EOR (cEOR) is one of the EOR techniques that shows an efficient oil recovery factor in a number of oilfields with low salinity and temperature ranges. However, the application of cEOR under the harsh conditions of reservoirs where most of today&rsquo;s crude oils come from remains a challenge. High temperatures, the presence of ions, divalent ions, and heterogeneous rock structures in such reservoirs restrict the application of cEOR. Polymer solutions, surfactants, alkaline-based solutions, and complex multi-components of them are common chemical displacing fluids that failed to show successful recovery results in hostile conditions for various reasons. Wormlike micellar solutions (WMS) are viscoelastic surfactants that possess advantageous characteristics for overcoming current cEOR challenges. In this study, we first review the major approaches and challenges of commonly used chemical agents for cEOR applications. Subsequently, we review special characteristics of WMS that make them promising materials for the future of cEOR.

]]>Fluids doi: 10.3390/fluids4030172

Authors: Elias Laribi Shun Ogawa Guilhem Dif-Pradalier Alexei Vasiliev Xavier Garbet Xavier Leoncini

Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to the obtained equations are then discussed. It appears that the presence of an azimuthal (poloidal) flow in the plasma can ensure radial confinement, while the presence of a longitudinal (toroidal) flow can enhance greatly the confinement. Moreover in the global physically reasonable situation, we find that no unstable point can emerge in the effective integrable Hamiltonian of the individual particles, hinting at some stability of the confinement when considering a toroidal geometry in the large aspect ratio limit.

]]>Fluids doi: 10.3390/fluids4030171

Authors: Santiago López Castaño Andrea Petronio Giovanni Petris Vincenzo Armenio

We validate and test two algorithms for the time integration of the Boussinesq form of the Navier&mdash;Stokes equations within the Large Eddy Simulation (LES) methodology for turbulent flows. The algorithms are implemented in the OpenFOAM framework. From one side, we have implemented an energy-conserving incremental-pressure Runge&ndash;Kutta (RK4) projection method for the solution of the Navier&ndash;Stokes equations together with a dynamic Lagrangian mixed model for momentum and scalar subgrid-scale (SGS) fluxes; from the other side we revisit the PISO algorithm present in OpenFOAM (pisoFoam) in conjunction with the dynamic eddy-viscosity model for SGS momentum fluxes and a Reynolds Analogy for the scalar SGS fluxes, and used for the study of turbulent channel flows and buoyancy-driven flows. In both cases the validity of the anisotropic filter function, suited for non-homogeneous hexahedral meshes, has been studied and proven to be useful for industrial LES. Preliminary tests on energy-conservation properties of the algorithms studied (without the inclusion of the subgrid-scale models) show the superiority of RK4 over pisoFoam, which exhibits dissipative features. We carried out additional tests for wall-bounded channel flow and for Rayleigh&ndash;B&egrave;nard convection in the turbulent regime, by running LES using both algorithms. Results show the RK4 algorithm together with the dynamic Lagrangian mixed model gives better results in the cases analyzed for both first- and second-order statistics. On the other hand, the dissipative features of pisoFoam detected in the previous tests reflect in a less accurate evaluation of the statistics of the turbulent field, although the presence of the subgrid-scale model improves the quality of the results compared to a correspondent coarse direct numerical simulation. In case of Rayleigh&ndash;B&eacute;nard convection, the results of pisoFoam improve with increasing values of Rayleigh number, and this may be attributed to the Reynolds Analogy used for the subgrid-scale temperature fluxes. Finally, we point out that the present analysis holds for hexahedral meshes. More research is need for extension of the methods proposed to general unstructured grids.

]]>Fluids doi: 10.3390/fluids4030170

Authors: Yahaya D. Baba Archibong Archibong-Eso Aliyu M. Aliyu Olawale T. Fajemidupe Joseph X. F. Ribeiro Liyun Lao Hoi Yeung

Slug translational velocity, described as the velocity of slug units, is the summation of the maximum mixture velocity in the slug body and the drift velocity. Existing prediction models in literature were developed based on observation from low viscosity liquids, neglecting the effects of fluid properties (i.e., viscosity). However, slug translational velocity is expected to be affected by the fluid viscosity. Here, we investigate the influence of high liquid viscosity on slug translational velocity in a horizontal pipeline of 76.2-mm internal diameter. Air and mineral oil with viscosities within the range of 1.0–5.5 Pa·s were used in this investigation. Measurement was by means of a pair of gamma densitometer with fast sampling frequencies (up to 250 Hz). The results obtained show that slug translational velocity increases with increase in liquid viscosity. Existing slug translational velocity prediction models in literature were assessed based on the present high viscosity data for which statistical analysis revealed discrepancies. In view of this, a new empirical correlation for the calculation of slug translational velocity in highly viscous two-phase flow is proposed. A comparison study and validation of the new correlation showed an improved prediction performance.

]]>Fluids doi: 10.3390/fluids4030169

Authors: Jason G. Miles Nicholas A. Battista

Jellyfish are majestic, energy-efficient, and one of the oldest species that inhabit the oceans. It is perhaps the second item, their efficiency, that has captivated scientists for decades into investigating their locomotive behavior. Yet, no one has specifically explored the role that their tentacles and oral arms may have on their potential swimming performance. We perform comparative in silico experiments to study how tentacle/oral arm number, length, placement, and density affect forward swimming speeds, cost of transport, and fluid mixing. An open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid–structure interaction problem of an idealized flexible jellyfish bell with poroelastic tentacles/oral arms in a viscous, incompressible fluid. Overall tentacles/oral arms inhibit forward swimming speeds, by appearing to suppress vortex formation. Nonlinear relationships between length and fluid scale (Reynolds Number) as well as tentacle/oral arm number, density, and placement are observed, illustrating that small changes in morphology could result in significant decreases in swimming speeds, in some cases by upwards of 80–90% between cases with or without tentacles/oral arms.

]]>Fluids doi: 10.3390/fluids4030168

Authors: Paiman Shafabakhsh Marwan Fahs Behzad Ataie-Ashtiani Craig T. Simmons

The Elder problem is one of the well-known examples of an unstable density-driven flow (DDF) and solute transport in porous media. The goal of this research is to investigate the influence of fracture networks on this benchmark problem due to the great importance of the fractured heterogeneity effect on unstable DDF. For this aim, the fractured Elder problem is solved using COMSOL Multiphysics, which is a finite element method simulator. Uniform and orthogonal fracture networks are embedded to analyze free convective flow and development of unstable salt plumes. The results indicate that the mesh sensitivity of the fractured Elder problem is greater than the homogeneous case. Furthermore, it has been shown that in the fractured cases, the onset of instability and free convection occur with lower critical Rayleigh number, which means that fracture networks have a destabilizing effect. Also, we examined the structural properties of fracture networks that control convective flow patterns, and the simulation results show that the strength of convection and instability at the beginning of the intrusion is proportional to the aperture size of the fractures. Moreover, the increase of the fracture&rsquo;s density leads different modes of transient convective modes, until a specific fracture density after which the transient convective modes become similar to the homogenous case.

]]>Fluids doi: 10.3390/fluids4030167

Authors: Maher Shehadi

Thermal plumes generated by human bodies can affect the temperature and humidity of the surrounding environment. An experimental study investigated the effects of thermal plumes formed by aircraft passengers on airflow and turbulence characteristics inside aircraft-cabins. An 11-row, wide-body B767 cabin mockup was used with actual seats, air diffusers and cabin profile. Thermal manikins were used simulating passengers in the cabin. Tracer gas and air speed inside the cabin were measured while the heat from the manikins was turned on and off to help understand the effects of the thermal heat released by the manikins. Results showed that tracer gas distribution were more uniformly and equally distributed around the release source and the air speed fluctuation were lower under cooler environments when the thermal manikins were turned off. Heated environments increased the values of turbulence kinetic energy and the turbulence intensity levels. However, the effects on the turbulence intensity were less significant compared to the turbulence kinetic energy. On the other hand, the dissipation rates were higher for unheated cases in the front and back sections of the mockup cabin. The relative uncertainty for tracer gas sampling ranged between &plusmn;5&ndash;14% for heated manikins versus &plusmn;8&ndash;17% for unheated manikins. Higher uncertainty levels accompanied the turbulence measurements due to the highly chaotic nature of the flow inside the cabin.

]]>Fluids doi: 10.3390/fluids4030166

Authors: Eilis Rosenbaum Mehrdad Massoudi Kaushik Dayal

We want to study the influence of bubbles on the viscosity of suspensions with a computational approach that also accounts for the arrangement of the bubbles due to shearing flow. This requires a large number of bubbles to properly simulate and requires a large amount of computational resources. Here we develop a set of equations to define the viscosity ratio from the simulation results to show the influence of the bubbles on the viscosity as a function of the volume fraction. One application of this work has been used to study a specific type of cement that has bubbles injected into the slurry while it is still fluid. The bubbles are added to reduce the density but they also improve the properties of the cement with the increase in viscosity. We show that the computed results match the few experimental results that have been reported.

]]>Fluids doi: 10.3390/fluids4030165

Authors: Adnan Darwish Ahmad Binit B. Singh Mark Doerre Ahmad M. Abubaker Masoud Arabghahestani Ahmad A. Salaimeh Nelson K. Akafuah

In this study, we evaluated the fundamental physical behavior during droplet formation and flow from a rotary bell spray in the absence of an electrostatic field. The impact of a wide range of operating parameters of the rotary bell sprayer, such as flow rates, rotational speeds, and spatial positioning, on droplet sizes and size distributions using a three-dimensional (3-D) mapping was studied. The results showed that increasing the rotational speed caused the Sauter mean diameter of the droplets to decrease while increasing flow rate increased the droplet sizes. The rotational speed effect, however, was dominant compared to the effect of flow rate. An increase in droplet size radially away from the cup was noted in the vicinity of the cup, nevertheless, as the lateral distances from the cup and rotational speed were increased, the droplet sizes within the flow field became more uniform. This result is of importance for painting industries, which are looking for optimal target distances for uniform painting appearance. Furthermore, the theoretical formulation was validated with experimental data, which provides a wider range of applicability in terms of environment and parameters that could be tested. This work also provides an abundance of measurements, which can serve as a database for the validation of future droplet disintegration simulations.

]]>Fluids doi: 10.3390/fluids4030164

Authors: Bourantas Zwick Joldes Loukopoulos Tavner Wittek Miller

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.

]]>Fluids doi: 10.3390/fluids4030163

Authors: Jesse T. Coburn Luca Sorriso-Valvo

We develop incompressible magnetohydrodynamic (IMHD) energy budget equations with a spatial filtering kernel and estimate the scaling of the structure functions. The Politano-Pouquet law is recovered as an upper bound on the scale-to-scale energy transfer. The primary result of this work is the relation of the scaling of IMHD invariants. It can be produced by hypothesizing a scale-independent energy transfer rate. These results have relevance in plasma regimes where the approximations of IMHD are justified. We measure structure functions with solar wind data and find support for the relations.

]]>Fluids doi: 10.3390/fluids4030162

Authors: Thorben Helmers Philip Kemper Jorg Thöming Ulrich Mießner

Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the entire channel cross-section, it enables the continuous phase to bypass the droplet through the corners. A consideration of the continuity equation generally relates the excess velocity to the mean flow velocity. We base the quantification of the bypass flow on a correlation for the droplet cap deformation from its static shape. The cap deformation reveals the forces of the flowing liquids exerted onto the interface and allows estimating the local driving pressure gradient for the bypass flow. The characterizing parameters are identified as the bypass length, the wall film thickness, the viscosity ratio between both phases and the C a number. The proposed model is adapted with a stochastic, metaheuristic optimization approach based on genetic algorithms. In addition, our model was successfully verified with high-speed camera measurements and published empirical data.

]]>Fluids doi: 10.3390/fluids4030161

Authors: Saadbin Khan Balaji Jayaraman

The structure of turbulent flow over non-flat surfaces is a topic of major interest in practical applications in both engineering and geophysical settings. A lot of work has been done in the fully rough regime at high Reynolds numbers where the effect on the outer layer turbulence structure and the resulting friction drag is well documented. It turns out that surface topology plays a significant role on the flow drag especially in the transitional roughness regime and therefore, is hard to characterize. Survey of literature shows that roughness function depends on the interaction of roughness height, flow Reynolds number, and topology shape. In addition, if the surface topology contains large enough scales then it can impact the outer layer dynamics and in turn modulate the total frictional force. Therefore, it is important to understand the mechanisms underlying drag increase from systematically varied surface undulations in order to better interpret quantifications based on mean statistics such as roughness function. In this study, we explore the mechanisms that modulate the turbulence structure over a two-dimensional (2D) sinusoidal wavy surface with a fixed amplitude, but varying slopes that are sufficiently small to generate only intermittent flow separation. To accomplish this, we perform a set of highly resolved direct numerical simulations (DNS) to model the turbulent flow between two infinitely wide 2D wavy plates at a friction Reynolds number, R e &tau; = 180 , which represents modest scale separation. We pursue two different but related flavors of analysis. The first one adopts a roughness characterization flavor of such wavy surfaces. The second one focuses on understanding the nonequilibrium near-surface turbulence structure and their impact on roughness characterization. Analysis of the different statistical quantifications show strong dependence on wave slope for the roughness function indicating drag increase due to enhanced turbulent stresses resulting from increased production of vertical velocity variance from the surface undulations.

]]>Fluids doi: 10.3390/fluids4030160

Authors: Dmitry Strunin Fatima Ahmed

We present numerical solutions of the semi-phenomenological model of self-propagating fluid pulses (auto-pulses) in the channel branching into two thinner channels, which simulates branching of a hypothetical artificial artery. The model is based on the lubrication theory coupled with elasticity and has the form of a single nonlinear partial differential equation with respect to the displacement of the elastic wall as a function of the distance along the channel and time. The equation is solved numerically using the 1D integrated radial basis function network method. Using homogeneous boundary conditions on the edges of space domain and continuity condition at the branching point, we obtained and analyzed solutions in the form of auto-pulses penetrating through the branching point from the thick channel into the thin channels. We evaluated magnitudes of the phenomenological coefficients responsible for the active motion of the walls in the model.

]]>Fluids doi: 10.3390/fluids4030159

Authors: Suraj Pawar Omer San

CFD Julia is a programming module developed for senior undergraduate or graduate-level coursework which teaches the foundations of computational fluid dynamics (CFD). The module comprises several programs written in general-purpose programming language Julia designed for high-performance numerical analysis and computational science. The paper explains various concepts related to spatial and temporal discretization, explicit and implicit numerical schemes, multi-step numerical schemes, higher-order shock-capturing numerical methods, and iterative solvers in CFD. These concepts are illustrated using the linear convection equation, the inviscid Burgers equation, and the two-dimensional Poisson equation. The paper covers finite difference implementation for equations in both conservative and non-conservative form. The paper also includes the development of one-dimensional solver for Euler equations and demonstrate it for the Sod shock tube problem. We show the application of finite difference schemes for developing two-dimensional incompressible Navier-Stokes solvers with different boundary conditions applied to the lid-driven cavity and vortex-merger problems. At the end of this paper, we develop hybrid Arakawa-spectral solver and pseudo-spectral solver for two-dimensional incompressible Navier-Stokes equations. Additionally, we compare the computational performance of these minimalist fashion Navier-Stokes solvers written in Julia and Python.

]]>Fluids doi: 10.3390/fluids4030158

Authors: Brett Peters Mesbah Uddin

This study investigated the unsteady acceleration aerodynamics of bluff bodies through the study of a channel mounted square cylinder undergoing free-stream acceleration of &plusmn;20 ms&minus;2 with Reynolds numbers spanning 3.2 &times; 104 to 3.6 &times; 105. To achieve this, a numerical simulation was created with a commercial finite volume unstructured computational fluid dynamics code, which was first validated using Improved Delayed Detached Eddy Simulation against experimental and direct numerical simulated results. Then, the free stream conditions were subjected to a periodic velocity signal where data were recorded and ensemble averaged over at least 30 distinct acceleration and deceleration data points. This enabled the comparison of body forces and flow field variations among accelerating, steady and decelerating free-stream conditions. Body force analysis determined that decelerating and accelerating drag forces varied &minus;47% and 44%, respectively, in comparison to steady free-stream conditions. In addition, several differences were also observed and explored such as near-body flow structures, wake dynamics, K&aacute;rm&aacute;n vortices and vorticity production during the aforementioned conditions. The primary interest of this study was for the future application towards road vehicles for predictive dynamic modeling and aerodynamic development.

]]>Fluids doi: 10.3390/fluids4030157

Authors: Ahmed Faraz Khan Philip John Roberts Alexey A. Burluka

A numerical and experimental investigation in to the role of gasoline surrogates and their reduced chemical kinetic mechanisms in spark ignition (SI) engine knocking has been carried out. In order to predict autoignition of gasoline in a spark ignition engine three reduced chemical kinetic mechanisms have been coupled with quasi-dimensional thermodynamic modelling approach. The modelling was supported by measurements of the knocking tendencies of three fuels of very different compositions yet an equivalent Research Octane Number (RON) of 90 (ULG90, PRF90 and 71.5% by volume toluene blended with n-heptane) as well as iso-octane. The experimental knock onsets provided a benchmark for the chemical kinetic predictions of autoignition and also highlighted the limitations of characterisation of the knock resistance of a gasoline in terms of the Research and Motoring octane numbers and the role of these parameters in surrogate formulation. Two approaches used to optimise the surrogate composition have been discussed and possible surrogates for ULG90 have been formulated and numerically studied. A discussion has also been made on the various surrogates from the literature which have been tested in shock tube and rapid compression machines for their autoignition times and are a source of chemical kinetic mechanism validation. The differences in the knock onsets of the tested fuels have been explained by modelling their reactivity using semi-detailed chemical kinetics. Through this work, the weaknesses and challenges of autoignition modelling in SI engines through gasoline surrogate chemical kinetics have been highlighted. Adequacy of a surrogate in simulating the autoignition behaviour of gasoline has also been investigated as it is more important for the surrogate to have the same reactivity as the gasoline at all engine relevant p &minus; T conditions than having the same RON and Motored Octane Number (MON).

]]>Fluids doi: 10.3390/fluids4030156

Authors: Toru Yamada Shugo Itoh Yohei Morinishi Shinji Tamano

This study puts emphasis on reducing the temperature error of dissipative particle dynamics (DPD) fluid by directly applying a minimal-stage third-order partitioned Runge-Kutta (PRK3) method to the time integration, which does not include any of additional governing equations and change in the DPD thermostat formulation. The error is estimated based on the average values of both kinetic and configurational temperatures. The result shows that the errors in both temperatures errors are greatly reduced by using the PRK3 scheme as comparing them to those of previous studies. Additionally, the comparison among three different PRK3 schemes demonstrates our recent findings that the symplecticity conservation of the system is important to reduce the temperature error of DPD fluid especially for large time increments. The computational efficiencies are also estimated for the PRK3 scheme as well as the existing ones. It was found from the estimation that the simulation using the PRK3 scheme is more than twice as efficient as those using the existing ones. Finally, the roles of both kinetic and configurational temperatures as error indicators are discussed by comparing them to the velocity autocorrelation function and the radial distribution function. It was found that the errors of these temperatures involve different characteristics, and thus both temperatures should be taken into account to comprehensively evaluate the numerical error of DPD.

]]>Fluids doi: 10.3390/fluids4030155

Authors: Simone Salvadori Mauro Carnevale Alessia Fanciulli Francesco Montomoli

In transonic high-pressure turbine stages, oblique shocks originating from vane trailing edges impact the suction side of each adjacent vane. High-pressure vanes are cooled to tolerate the combustor exit-temperature levels, then it is highly probable that shock impingement will occur in proximity to a row of cooling holes. The presence of such a shock, together with the inevitable manufacturing deviations, alters the location of the shock impingement and of the performance parameters of each cooling hole. The present work provides a general description of the aero-thermal field that occurs on the rear suction side of a cooled vane. Computational Fluid Dynamics (CFD) is used to evaluate the deterministic response of the selected configurations in terms of adiabatic effectiveness, discharge coefficient, blowing ratio, density ratio, and momentum ratio. Turbulence is modelled by using both the Shear Stress Transport method (SST) and the Reynolds Stress Model (RSM) implemented in ANSYS&reg; FLUENT&reg;. The obtained results are compared with the experimental data obtained by the Institut f&uuml;r Thermische Str&ouml;mungsmaschinen in Karlsruhe. Two uncertainty quantification methodologies based on Hermite polynomials and Pad&egrave;&ndash;Legendre approximants are used to consider the probability distribution of the geometrical parameters and to evaluate the response surfaces for the system response quantities. Trailing-edge and cooling-hole diameters have been considered to be aleatory unknowns. Uncertainty quantification analysis allows for the assessment of the mutual effects on global and local parameters of the cooling device. Obtained results demonstrate that most of the parameters are independent by the variation of the aleatory unknowns while the standard deviation of the blowing ratio associated with the hole diameter uncertainty is around 12%, with no impact by the trailing-edge thickness. No relevant advantages are found using either SST model or RSM in combination with Hermite polynomials and Pad&egrave;&ndash;Legendre approximants.

]]>Fluids doi: 10.3390/fluids4030154

Authors: Aadi Khanal Ruud Weijermars

A long overdue distinction between so-called variant and invariant complex potentials is proposed here for the first time. Invariant complex potentials describe physical flows where a switch of the real and imaginary parts of the function will still describe the same type of physical flow (but only rotated by &pi;/2). Such invariants can be formulated with Euler&rsquo;s formula to depict the same flow for any arbitrary orientation with respect to the coordinate system used. In contrast, variant complex potentials, when swapping their real and imaginary parts, will result in two fundamentally different physical flows. Next, we show that the contour integrals of the real and imaginary part of simple variant and invariant complex potentials generally do not generate any discernable branch cut problems. However, complex potentials due to the multiple superpositions of simple flows, even when invariant, may involve many options for selecting the branch cut locations. Examples of such branch cut choices are given for so-called areal doublets and areal dipoles, which are powerful tools to describe the streamlines and pressure fields for flow in porous media with enhanced permeability flow channels. After a discussion of the branch cut solutions, applications to a series of synthetic and field examples with enhanced permeability flow channels are given with examples of the streamline and pressure field solutions.

]]>Fluids doi: 10.3390/fluids4030153

Authors: Omar M. A. M. Ibrahim Shigeo Yoshida Masahiro Hamasaki Ao Takada

Complex terrain can influence wind turbine wakes and wind speed profiles in a wind farm. Consequently, predicting the performance of wind turbines and energy production over complex terrain is more difficult than it is over flat terrain. In this preliminary study, an engineering wake model, that considers acceleration on a two-dimensional hill, was developed based on the momentum theory. The model consists of the wake width and wake wind speed. The equation to calculate the rotor thrust, which is calculated by the wake wind speed profiles, was also formulated. Then, a wind-tunnel test was performed in simple flow conditions in order to investigate wake development over a two-dimensional hill. After this the wake model was compared with the wind-tunnel test, and the results obtained by using the new wake model were close to the wind-tunnel test results. Using the new wake model, it was possible to estimate the wake shrinkage in an accelerating two-dimensional wind field.

]]>Fluids doi: 10.3390/fluids4030152

Authors: Thomas Guérin Anouk de Bakker Xavier Bertin

More than three decades ago, it was noted that the ocean infragravity bound wave increasingly lags behind the forcing short-wave groups when propagating towards the shore. To date, the most recent theoretical prediction of this so-called phase lag remained a first-order approximation in terms of depth variations. Here, a new semi-analytical solution is proposed which does not rely on this approximation. Strong agreement is obtained when the new solution is compared with high-resolution laboratory data involving both bichromatic and random wave conditions. This newly proposed theoretical phase lag is then extensively compared with the former one, highlighting an increasing discrepancy between the two solutions as the relative bottom slope increases. The four influencing parameters, namely the bottom slope, the water depth, the incident short-wave peak period and the incident group period, are shown to impact, each in a specific way, the bound wave phase lag. While the latter is seen to increase with lower water depths and/or with higher short-wave peak periods, both the bottom slope and the group period can affect the phase lag in a different manner. Indeed, steeper bed slopes induce lower phase lags in shallow water but higher ones in deep water, while higher group periods induce higher phase lags for gentle slopes but lower ones for steep slopes.

]]>Fluids doi: 10.3390/fluids4030151

Authors: Shaoguang Wang Xiuling Wang

Recent research has suggested that noise barriers have significant impacts on near-road automobile emissions reduction. T-shaped noise barriers have better performance on reducing noise than others, however, their effects on automobile emissions reduction are not clear. In this research, commercial software ANSYS&reg;Fluent 19.2 (Ansys Inc., Canonsburg, PA, USA) was applied to simulate the noise barrier shape and different inflow wind shear condition effects on highway automobiles emission dispersion. Various Reynolds Averaged Navier-Stokes (RANS) models were tested. The realizable k-&epsilon; turbulence model was selected to simulate the turbulent flow caused by fast moving vehicles on highway based on the comparison results. A non-reacting species transport model was applied to simulate emission dispersion. Results showed that the T-shaped barrier was able to help reduce highway automobiles emission concentration in downstream areas more than the rectangular barrier. An optimized range of the T-shape was proposed; under the inflow condition without wind shear, the noise barrier shape effects on automobiles emission reduction were not significant.

]]>Fluids doi: 10.3390/fluids4030150

Authors: Tadzio Levato Leonardo V. Goncalves Vincenzo Giannini

The idea of using a gas-mixture comprising atoms with a high mass number in order to increase proton energies in laser induced plasma acceleration at critical density is investigated by means of 2D PIC (Particle-In-Cell) simulations. Comparing and discussing the case of a pure hydrogen plasma and that of a plasma containing higher mass number species with a small percentage of hydrogen, we demonstrate that the mixture enhances the energies of the accelerated protons. We also show that using a gas-mixture introduces the possibility of using the densities ratio in order to change the relative acceleration of the species.

]]>Fluids doi: 10.3390/fluids4030149

Authors: Hossein Asadi Mohammad Taeibi-Rahni Amir Mahdi Akbarzadeh Khodayar Javadi Goodarz Ahmadi

The rupturing process of a membrane, located between two fluids at the center of a three-dimensional channel, is numerically investigated. The smoothed particle hydrodynamics (SPH) and the finite element method (FEM) are used, respectively, for modeling the fluid and solid phases. A range of pressure differences and membrane thicknesses are studied and two different rupturing processes are identified. These processes differ in the time scale of the rupture, the location of the rupture initiation, the level of destruction and the driving mechanism.

]]>Fluids doi: 10.3390/fluids4030148

Authors: Chunhui Zhang Charles Patrick Bounds Lee Foster Mesbah Uddin

In today&rsquo;s road vehicle design processes, Computational Fluid Dynamics (CFD) has emerged as one of the major investigative tools for aerodynamics analyses. The age-old CFD methodology based on the Reynolds Averaged Navier&ndash;Stokes (RANS) approach is still considered as the most popular turbulence modeling approach in automotive industries due to its acceptable accuracy and affordable computational cost for predicting flows involving complex geometries. This popular use of RANS still persists in spite of the well-known fact that, for automotive flows, RANS turbulence models often fail to characterize the associated flow-field properly. It is even true that more often, the RANS approach fails to predict correct integral aerodynamic quantities like lift, drag, or moment coefficients, and as such, they are used to assess the relative magnitude and direction of a trend. Moreover, even for such purposes, notable disagreements generally exist between results predicted by different RANS models. Thanks to fast advances in computer technology, increasing popularity has been seen in the use of the hybrid Detached Eddy Simulation (DES), which blends the RANS approach with Large Eddy Simulation (LES). The DES methodology demonstrated a high potential of being more accurate and informative than the RANS approaches. Whilst evaluations of RANS and DES models on various applications are abundant in the literature, such evaluations on full-car models are relatively fewer. In this study, four RANS models that are widely used in engineering applications, i.e., the realizable k &minus; &epsilon; two-layer, Abe&ndash;Kondoh&ndash;Nagano (AKN) k &minus; &epsilon; low-Reynolds, SST k &minus; &omega; , and V2F are evaluated on a full-scale passenger vehicle with two different front-end configurations. In addition, both cases are run with two DES models to assess the differences between the flow predictions obtained using RANS and DES.

]]>Fluids doi: 10.3390/fluids4030147

Authors: Peter Vadasz

A review on instability and consequent natural convection in rotating porous media is presented. Taylor-Proudman columns and geostrophic flows exist in rotating porous media just the same as in pure fluids. The latter leads to a tendency towards two-dimensionality. Natural convection resulting from density gradients in a gravity field as well as natural convection induced by density gradients due to the centripetal acceleration are being considered. The former is the result of gravity-induced buoyancy, the latter is due to centripetally-induced buoyancy. The effect of Coriolis acceleration is also discussed. Linear stability analysis as well as weak nonlinear solutions are being derived and presented.

]]>Fluids doi: 10.3390/fluids4030146

Authors: Aaron Endres Thomas Sattelmayer

Boundary layer flashback from the combustion chamber into the premixing section is a threat associated with the premixed combustion of hydrogen-containing fuels in gas turbines. In this study, the effect of pressure on the confined flashback behaviour of hydrogen-air flames was investigated numerically. This was done by means of large eddy simulations with finite rate chemistry as well as detailed chemical kinetics and diffusion models at pressures between 0.5 bar and 3 bar. It was found that the flashback propensity increases with increasing pressure. The separation zone size and the turbulent flame speed at flashback conditions decrease with increasing pressure, which decreases flashback propensity. At the same time the quenching distance decreases with increasing pressure, which increases flashback propensity. It is not possible to predict the occurrence of boundary layer flashback based on the turbulent flame speed or the ratio of separation zone size to quenching distance alone. Instead the interaction of all effects has to be accounted for when modelling boundary layer flashback. It was further found that the pressure rise ahead of the flame cannot be approximated by one-dimensional analyses and that the assumptions of the boundary layer theory are not satisfied during confined boundary layer flashback.

]]>Fluids doi: 10.3390/fluids4030145

Authors: Tiwei Wei Herman Oprins Vladimir Cherman Eric Beyne Martine Baelmans

Liquid microjet impingement cooling has shown the potential to be the solution for heat removal from electronic devices such as very-large-scale integration (VLSI) chips. The post-impingement dynamics of the jet, specifically the interaction between the liquid fronts on the surface engendered by the jets is a critical criterion improving the heat transfer characteristics. While some seminally important experimental studies have investigated this attribute, the amount of accurate data and analysis is limited by the shortcomings of real-life experiments. In this article, numerical investigations into the fluid dynamics and heat transfer in microjet cooling systems are carried out. Specifically, this paper addresses the question regarding the necessary fidelity of the simulations. Different Reynolds-averaged Navier&ndash;Stokes (RANS) models are compared to the Large Eddy Simulations (LES) simulation and the potential fidelity of different eddy-viscosity-based closures is clearly shown. Recommendations are made regarding the RANS closures that should give the best performance. It is demonstrated that the transition Shear Stress Transport (SST) model and k - &omega; SST model both show excellent ability to predict the local or average Nu, and also local level pressure coefficient f with less than 5% difference in the range of 30 &lt; Red &lt; 4000, compared with the reference LES model. For the experimental measurements in the range of 130 &lt; Red &lt; 1400, the LES model, transition SST model and k - &omega; SST model all show less than 25% prediction error. Moreover, it is shown that the validity of the unit cell assumption for the temperature and flow distribution depends on the flow rate.

]]>Fluids doi: 10.3390/fluids4030144

Authors: Taraprasad Bhowmick Michele Iovieno

Turbulent mixing through atmospheric cloud and clear air interface plays an important role in the life of a cloud. Entrainment and detrainment of clear air and cloudy volume result in mixing across the interface, which broadens the cloud droplet spectrum. In this study, we simulate the transient evolution of a turbulent cloud top interface with three initial mono-disperse cloud droplet population, using a pseudo-spectral Direct Numerical Simulation (DNS) along with Lagrangian droplet equations, including collision and coalescence. Transient evolution of in-cloud turbulent kinetic energy (TKE), density of water vapour and temperature is carried out as an initial value problem exhibiting transient decay. Mixing in between the clear air and cloudy volume produced turbulent fluctuations in the density of water vapour and temperature, resulting in supersaturation fluctuations. Small scale turbulence, local supersaturation conditions and gravitational forces have different weights on the droplet population depending on their sizes. Larger droplet populations, with initial 25 and 18 &mu; m radii, show significant growth by droplet-droplet collision and a higher rate of gravitational sedimentation. However, the smaller droplets, with an initial 6 &mu; m radius, did not show any collision but a large size distribution broadening due to differential condensation/evaporation induced by the mixing, without being influenced by gravity significantly.

]]>Fluids doi: 10.3390/fluids4030143

Authors: Yorgos G. Stergiou Aggelos T. Keramydas Antonios D. Anastasiou Aikaterini A. Mouza Spiros V. Paras

The study of hemodynamics is particularly important in medicine and biomedical engineering as it is crucial for the design of new implantable devices and for understanding the mechanism of various diseases related to blood flow. In this study, we experimentally identify the cell free layer (CFL) width, which is the result of the Fahraeus&ndash;Lindqvist effect, as well as the axial velocity distribution of blood flow in microvessels. The CFL extent was determined using microscopic photography, while the blood velocity was measured by micro-particle image velocimetry (&mu;-PIV). Based on the experimental results, we formulated a correlation for the prediction of the CFL width in small caliber (D &lt; 300 &mu;m) vessels as a function of a modified Reynolds number (Re&infin;) and the hematocrit (Hct). This correlation along with the lateral distribution of blood viscosity were used as input to a &ldquo;two-regions&rdquo; computational model. The reliability of the code was checked by comparing the experimentally obtained axial velocity profiles with those calculated by the computational fluid dynamics (CFD) simulations. We propose a methodology for calculating the friction loses during blood flow in &mu;-vessels, where the Fahraeus&ndash;Lindqvist effect plays a prominent role, and show that the pressure drop may be overestimated by 80% to 150% if the CFL is neglected.

]]>Fluids doi: 10.3390/fluids4030142

Authors: Xin He Kai Zhang Chunpei Cai

This paper presents our recent work on investigating velocity slip boundary conditions&rsquo; effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

]]>Fluids doi: 10.3390/fluids4030141

Authors: Manfredo Guilizzoni Maurizio Santini Stephanie Fest-Santini

Drop impacts (onto dry or wet surfaces or into deep pools) are important in a wide range of applications, and, consequently, many studies, both experimental and numerical, are available in the literature. However, such works are focused either on statistical analyses of drop populations or on single drops. The literature is heavily lacking in information about the mutual interactions between a few drops during the impact. This work describes a computational fluid dynamics (CFD) study on the impact of two, three, and four synchronized drops into a deep pool. The two-phase finite-volume solver interFoam of the open source CFD package OpenFOAM&reg; was used. After validation with respect to high speed videos, to confirm the performance of the solver in this field, impact conditions and aspects that would have been difficult to obtain and to study in experiments were investigated: namely, the energy conversion during the crater evolution, the effect of varying drop interspace and surface tension, and multiple drop impacts. The results show the very significant effect of these aspects. This implies that an extension of the results of single-drop, distilled-water laboratory experiments to real applications may not be reliable.

]]>Fluids doi: 10.3390/fluids4030140

Authors: Moses Karakouzian Amilcar Chavez Donald Hayes Mohammad Nazari-Sharabian

Bridge deck splashing causes deterioration to a bridge&rsquo;s structure and renders the bridge unsafe for motorists and pedestrians. The traditional countermeasure for bridge deck splashing has been pier extension. Pier extensions move the pier wave and the associated splash away from the bridge deck, but retrofitting existing bridges with pier extensions is costly. This research evaluates the use of a bulbous added to the pier as an alternative to pier extension. A bulb placed on the upstream side of a bridge pier affects the splashing. The energy in the passing water is redirected from the impact by streamlining the flow. This study proposes a mathematical model for bulbous pier design, based on a model used for a mono-hull ship. Under the mono-hull model, the bulb length extends, reaching the region where viscous resistance is dominant. Unlike wave-making resistance, which is achieved through modeling, the proposed model does not require modeling to calculate pier wave reduction.

]]>Fluids doi: 10.3390/fluids4030139

Authors: Daniel Butcher Adrian Spencer

Techniques for the experimental determination of velocity fields such as particle image velocimetry (PIV) can often be hampered by spurious vectors or sparse regions of measurement which may occur due to a number of reasons. Commonly used methods for detecting and replacing erroneous values are often based on statistical measures of the surrounding vectors and may be influenced by further poor data quality in the region. A new method is presented in this paper using Linear Stochastic Estimation for vector replacement (LSEVR) which allows for increased flexibility in situations with regions of spurious vectors. LSEVR is applied to PIV dataset to demonstrate and assess its performance relative to commonly used bilinear and bicubic interpolation methods. For replacement of a single vector, all methods performed well, with LSEVR having an average error of 11% in comparison to 14% and 18% for bilinear and bicubic interpolation respectively. A more significant difference was found in replacement of clusters of vectors which showed average vector angle errors of 10&deg;, 9&deg; and 6&deg; for bilinear, bicubic and LSEVR respectively. Error in magnitude was 3% for both interpolation techniques and 1% for LSEVR showing a clear benefit to using LSEVR for conditions that require multiple clustered vectors to be replaced.

]]>Fluids doi: 10.3390/fluids4030138

Authors: Anqi Bao Eduardo Gildin Abhinav Narasingam Joseph S. Kwon

Learning reservoir flow dynamics is of primary importance in creating robust predictive models for reservoir management including hydraulic fracturing processes. Physics-based models are to a certain extent exact, but they entail heavy computational infrastructure for simulating a wide variety of parameters and production scenarios. Reduced-order models offer computational advantages without compromising solution accuracy, especially if they can assimilate large volumes of production data without having to reconstruct the original model (data-driven models). Dynamic mode decomposition (DMD) entails the extraction of relevant spatial structure (modes) based on data (snapshots) that can be used to predict the behavior of reservoir fluid flow in porous media. In this paper, we will further enhance the application of the DMD, by introducing sparse DMD and local DMD. The former is particularly useful when there is a limited number of sparse measurements as in the case of reservoir simulation, and the latter can improve the accuracy of developed DMD models when the process dynamics show a moving boundary behavior like hydraulic fracturing. For demonstration purposes, we first show the methodology applied to (flow only) single- and two-phase reservoir models using the SPE10 benchmark. Both online and offline processes will be used for evaluation. We observe that we only require a few DMD modes, which are determined by the sparse DMD structure, to capture the behavior of the reservoir models. Then, we applied the local DMDc for creating a proxy for application in a hydraulic fracturing process. We also assessed the trade-offs between problem size and computational time for each reservoir model. The novelty of our method is the application of sparse DMD and local DMDc, which is a data-driven technique for fast and accurate simulations.

]]>Fluids doi: 10.3390/fluids4030137

Authors: Mohamed Salah Idrissi Nabil Ben Salah Mouldi Chrigui

Hazardous gas dispersion within a complex urban environment in 1:1 scaled geometry of German cities, Hanover and Frankfurt, is predicted using an advanced turbulence model. The investigation involves a large group of real buildings with a high level of details. For this purpose, Computer Aided Design (CAD) of two configurations are cleaned, then fine grids meshed in. Weather conditions are introduced using power law velocity profiles at inlets boundary. The investigation focused on the effects of release locations and material properties of the contaminants (e.g., densities) on the convection/diffusion of pollutants within complex urban area. Two geometries demonstrating different topologies and boundaries conditions are investigated. Pollutants are introduced into the computational domain through chimney and/or pipe leakages in various locations. Simulations are carried out using Large Eddy Simulation (LES) turbulence model and species transport for the pollutants. The weather conditions are accounted for using a logarithmic velocity profile at inlets. CH4 and CO2 distributions, as well as turbulence quantities and velocity profiles, show important influences on the dispersion behavior of the hazardous gas.

]]>Fluids doi: 10.3390/fluids4030136

Authors: Wenyuan Fan Henryk Anglart

The presence of a moving interface in two-phase flows challenges the accurate computational fluid dynamics (CFD) modeling, especially when the flow is turbulent. For such flows, single-phase-based turbulence models are usually used for the turbulence modeling together with certain modifications including the turbulence damping around the interface. Due to the insufficient understanding of the damping mechanism, the phenomenological modeling approach is always used. Egorov&rsquo;s model is the most widely-used turbulence damping model due to its simple formulation and implementation. However, the original Egorov model suffers from the mesh size dependency issue and uses a questionable symmetric treatment for both liquid and gas phases. By introducing more physics, this paper introduces a new length scale for Egorov&rsquo;s model, making it independent of mesh sizes in the tangential direction of the interface. An asymmetric treatment is also developed, which leads to more physical predictions for both the turbulent kinetic energy and the velocity field.

]]>Fluids doi: 10.3390/fluids4030135

Authors: Francesco Farsaci Ester Tellone Antonio Galtieri Silvana Ficarra

In this paper, we formulate a thermodynamic model of hemoglobin that describes, by a physical point of view, phenomena favoring the binding of oxygen to the protein. Our study is based on theoretical methods extrapolated by experimental data. After some remarks on the non-equilibrium thermodynamic theory with internal variables, some thermodynamic functions are determined by the value of the complex dielectric constant. In previous papers, we determined the explicit expression of a dielectric constant as a function of a complex dielectric modulus and frequency. The knowledge of these functions allows a new characterization of the material and leads to the study of new phenomena that has yet to be studied. In detail, we introduce the concept of &ldquo;hemoglobe&rdquo;, a model that considers the hemoglobin molecule as a plane capacitor, the dielectric of which is almost entirely constituted by the quaternary structure of the protein. This model is suggested by considering a phenomenological coefficient of the non-equilibrium thermodynamic theory related to the displacement polarization current. The comparison of the capacity determined by the mean of this coefficient, and determined by geometrical considerations, gives similar results; although more thermodynamic information is derived by the capacity determined considering the aforementioned coefficient. This was applied to the normal human hemoglobin, homozygous sickle hemoglobin, and sickle cell hemoglobin C disease. Moreover, the energy of the capacitor of the three hemoglobin was determined. Through the identification of displacement currents, the introduction of this model presents new perspectives and helps to explain hemoglobin functionality through a physical point of view.

]]>Fluids doi: 10.3390/fluids4030134

Authors: Daniel Butcher Adrian Spencer

This article describes a proper-orthogonal-decomposition (POD) based methodology proposed for the identification and separation of coherent and turbulent velocity fluctuations. Typically, POD filtering requires assumptions to be made on the cumulative energy content of coherent modes and can therefore exclude smaller, but important contributions from lower energy modes. This work introduces a suggested new metric to consider in the selection of POD modes to be included in a reconstruction of coherent and turbulent features. Cross-correlation of POD spatial modes derived from independent samples is used to identify modes descriptive of either coherent (high-correlation) or incoherent (low-correlation) features. The technique is demonstrated through application to a cylinder in cross-flow allowing appropriate analysis to be carried out on the coherent and turbulent velocity fields separately. This approach allows identification of coherent motions associated with cross-flow transport and vortex shedding, such as integral length scales. Turbulent flow characteristics may be analysed independently from the coherent motions, allowing for the extraction of properties such as turbulent length scale.

]]>Fluids doi: 10.3390/fluids4030133

Authors: Evgenii S. Baranovskii Anastasia A. Domnich Mikhail A. Artemov

We study an optimal control problem for the mathematical model that describes steady non-isothermal creeping flows of an incompressible fluid through a locally Lipschitz bounded domain. The control parameters are the pressure and the temperature on the in-flow and out-flow parts of the boundary of the flow domain. We propose the weak formulation of the problem and prove the existence of weak solutions that minimize a given cost functional. It is also shown that the marginal function of this control system is lower semi-continuous.

]]>Fluids doi: 10.3390/fluids4030132

Authors: Sumit Kumar Patel Joseph Mathew

A method for shock capturing by adaptive filtering for use with high-resolution, high-order schemes for Large Eddy Simulations (LES) is presented. The LES method used in all the examples here employs the Explicit Filtering approach and the spatial derivatives are obtained with sixth-order, compact, finite differences. The adaptation is to drop the order of the explicit filter to two at gridpoints where a shock is detected, and to then increase the order from 2 to 10 in steps at successive gridpoints away from the shock. The method is found to be effective in a series of tests of common inviscid 1D and 2D problems of shock propagation and propagation of waves through shocks. As a prelude to LES, the 3D Taylor&ndash;Green problem for the inviscid and a finite viscosity case were simulated. An assessment of the overall performance of the method for LES was carried out by simulating an underexpanded round jet at a Reynolds number of 6.09 million, based in centerline velocity and diameter at nozzle exit plane. Very close quantitative agreement was found for the development of centerline mean pressure when compared to experiment. Simulations on several increasingly finer grids showed a monotonic extension of the computed part of the inertial range, with little change to low frequency content. Amplitudes and locations of large changes in pressure through several cells were captured accurately. A similar performance was observed for LES of an impinging jet containing normal and curved shocks.

]]>Fluids doi: 10.3390/fluids4030131

Authors: Maria Teresa Cidade João Miguel Nóbrega

Rheology, defined as the science of deformation and flow of matter, is a multidisciplinary scientific field, covering both fundamental and applied approaches [...]

]]>Fluids doi: 10.3390/fluids4030130

Authors: Tetsuya Suekane Tomotaka Koe Pablo Marin Barbancho

Viscous fingering is fluid dynamics instability induced on the displacement front when a less viscous fluid (LVF) displaces a more viscous fluid (MVF), thereby reducing the displacement efficiency. The displacement of a denser fluid by a less dense fluid produces a gravitational tongue. This gravitational segregation also reduces the displacement efficiency. In this study, the three-dimensional structure of the fingering pattern at the viscous fingering to gravitational segregation boundary was examined using X-ray microtomography on a packed bed of particles. At low gravity numbers, viscous fingering resembled that without gravity characterized by nonlinear interaction including tip-splitting, shielding, and coalescence. At intermediate gravity numbers, viscous fingering is associated with the gravitational tongue due to segregation. At high gravity numbers, a clear gravitational tongue penetrates from the inlet to the outlet. Consequently, the concentration near the injection point decreases and exhibits a flat profile in the flow direction. The displacement efficiency decreases with increasing gravity number, with the highest value achieved without gravity but depends on many factors, including the viscosity ratio and P&eacute;clet number.

]]>Fluids doi: 10.3390/fluids4030129

Authors: Ângela M. Ribau Luís L. Ferrás Maria L. Morgado Magda Rebelo Alexandre M. Afonso

This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille&ndash;Couette flows, described by the recently proposed (Ferr&aacute;s et al., A Generalised Phan-Thien&ndash;Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien&ndash;Tanner constitutive equation. This generalised version considers the Mittag&ndash;Leffler function instead of the classical linear or exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The analytical solutions derived in this work allow a better understanding of the model, and therefore contribute to improve the modelling of complex materials, and will provide an interesting challenge to computational rheologists, to benchmarking and to code verification.

]]>Fluids doi: 10.3390/fluids4030128

Authors: Di Zhang Daniel R. Cadel Eric G. Paterson K. Todd Lowe

A hybrid Reynolds-averaged Navier Stokes/large-eddy simulation (RANS/LES) turbulence model integrated with a transition formulation is developed and tested on a surrogate model problem through a joint experimental and computational fluid dynamic approach. The model problem consists of a circular cylinder for generating coherent unsteadiness and a downstream airfoil in the cylinder wake. The cylinder flow is subcritical, with a Reynolds number of 64,000 based upon the cylinder diameter. The quantitative dynamics of vortex shedding and Reynolds stresses in the cylinder near wake are well captured, owing to the turbulence-resolving large eddy simulation mode that was activated in the wake. The hybrid model switched between RANS and LES modes outside the boundary layers, as expected. According to the experimental and simulation results, the airfoil encountered local flow angle variations up to &plusmn;50&deg;. Further analysis through a phase-averaging technique found phase lags in the airfoil boundary layer along the chordwise locations, and both the phase-averaged and mean velocity profiles collapsed into the Law-of-the-wall in the range of 0 &lt; y + &lt; 50 . The features of high blade-loading fluctuations due to unsteadiness and transitional boundary layers are of interest in the aerodynamic studies of full-scale wind turbine blades, making the current model problem a comprehensive benchmark case for future model development and validation.

]]>Fluids doi: 10.3390/fluids4030127

Authors: Margaritis Kostoglou Anastasios Karabelas

A performance simulator of spiral wound membrane (SWM) modules used for desalination is a valuable tool for process design and optimization. The existing state-of-the-art mesoscale simulation tools account for the spatial non-uniformities created by the operation itself (flow, pressure, and concentration distributions) but they assume uniform membrane properties. However, experimental studies reveal that membrane properties are by no means uniform. Therefore, the need arises to account for this non-uniformity in simulation tools thus enabling a systematic assessment of its impact, among other benefits; a first step toward this goal is presented herein. In particular, the issue of an organic fouling layer growing on a membrane with non-uniform permeability is analyzed. Several mathematical treatments of the problem are discussed and indicative results are presented. The concept of fouling layer thickness probability density function is suggested as a means to introduce sub-grid level calculations in existing simulation tools. The analysis leads to the selection of an appropriate methodology to incorporate this effect in the dynamic simulation of fouling layer evolution at the membrane-sheet scale.

]]>Fluids doi: 10.3390/fluids4030126

Authors: Shohreh Amini Shahab Mohaghegh

Reservoir simulation models are the major tools for studying fluid flow behavior in hydrocarbon reservoirs. These models are constructed based on geological models, which are developed by integrating data from geology, geophysics, and petro-physics. As the complexity of a reservoir simulation model increases, so does the computation time. Therefore, to perform any comprehensive study which involves thousands of simulation runs, a very long period of time is required. Several efforts have been made to develop proxy models that can be used as a substitute for complex reservoir simulation models. These proxy models aim at generating the outputs of the numerical fluid flow models in a very short period of time. This research is focused on developing a proxy fluid flow model using artificial intelligence and machine learning techniques. In this work, the proxy model is developed for a real case CO2 sequestration project in which the objective is to evaluate the dynamic reservoir parameters (pressure, saturation, and CO2 mole fraction) under various CO2 injection scenarios. The data-driven model that is developed is able to generate pressure, saturation, and CO2 mole fraction throughout the reservoir with significantly less computational effort and considerably shorter period of time compared to the numerical reservoir simulation model.

]]>Fluids doi: 10.3390/fluids4030125

Authors: U. Mahabaleshwar P. Vinay Kumar K. Nagaraju Gabriella Bognár S. Nayakar

The viscous fluid flow past a semi-infinite porous solid, which is proportionally sheared at one boundary with the possibility of the fluid slipping according to Navier’s slip or second order slip, is considered here. Such an assumption takes into consideration several of the boundary conditions used in the literature, and is a generalization of them. Upon introducing a similarity transformation, the governing equations for the problem under consideration reduces to a system of nonlinear partial differential equations. Interestingly, we were able to obtain an exact analytical solution for the velocity, though the equation is nonlinear. The flow through the porous solid is assumed to obey the Brinkman equation, and is considered relevant to several applications.

]]>Fluids doi: 10.3390/fluids4030124

Authors: Masoud Jabbari James McDonough Evan Mitsoulis Jesper Henri Hattel

In this paper, a first-order projection method is used to solve the Navier&ndash;Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity. The flow structure in a cavity of aspect ratio &delta; = 1 and Reynolds numbers ( 100 , 400 , 1000 ) is compared with existing results to validate the code. We then apply the developed code to flow of a generalised Newtonian fluid with the well-known Ostwald&ndash;de Waele power-law model. Results show that, by decreasing n (further deviation from Newtonian behaviour) from 1 to 0.9, the peak values of the velocity decrease while the centre of the main vortex moves towards the upper right corner of the cavity. However, for n = 0.5 , the behaviour is reversed and the main vortex shifts back towards the centre of the cavity. We moreover demonstrate that, for the deeper cavities, &delta; = 2 , 4 , as the shear-thinning parameter n decreased the top-main vortex expands towards the bottom surface, and correspondingly the secondary flow becomes less pronounced in the plane perpendicular to the cavity lid.

]]>Fluids doi: 10.3390/fluids4030123

Authors: Amir Ansari Shahab D. Mohaghegh Mehrdad Shahnam Jean-François Dietiker

Simulations can reduce the time and cost to develop and deploy advanced technologies and enable their rapid scale-up for fossil fuel-based energy systems. However, to ensure their usefulness in practice, the credibility of the simulations needs to be established with uncertainty quantification (UQ) methods. The National Energy Technology Laboratory (NETL) has been applying non-intrusive UQ methodologies to categorize and quantify uncertainties in computational fluid dynamics (CFD) simulations of gas-solid multiphase flows. To reduce the computational cost associated with gas-solid flow simulations required for UQ analysis, techniques commonly used in the area of artificial intelligence (AI) and data mining are used to construct smart proxy models, which can reduce the computational cost of conducting large numbers of multiphase CFD simulations. The feasibility of using AI and machine learning to construct a smart proxy for a gas-solid multiphase flow has been investigated by looking at the flow and particle behavior in a non-reacting rectangular fluidized bed. The NETL&rsquo;s in house multiphase solver, Multiphase Flow with Interphase eXchanges (MFiX), was used to generate simulation data for the rectangular fluidized bed. The artificial neural network (ANN) was used to construct a CFD smart proxy, which is able to reproduce the CFD results with reasonable error (about 10%). Several blind cases were used to validate this technology. The results show a good agreement with CFD runs while the approach is less computationally expensive. The developed model can be used to generate the time averaged results of any given fluidized bed with the same geometry with different inlet velocity in couple of minutes.

]]>Fluids doi: 10.3390/fluids4030122

Authors: Alessandro Coclite Alberto M. Gambaruto

Motivated by red blood cell dynamics and injectable capsules for drug delivery, in this paper, a computational study of capsule ejection from a narrow channel into a reservoir is undertaken for a combination of varying deformable capsule sizes and channel dimensions. A mass-spring membrane model is coupled to an Immersed Boundary&ndash;Lattice Boltzmann model solver. The aim of the present work is the description of the capsules&rsquo; motion, deformation and the response of the fluid due to the complex particles&rsquo; dynamics. The interactions between the capsules affect the local velocity field and are responsible for the dynamics observed. Capsule membrane deformability is also seen to affect inter-capsule interaction. We observe that the train of three particles locally homogenises the velocity field and the leading capsule travels faster than the other two trailing capsules. Variations in the size of reservoir do not seem to be relevant, while the ratio of capsule diameter to channel diameter as well as the ratio of capsule diameter to inter-capsule spacing play a major role. This flow set-up has not been covered in the literature, and consequently we focus on describing capsule motion, membrane deformation and fluid dynamics, as a preliminary investigation in this field.

]]>Fluids doi: 10.3390/fluids4030121

Authors: Leo Dostal

The influence of a strong and gusty wind field on ocean waves is investigated. How the random wind affects solitary waves is analyzed in order to obtain insights about wave generation by randomly time varying wind forcing. Using the Euler equations of fluid dynamics and the method of multiple scales, a random nonlinear Schr&ouml;dinger equation and a random modified nonlinear Schr&ouml;dinger equation are obtained for randomly wind forced nonlinear deep water waves. Miles theory is used for modeling the pressure variation at the wave surface resulting from the wind velocity field. The nonlinear Schr&ouml;dinger equation and the modified nonlinear Schr&ouml;dinger equation are computed using a relaxation pseudo spectral scheme. The results show that the influence of gusty wind on solitary waves leads to a randomly increasing ocean wave envelope. However, in a laboratory setup with much smaller wave amplitudes and higher wave frequencies, the influence of water viscosity is much higher. This leads to fluctuating solutions, which are sensitive to wind forcing.

]]>Fluids doi: 10.3390/fluids4030120

Authors: Anthony Khoury Eduardo Divo Alain Kassab Sai Kakuturu Lakshmi Reddi

Performance data on earth dams and levees continue to indicate that piping is one of the major causes of failure. Current criteria for prevention of piping in earth dams and levees have remained largely empirical. This paper aims at developing a mechanistic understanding of the conditions necessary to prevent piping and to enhance the likelihood of self-healing of cracks in levees subjected to hydrodynamic loading from astronomical and meteorological (including hurricane storm surge-induced) forces. Systematic experimental investigations are performed to evaluate erosion in finite-length cracks as a result of transient hydrodynamic loading. Here, a novel application of the localized collocation meshless method (LCMM) to the hydrodynamic and poroelastic problem is introduced to arrive at high-fidelity field solutions. Results from the LCMM numerical simulations are designed to be used as an input, along with the soil and erosion parameters obtained experimentally, to characterize progressive piping.

]]>Fluids doi: 10.3390/fluids4030119

Authors: Anvar Gilmanov Alexander Barker Henryk Stolarski Fotis Sotiropoulos

When flow-induced forces are altered at the blood vessel, maladaptive remodeling can occur. One reason such remodeling may occur has to do with the abnormal functioning of the aortic heart valve due to disease, calcification, injury, or an improperly-designed prosthetic valve, which restricts the opening of the valve leaflets and drastically alters the hemodynamics in the ascending aorta. While the specifics underlying the fundamental mechanisms leading to changes in heart valve function may differ from one cause to another, one common and important change is in leaflet stiffness and/or mass. Here, we examine the link between valve stiffness and mass and the hemodynamic environment in aorta by coupling magnetic resonance imaging (MRI) with high-resolution fluid&ndash;structure interaction (FSI) computational fluid dynamics to simulate blood flow in a patient-specific model. The thoracic aorta and a native aortic valve were re-constructed in the FSI model from the MRI data and used for the simulations. The effect of valve stiffness and mass is parametrically investigated by varying the thickness (h) of the leaflets (h = 0.6, 2, 4 mm). The FSI simulations were designed to investigate systematically progressively higher levels of valve stiffness by increasing valve thickness and quantifying hemodynamic parameters known to be linked to aortopathy and valve disease. The computed results reveal dramatic differences in all hemodynamic parameters: (1) the geometric orifice area (GOA), (2) the maximum velocity V max of the jet passing through the aortic orifice area, (3) the rate of energy dissipation E ˙ diss ( t ) , (4) the total loss of energy E diss , (5) the kinetic energy of the blood flow E kin ( t ) , and (6) the average magnitude of vorticity &Omega; a ( t ) , illustrating the change in hemodynamics that occur due to the presence of aortic valve stenosis.

]]>Fluids doi: 10.3390/fluids4030118

Authors: Hung-Chu Hsu

I present an exact and explicit solution to the nonlinear governing equations in the equatorial f-plane, describing geophysical edge waves propagating over a plane-sloping beach, in the presence of underlying uniform currents. I also derive the analytical expressions of geophysical edge wave dynamics and the mass transport velocity.

]]>Fluids doi: 10.3390/fluids4030117

Authors: Josef Hasslberger Svenja Marten Markus Klein

A local flow topology analysis was conducted for laminar particle-affected flows. Based on the invariants of the velocity gradient tensor, all possible flow structures can be categorized into two focal and two nodal topologies for incompressible flows. The underlying field descriptions for bubble- and droplet-affected flows in the creeping flow regime were determined analytically for two different boundary conditions. A nodal-to-focal-to-nodal transition can be observed in both phases and the focal topologies are predominant in the interior phase. It was also found that the topology distribution in the interior phase is independent of the dynamic viscosity ratio and the boundary conditions, which is not the case in the exterior phase. The focal region in the exterior phase extends to infinity for the far-field boundary condition, whereas it is bounded to a tire-like zone attached to the bubble or droplet for the near-field boundary condition. Furthermore, the existence of a narrow band of intermediate nodal topologies was demonstrated analytically, which raises the question on the origin of this behavior. To complement the findings about the flow topology classification, the strengths of the underlying vorticity and invariant fields are discussed, including their dependency on the considered phase and boundary condition.

]]>Fluids doi: 10.3390/fluids4030115

Authors: Fluids Editorial Office Fluids Editorial Office

This article [...]

]]>Fluids doi: 10.3390/fluids4030116

Authors: Rajinder Pal

The second law of thermodynamics is indispensable in engineering applications. It allows us to determine if a given process is feasible or not, and if the given process is feasible, how efficient or inefficient is the process. Thus, the second law plays a key role in the design and operation of engineering processes, such as steam power plants and refrigeration processes. Nevertheless students often find the second law and its applications most difficult to comprehend. The second law revolves around the concepts of entropy and entropy generation. The feasibility of a process and its efficiency are directly related to entropy generation in the process. As entropy generation occurs in all flow processes due to friction in fluids, fluid mechanics can be used as a tool to teach the second law of thermodynamics and related concepts to students. In this article, flow through packed beds and consolidated porous media is analyzed in terms of entropy generation. The link between entropy generation and mechanical energy dissipation is established in such flows in terms of the directly measurable quantities such as pressure drop. Equations are developed to predict the entropy generation rates in terms of superficial fluid velocity, porous medium characteristics, and fluid properties. The predictions of the proposed equations are presented and discussed. Factors affecting the rate of entropy generation in flow through packed beds and consolidated porous media are identified and explained.

]]>Fluids doi: 10.3390/fluids4030114

Authors: Dejan Brkić Pavel Praks

Even a relatively simple equation such as Colebrook&rsquo;s offers a lot of possibilities to students to increase their computational skills. The Colebrook&rsquo;s equation is implicit in the flow friction factor and, therefore, it needs to be solved iteratively or using explicit approximations, which need to be developed using different approaches. Various procedures can be used for iterative methods, such as single the fixed-point iterative method, Newton&ndash;Raphson, and other types of multi-point iterative methods, iterative methods in a combination with Pad&eacute; polynomials, special functions such as Lambert W, artificial intelligence such as neural networks, etc. In addition, to develop explicit approximations or to improve their accuracy, regression analysis, genetic algorithms, and curve fitting techniques can be used too. In this learning numerical exercise, a few numerical examples will be shown along with the explanation of the estimated pedagogical impact for university students. Students can see what the difference is between the classical vs. floating-point algebra used in computers.

]]>Fluids doi: 10.3390/fluids4020113

Authors: Luis F. Cremades Rey Denis F. Hinz Mahdi Abkar

Reynolds-averaged Navier-Stokes (RANS) models are widely used for the simulation of engineering problems. The turbulent-viscosity hypothesis is a central assumption to achieve closures in this class of models. This assumption introduces structural or so-called epistemic uncertainty. Estimating that epistemic uncertainty is a promising approach towards improving the reliability of RANS simulations. In this study, we adopt a methodology to estimate the epistemic uncertainty by perturbing the Reynolds stress tensor. We focus on the perturbation of the turbulent kinetic energy and the eigenvalues separately. We first implement this methodology in the open source package OpenFOAM. Then, we apply this framework to the backward-facing step benchmark case and compare the results with the unperturbed RANS model, available direct numerical simulation data and available experimental data. It is shown that the perturbation of both parameters successfully estimate the region bounding the most accurate results.

]]>Fluids doi: 10.3390/fluids4020112

Authors: Moses Karakouzian Mohammad Nazari-Sharabian Mehrdad Karami

This study investigated the impact of overburden height on the hydraulic fracturing of a concrete-lined pressure tunnel, excavated in intact rock, under steady-state and transient-state conditions. Moreover, the Norwegian design criterion that only suggests increasing the overburden height as a countermeasure against hydraulic fracturing was evaluated. The Mohr&ndash;Coulomb failure criterion was implemented to investigate failure in the rock elements adjacent to the lining. A pressure tunnel with an inner diameter of 3.6 m was modeled in Abaqus Finite Element Analysis (FEA), using the finite element method (FEM). It was assumed that transient pressures occur inside the tunnel due to control gate closure in a hydroelectric power plant, downstream of the tunnel, in three different closure modes: fast (14 s), normal (18 s), and slow (26 s). For steady-state conditions, the results indicated that resistance to the fracturing of the rock increased with increasing the rock friction angle, as well as the overburden height. However, the influence of the friction angle on the resistance to rock fracture was much larger than that of the overburden height. For transient-state conditions, the results showed that, in fast, normal, and slow control gate closure modes, the required overburden heights to failure were respectively 1.07, 0.8, and 0.67 times the static head of water in the tunnel under a steady-state condition. It was concluded that increasing the height of overburden should not be the absolute solution to prevent hydraulic fracturing in pressure tunnels.

]]>Fluids doi: 10.3390/fluids4020111

Authors: Harsha Vaddireddy Omer San

Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg&ndash;de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.

]]>Fluids doi: 10.3390/fluids4020110

Authors: Sílvio M.A. Gama Roman Chertovskih Vladislav Zheligovsky

We present examples of Pad&eacute; approximations of the &alpha; -effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the standard multiscale formalism are employed. Algebraically, the simplest case is that of a two-dimensional parity-invariant six-fold rotation-symmetric flow where eddy viscosity is negative, indicating intervals of large-scale instability of the flow. Turning to the kinematic dynamo problem for three-dimensional flows of an incompressible fluid, we explore the application of Pad&eacute; approximants for the computation of tensors of magnetic &alpha; -effect and, for parity-invariant flows, of magnetic eddy diffusivity. We construct Pad&eacute; approximants of the tensors expanded in power series in the inverse molecular diffusivity 1 / &eta; around 1 / &eta; = 0 . This yields the values of the dominant growth rate to satisfactory accuracy for &eta; , several dozen times smaller than the threshold, above which the power series is convergent. We do computations in Fortran in the standard &ldquo;double&rdquo; (real*8) and extended &ldquo;quadruple&rdquo; (real*16) precision, and perform symbolic calculations in Mathematica.

]]>Fluids doi: 10.3390/fluids4020109

Authors: Balaji Jayaraman S M Abdullah Al Mamun Chen Lu

Sparse linear estimation of fluid flows using data-driven proper orthogonal decomposition (POD) basis is systematically explored in this work. Fluid flows are manifestations of nonlinear multiscale partial differential equations (PDE) dynamical systems with inherent scale separation that impact the system dimensionality. Given that sparse reconstruction is inherently an ill-posed problem, the most successful approaches require the knowledge of the underlying low-dimensional space spanning the manifold in which the system resides. In this paper, we adopt an approach that learns basis from singular value decomposition (SVD) of training data to recover sparse information. This results in a set of four design parameters for sparse recovery, namely, the choice of basis, system dimension required for sufficiently accurate reconstruction, sensor budget and their placement. The choice of design parameters implicitly determines the choice of algorithm as either l 2 minimization reconstruction or sparsity promoting l 1 minimization reconstruction. In this work, we systematically explore the implications of these design parameters on reconstruction accuracy so that practical recommendations can be identified. We observe that greedy-smart sensor placement, particularly interpolation points from the discrete empirical interpolation method (DEIM), provide the best balance of computational complexity and accurate reconstruction.

]]>Fluids doi: 10.3390/fluids4020108

Authors: Azhar Iqbal Nur Nadiah Abd Hamid Ahmad Izani Md. Ismail

The non-linear Schr&ouml;dinger (NLS) equation has often been used as a model equation in the study of quantum states of physical systems. Numerical solution of NLS equation is obtained using cubic B-spline Galerkin method. We have applied the Crank&ndash;Nicolson scheme for time discretization and the cubic B-spline basis function for space discretization. Three numerical problems, including single soliton, interaction of two solitons and birth of standing soliton, are demonstrated to evaluate to the performance and accuracy of the method. The error norms and conservation laws are determined and found to be in good agreement with the published results. The obtained results show that the approach is feasible and accurate. The proposed method has almost second order convergence. The linear stability of the method is performed using the Von Neumann method.

]]>Fluids doi: 10.3390/fluids4020107

Authors: Xingxing Huang Xavier Escaler

To have a safe structural design, an analysis of the dynamic behavior of a Francis turbine runner with consideration of the added mass effects of surrounding water is necessary during design phase. Both in design and at off-design operations, large-scale forms of attached cavitation may appear on runner blades and can change the added mass effects of the surrounding fluid in relation to a single water domain. Consequently, a numerical investigation of the modal response of a Francis runner has been carried out by reproducing the presence of various sizes of leading edge cavitation (LEC) and trailing edge cavitation (TEC). The fluid&ndash;structure interaction problem has been solved by means of an acoustic-structural coupling method. The calculated added mass effects with cavitation have been compared with those corresponding to the pure water condition without cavitation. Firstly, a single blade has been investigated to evaluate the level of significance for the proposed cavity shapes and dimensions. Afterwards, based on the results obtained, the complete runner structure has been considered, factoring in similar cavity shapes and locations. The results prove that significant added mass effects are induced on the entire runner by the attached cavitation that increase the natural frequencies of the first modes. Moreover, the added mass effects increase with cavity size and amplitude of blade deformation below the cavity.

]]>Fluids doi: 10.3390/fluids4020106

Authors: Spiros V. Paras Athanasios G. Kanaris

The term &ldquo;biomedical engineering&rdquo; refers to the application of the principles and problem-solving techniques of engineering to biology and medicine [...]

]]>Fluids doi: 10.3390/fluids4020105

Authors: James N. Steer Mark L. McAllister Alistair G. L. Borthwick Ton S. van den Bremer

The coupled nonlinear Schr&ouml;dinger equation (CNLSE) is a wave envelope evolution equation applicable to two crossing, narrow-banded wave systems. Modulational instability (MI), a feature of the nonlinear Schr&ouml;dinger wave equation, is characterized (to first order) by an exponential growth of sideband components and the formation of distinct wave pulses, often containing extreme waves. Linear stability analysis of the CNLSE shows the effect of crossing angle, &theta; , on MI, and reveals instabilities between 0 ∘ &lt; &theta; &lt; 35 ∘ , 46 ∘ &lt; &theta; &lt; 143 ∘ , and 145 ∘ &lt; &theta; &lt; 180 ∘ . Herein, the modulational stability of crossing wavetrains seeded with symmetrical sidebands is determined experimentally from tests in a circular wave basin. Experiments were carried out at 12 crossing angles between 0 ∘ &le; &theta; &le; 88 ∘ , and strong unidirectional sideband growth was observed. This growth reduced significantly at angles beyond &theta; &asymp; 20 ∘ , reaching complete stability at &theta; = 30&ndash;40 ∘ . We find satisfactory agreement between numerical predictions (using a time-marching CNLSE solver) and experimental measurements for all crossing angles.

]]>Fluids doi: 10.3390/fluids4020104

Authors: Glenn R. Flierl Philip J. Morrison Rohith Vilasur Swaminathan

We explore the theory of isolated vortices in strongly sheared, deep zonal flows and the stability of these banded jets, as occur in Jupiter&rsquo;s atmosphere This is done using the standard 2-layer quasigeostrophic model with the lower layer depth becoming infinite; however, this model differs from the usual layer model because the lower layer is not assumed to be motionless but has a steady configuration of alternating zonal flows. Steady state vortices are obtained by a simulated annealing computational method as generalized to fluid problems with constraints and also used in the used in the context of magnetohydrodynamics. Various cases of vortices with a constant potential vorticity anomaly atop zonal winds and the stability of the underlying winds are considered using a mix of computational and analytical techniques.

]]>Fluids doi: 10.3390/fluids4020103

Authors: Rajinder Pal

Entropy and entropy generation are abstract and illusive concepts for undergraduate students. In general, students find it difficult to visualize entropy generation in real (irreversible) processes, especially at a mechanistic level. Fluid mechanics laboratory can assist students in making the concepts of entropy and entropy generation more tangible. In flow of real fluids, dissipation of mechanical energy takes place due to friction in fluids. The dissipation of mechanical energy in pipeline flow is reflected in loss of pressure of fluid. The degradation of high quality mechanical energy into low quality frictional heat (internal energy) is simultaneously reflected in the generation of entropy. Thus, experiments involving measurements of pressure gradient as a function of flow rate in pipes offer an opportunity for students to visualize and quantify entropy generation in real processes. In this article, the background in fluid mechanics and thermodynamics relevant to the concepts of mechanical energy dissipation, entropy and entropy generation are reviewed briefly. The link between entropy generation and mechanical energy dissipation in pipe flow experiments is demonstrated both theoretically and experimentally. The rate of entropy generation in pipeline flow of Newtonian fluids is quantified through measurements of pressure gradient as a function of flow rate for a number of test fluids. The factors affecting the rate of entropy generation in pipeline flows are discussed.

]]>Fluids doi: 10.3390/fluids4020102

Authors: Farzad Mohebbi Ben Evans Mathieu Sellier

This paper presents a novel and accurate method to implement the Kutta condition in solving subsonic (subcritical) inviscid isentropic compressible flow over isolated airfoils using the stream function equation. The proposed method relies on body-fitted grid generation and solving the stream function equation for compressible flows in computational domain using finite-difference method. An expression is derived for implementing the Kutta condition for the airfoils with both finite angles and cusped trailing edges. A comparison of the results obtained from the proposed numerical method and the results from experimental and other numerical methods reveals that they are in excellent agreement, which confirms the accuracy and correctness of the proposed method.

]]>Fluids doi: 10.3390/fluids4020101

Authors: Baole Wen Gregory P. Chini

We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the counterclockwise direction and one ‘antinatural’ roll rotating in the clockwise direction. As the inclination angle ϕ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal—for the first time in single-species porous medium convection—the existence of spatially-localized convective states at large ϕ , which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different ϕ , we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of ϕ .

]]>Fluids doi: 10.3390/fluids4020100

Authors: Jorge Silva-Leon Andrea Cioncolini

This paper presents experimental results on the vortex shedding frequency measured behind a bent cylinder. Experiments were conducted in a wind tunnel covering Reynolds numbers between 50 and 500, a range of interest for flow sensing, flow control, and energy harvesting applications. The bent cylinder comprised a vertical leg always oriented at normal incidence with respect to the free-stream flow, and an inclined leg whose inclination was varied during the tests between 90&deg; and 15&deg;. The bent cylinder was oriented in the wind tunnel with the vertical leg upstream and the inclined leg downstream, and the vortex shedding frequency was measured with hot-wire anemometry at several locations behind the inclined leg. The present bent cylinder design improves upon those previously considered by providing a finer control on the upstream boundary condition acting upon the inclined leg, which in the present design is not affected by the yaw angle of the inclined leg. With the exception of free-end effects, only noticeable for certain inclinations and Reynolds number values, inclination effects were surprisingly not observed, and the frequency of vortex shedding measured behind the inclined leg of the bent cylinder was consistent (within a few percent) with the cross-flow vortex shedding frequency at the same flow velocity. The present results corroborate and significantly extend the limited observations on bent cylinders available in the literature, further highlighting the importance of the upstream boundary condition on the vortex shedding process with inclined cylinders.

]]>Fluids doi: 10.3390/fluids4020099

Authors: Jie Zhang Michel Benoit Olivier Kimmoun Amin Chabchoub Hung-Chu Hsu

The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability of large waves. Indeed, more efforts are required to improve the understanding of extreme wave statistics variations in such conditions. To achieve this goal, large scale experiments of unidirectional irregular waves propagating over a variable bottom profile considering different transition water depths were performed. The validation of two highly nonlinear numerical models was performed for one representative case. The collected data were examined and interpreted by using spectral or bispectral analysis as well as statistical analysis. The higher probability of occurrence of large waves was confirmed by the statistical distributions built from the measured free surface elevation time series as well as by the local maximum values of skewness and kurtosis around the end of the slope. Strong second-order nonlinear effects were highlighted as waves propagate into the shallower region. A significant amount of wave energy was transmitted to low-frequency modes. Based on the experimental data, we conclude that the formation of extreme waves is mainly related to the second-order effect, which is also responsible for the generation of long waves. It is shown that higher-order nonlinearities are negligible in these sets of experiments. Several existing models for wave height distributions were compared and analysed. It appears that the generalised Boccotti&rsquo;s distribution can predict the exceedance of large wave heights with good confidence.

]]>Fluids doi: 10.3390/fluids4020098

Authors: Bruno M.M. Pereira Gonçalo A.S. Dias Filipe S. Cal Kumbakonam R. Rajagopal Juha H. Videman

We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.

]]>Fluids doi: 10.3390/fluids4020097

Authors: Eden Furtak-Cole Aleksey S. Telyakovskiy

Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and boundary conditions in practice, or know the magnitude of effects neglected by the 1D model. Furthermore, when multiple simplifying assumptions are made, the sources of discrepancy between modeled and observed data are difficult to identify. We derive one such model of viscous flow in a parabolic fissure from first principals. The parabolic fissure is formed by extruding an upward opening parabola in a horizontal direction. In this setting, permeability is a power law function of height, resulting in a generalized Boussinesq equation. To gauge the effects neglected by this model, 3D Navier-Stokes multiphase flow simulations are conducted for the same geometry. Parameter variations are performed to assess the nature of errors induced by applying the 1D model to a realistic scenario, where the initial and boundary conditions can not be matched exactly. Numerical simulations reveal an undercutting effect observed in laboratory experiments, but not modeled when the Dupuit-Forchheimer assumption is applied. By selectively controlling the effects placed on the free surface in 3D simulations, we are able to demonstrate that free surface slope is the primary driver of the undercutting effect. A consistent lag and overshoot flow regime is observed in the 3D simulations as compared to the 1D model, based on the choice of initial condition. This implies that the undercutting effect is partially induced by the initial condition. Additionally, the presented numerical evidence shows that some of the flow behavior unaccounted for in the 1D model scales with the 1D model parameters.

]]>Fluids doi: 10.3390/fluids4020096

Authors: Georgi Gary Rozenman Shenhe Fu Ady Arie Lev Shemer

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

]]>Fluids doi: 10.3390/fluids4020095

Authors: D. Andrew S. Rees Andrew P. Bassom

We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise.

]]>Fluids doi: 10.3390/fluids4020094

Authors: Cornel Marius Murea

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid&ndash;structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier&ndash;Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid&ndash;structure domain where the fluid&ndash;structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid&ndash;structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.

]]>Fluids doi: 10.3390/fluids4020093

Authors: Naser Hamedi Lars-Göran Westerberg

In this paper, the static interaction of a train of three cylinders in a Bingham fluid is studied numerically using Computational Fluid Dynamics. The variation of drag forces for the cylinders in several configurations is investigated. Positions of the particles in relation to the reference particle are recognized by the separation distance between the cylinders. A steady state field is considered, with Bingham numbers between 5 and 150. Several separation distances (d) were considered, such that 2.0D &le; d &le; 6.0D where D is the cylinder diameter. The Reynolds number was chosen in the range of 5 &le; Re &le; 40. In particular, the effect of the separation distance, Reynolds number and Bingham number on the shape and size of the unyielded regions was investigated. The functional dependence of this region and the drag coefficient is explored. The present results reveal the significant influence of the gap between the cylinders on the drag force and the shape of the unyielded regions surrounding the cylinders. It was found that there are several configurations in which the drag forces over the first and the third cylinders are almost equal depending on variation of the Bi, Re and the separation distance.

]]>Fluids doi: 10.3390/fluids4020092

Authors: Aarne Lees Hussein Aluie

The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of &ldquo;baropycnal work&rdquo;, which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 1024 3 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates.

]]>Fluids doi: 10.3390/fluids4020091

Authors: Usama Kadri

Time reversal of free-surface water (gravity) waves due to a sudden change in the effective gravity has been extensively studied in recent years. Here, we show that an analogy to time-reversal can be obtained using nonlinear acoustic-gravity wave theory. More specifically, we present a mathematical model for the evolution of a time-reversed gravity wave packet from a nonlinear resonant triad perspective. We show that the sudden appearance of an acoustic mode in analogy to a sudden vertical oscillation of the liquid film, can resonate effectively with the original gravity wave packet causing energy pumping into an oppositely propagating (time-reversed) surface gravity wave of an almost identical shape.

]]>Fluids doi: 10.3390/fluids4020090

Authors: Palanisamy Mohan Kumar Mohan Ram Surya Krishnamoorthi Sivalingam Teik-Cheng Lim Seeram Ramakrishna He Wei

Darrieus-type Vertical Axis Wind Turbines (VAWT) are promising for small scale decentralized power generation because of their unique advantages such as simple design, insensitive to wind direction, reliability, and ease of maintenance. Despite these positive aspects, poor self-starting capability and low efficiency in weak and unsteady winds deteriorate further development. Adaptive Hybrid Darrieus Turbine (AHDT) was proposed by the author in the past study as a potential solution to enhance low wind speed characteristics. The objective of the current research is to optimize the parameters of AHDT. AHDT integrates a dynamically varying Savonius rotor with a Darrieus rotor. A fully detailed 2D numerical study employing Reynold-Averaged Navier Stokes (RANS) is carried out to investigate the impact of the Darrieus rotor diameter (DR) on the Savonius rotor (DT) with regard to hybrid turbine performance. The power coefficient of the Darrieus rotor is evaluated when the Savonius rotor is in the closed condition (cylinder) of various diameters. The influence of Reynolds number (Re) on the torque coefficient is examined. Power loss of 58.3% and 25% is reported for DR/DT ratio of 1.5 and 2 respectively for AHDT with solidity 0.5 at 9 m/s. The flow interaction between the Savonius rotor in closed configuration reveals the formation of von Karman vortices that interact with Darrieus blades resulting in flow detachment. An optimum diametrical ratio (DR/DT) of 3 is found to yield the maximum power coefficient of the Darrieus rotor.

]]>Fluids doi: 10.3390/fluids4020089

Authors: Vahid Goodarzi Ardakani Xin Tu Alberto M. Gambaruto Iolanda Velho Jorge Tiago Adélia Sequeira Ricardo Pereira

The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed.

]]>Fluids doi: 10.3390/fluids4020088

Authors: Motoyuki Kawase Aldo Rona

A proof of concept is provided by computational fluid dynamic simulations of a new recirculating type casing treatment. This treatment aims at extending the stable operating range of highly loaded axial compressors, so to improve the safety of sorties of high-speed, high-performance aircraft powered by high specific thrust engines. This casing treatment, featuring an axisymmetric recirculation channel, is evaluated on the NASA rotor 37 test case by steady and unsteady Reynolds Averaged Navier Stokes (RANS) simulations, using the realizable k-&epsilon; model. Flow blockage at the recirculation channel outlet was mitigated by chamfering the exit of the recirculation channel inner wall. The channel axial location from the rotor blade tip leading edge was optimized parametrically over the range &minus;4.6% to 47.6% of the rotor tip axial chord c z . Locating the channel at 18.2% c z provided the best stall margin gain of approximately 5.5% compared to the untreated rotor. No rotor adiabatic efficiency was lost by the application of this casing treatment. The investigation into the flow structure with the recirculating channel gave a good insight into how the new casing treatment generates this benefit. The combination of stall margin gain at no rotor adiabatic efficiency loss makes this design attractive for applications to high-speed gas turbine engines.

]]>Fluids doi: 10.3390/fluids4020087

Authors: Andrea Cioncolini Mostafa R.A. Nabawy Jorge Silva-Leon Joseph O’Connor Alistair Revell

This paper presents results from experiments and simplified numerical simulations on the flow-induced dynamics and power generation of inverted flags that combine flexible piezoelectric strips with photovoltaic cells to simultaneously harvest kinetic wind energy and solar radiant energy. Experiments were conducted in a wind tunnel under controlled wind excitation and light exposure, focusing in particular on the dynamics and power generation of the inverted flag harvester. Numerical simulations were carried out using a lattice-Boltzmann fluid solver coupled with a finite element structural solver via the immersed-boundary method, focusing in particular on minimizing the simulation run time. The power generated during the tests shows that the proposed inverted flag harvester is a promising concept, capable of producing enough power (on the order of 1 mW) to supply low-power electronic devices in a range of applications where distributed power generation is needed. Notwithstanding key simplifications implemented in the numerical model to achieve a fast execution, simulations and measurements are in good agreement, confirming that the lattice-Boltzmann method is a viable and time-effective alternative to classic Navier&ndash;Stokes-based solvers when dealing with strongly coupled fluid&ndash;structure interaction problems characterized by large structural displacements.

]]>Fluids doi: 10.3390/fluids4020086

Authors: Abel López-Villa Abraham Medina F. J. Higuera Jonatan R. Mac Intyre Carlos Alberto Perazzo Juan Manuel Gomba

Spontaneous radial imbibition into thin circular samples of porous material when they have been subjected to radial temperature differences was analyzed theoretically and experimentally. The use of the Darcy equation allowed us to take into account temperature variations in the dynamic viscosity and surface tension in order to find the one-dimensional equation for the imbibition fronts. Experiments using blotting paper showed a good fit between the experimental data and theoretical profiles through the estimation of a single parameter.

]]>Fluids doi: 10.3390/fluids4020085

Authors: Gholami Vida Mohaghegh D. Shahab Maysami Mohammad

Large CO2-enhanced oil recovery (EOR) projects usually contain an abundance of geological and good performance data. While this volume of data leads to robust models, it often results in difficult to manage, slow-running numerical flow models. To dramatically reduce the numerical run-times associated with the traditional simulation techniques, this work investigated the feasibility of using artificial intelligence and machine learning technologies to develop a smart proxy model of the Scurry Area Canyon Reef Operators Committee (SACROC) oilfield, located in the Permian Basin, TX, USA. Smart proxy models can be used to facilitate injection-production optimization for CO2-EOR projects. The use of a coupled grid-based, and well-based surrogate reservoir model (SRM) (also known as smart proxy modeling) was investigated as the base of the optimization. A fit-for-purpose coupled SRM, which executes in seconds, was built based on high-resolution numerical reservoir simulation models of the northern platform of the SACROC oilfield. This study is unique as it is the first application of coupled SRM at a large oilfield. The developed SRM was able to identify the dynamic reservoir properties (pressure, saturations, and component mole-fraction) at every grid-block, along with the production characteristics (pressure and rate) at each well. Recent attempts to use machine learning and pattern recognition to build proxy models have been simplistic, with limited predictive capabilities. The geological model used in this study is comprised of more than nine million grid blocks. The high correlation between the actual component and SRM, which can be visualized by mapping the properties, along with the fast footprint of the developed model demonstrate the successful application of this methodology.

]]>Fluids doi: 10.3390/fluids4020084

Authors: Takuji Waseda Wataru Fujimoto Amin Chabchoub

Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schr&ouml;dinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497&ndash;21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin&ndash;Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA.

]]>Fluids doi: 10.3390/fluids4020083

Authors: Dmitry Kachulin Alexander Dyachenko Andrey Gelash

We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water&mdash;breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow of ideal incompressible fluid with a free surface written in conformal variables. The breather collisions are inelastic. However, the breathers can still propagate as stable localised wave groups after the interaction. To generate initial conditions in the form of separate breathers we use the reduced model&mdash;the Zakharov equation. We present an explicit expression for the four-wave interaction coefficient and third order accuracy formulas to recover physical variables in the Zakharov model. The suggested procedure allows the generation of breathers of controlled phase which propagate stably in the fully nonlinear model, demonstrating only minor radiation of incoherent waves. We perform a detailed study of breather collision dynamics depending on their relative phase. In 2018 Kachulin and Gelash predicted new effects of breather interactions using the Dyachenko&ndash;Zakharov equation. Here we show that all these effects can be observed in the fully nonlinear model. Namely, we report that the relative phase controls the process of energy exchange between breathers, level of energy loses, and space positions of breathers after the collision.

]]>Fluids doi: 10.3390/fluids4020082

Authors: Markus Scholle Philip H. Gaskell Florian Marner

Models based on a potential field description and corresponding first integral formulation, embodying a reduction of the associated dynamic boundary condition at a free surface to one of a standard Dirichlet-Neumann type, are used to explore the problem of continuous gravity-driven film flow down an inclined piece-wise planar substrate in the absence of inertia. Numerical solutions of the first integral equations are compared with analytical ones from a linearised form of a reduced equation set resulting from application of the long-wave approximation. The results obtained are shown to: (i) be in very close agreement with existing, comparable experimental data and complementary numerical predictions for isolated step-like topography available in the open literature; (ii) exhibit the same qualitative behaviour for a range of Capillary numbers and step heights/depths, becoming quantitively similar when both are small. A novel outcome of the formulation adopted is identification of an analytic criteria enabling a simple classification procedure for specifying the characteristic nature of the free surface disturbance formed; leading subsequently to the generation of a related, practically relevant, characteristic parameter map in terms of the substrate inclination angle and the Capillary number of the associated flow.

]]>Fluids doi: 10.3390/fluids4020081

Authors: Guillermo Araya

One of the key factors in simulating realistic wall-bounded flows at high Reynolds numbers is the selection of an appropriate turbulence model for the steady Reynolds Averaged Navier&ndash;Stokes equations (RANS) equations. In this investigation, the performance of several turbulence models was explored for the simulation of steady, compressible, turbulent flow on complex geometries (concave and convex surface curvatures) and unstructured grids. The turbulence models considered were the Spalart&ndash;Allmaras model, the Wilcox k- &omega; model and the Menter shear stress transport (SST) model. The FLITE3D flow solver was employed, which utilizes a stabilized finite volume method with discontinuity capturing. A numerical benchmarking of the different models was performed for classical Computational Fluid Dynamic (CFD) cases, such as supersonic flow over an isothermal flat plate, transonic flow over the RAE2822 airfoil, the ONERA M6 wing and a generic F15 aircraft configuration. Validation was performed by means of available experimental data from the literature as well as high spatial/temporal resolution Direct Numerical Simulation (DNS). For attached or mildly separated flows, the performance of all turbulence models was consistent. However, the contrary was observed in separated flows with recirculation zones. Particularly, the Menter SST model showed the best compromise between accurately describing the physics of the flow and numerical stability.

]]>Fluids doi: 10.3390/fluids4020080

Authors: Allatchi Hassan Barkai Mahmoud El Hajem Tom Lacassagne Jean-Yves Champagne

The vacuum airlift column process was patented in 2007 and is under development. The experimental study of its hydrodynamics is one of the axes explored to optimize its design and operation. The object of the study presented in this paper is to determine the functions of phase indicator (gas holdup, superficial gas velocity and bubble size) of the gas&ndash;liquid flow. The experimental analysis is carried out using a two-phase instrumentation consisting of an optical fiber bi-probe. The use of experimental techniques has made it possible to better understand the hydrodynamics of a two-phase flow. The optical bi-probe placed between two column flanges made it possible to have a complete mapping of the flow of the dispersed phase. The use of a mass flow meter and an ultrasonic flowmeter, in different flow configurations, provided data on the column operation.

]]>Fluids doi: 10.3390/fluids4020079

Authors: Shahid Rabbani Hamid Abderrahmane Mohamed Sassi

We present a comparative study of the onset and propagation dynamics of the fingering phenomenon in uniform porous media with a radial configuration. With the help of the Finite Element Method (FEM)-based 2D simulations and image processing techniques, we investigate finger morphology, growth rate, interfacial length, finger length and the number of fingers which are affected due to inertial forces and convective acceleration in a two-phase porous media flow. We considered a modified Darcy&rsquo;s law with inertial force coupled with convective acceleration and investigate their impact on interfacial instability with different velocity-viscosity combinations. Interestingly, the consequences of inertial corrections become significant with changes in viscosity at high Reynolds numbers. Due to the intrinsic bifurcation nature of inertial forces in the radial flow geometry, finger morphology is changed mostly at high viscosity ratios. We find that the effects of inertia and convective acceleration are markedly significant at relatively high Reynolds numbers while the interfacial length and the number of fingers&mdash;which are important parameters for Enhanced Oil Recovery (EOR)&mdash;are most affected by the neglecting of these forces. Moreover, at high Reynolds numbers, the rate of growth of fingering instabilities and the fractal number tend to deviate from that for Darcy&rsquo;s law.

]]>Fluids doi: 10.3390/fluids4020078

Authors: Sk. Mashfiqur Rahman Omer San

In this paper, we investigate the performance of a relaxation filtering approach for the Euler turbulence using a central seven-point stencil reconstruction scheme. High-resolution numerical experiments are performed for both multi-mode and single-mode inviscid Rayleigh&ndash;Taylor instability (RTI) problems in two-dimensional canonical settings. In our numerical assessments, we focus on the computational performance considering both time evolution of the flow field and its spectral resolution up to three decades of inertial range. Our assessments also include an implicit large eddy simulation (ILES) approach that is based on a fifth-order weighted essential non-oscillatory (WENO) with built-in numerical dissipation due to its upwind-based reconstruction architecture. We show that the relaxation filtering approach equipped with a central seven-point stencil, sixth-order accurate discrete filter yields accurate results efficiently, since there is no additional cost associated with the computation of the smoothness indicators and interface Riemann solvers. Our a-posteriori spectral analysis also demonstrates that its resolution capacity is sufficiently high to capture the details of the flow behavior induced by the instability. Furthermore, its resolution capability can be effectively controlled by the filter shape and strength.

]]>Fluids doi: 10.3390/fluids4020077

Authors: Toshio Tagawa Kewei Song

The stability of an electrically conducting fluid flow in a cylinder driven by a multi-pole rotating magnetic field is numerically studied. A time-averaged Lorentz force term including the electric potential is derived on the condition that the skin effect can be neglected and then it is incorporated into the Navier-Stokes equation as a body force term. The axisymmetric velocity profile of the basic flow for the case of an infinitely long cylinder depends on the number of pole-pairs and the Hartmann number. A set of linearized disturbance equations to obtain a neutral state was successfully solved using the highly simplified marker and cell (HSMAC) method together with a Newton&ndash;Raphson method. For various cases of the basic flow, depending on both the number of pole-pairs and the Hartmann number, the corresponding critical rotational Reynolds numbers for the onset of secondary flow were obtained instead of using the conventional magnetic Taylor number. The linear stability analyses reveal that the critical Reynolds number takes its minimum at a certain value of the Hartmann number. On the other hand, the velocity profile for cases of a finite length cylinder having a no-slip condition at the flat walls generates the B&ouml;dewadt boundary layers and such flows need to be computed including the non-linear terms of the Navier-Stokes equation.

]]>Fluids doi: 10.3390/fluids4020076

Authors: Rouhollah Basirat Kamran Goshtasbi Morteza Ahmadi

Hydraulic fracturing (HF) treatment is performed to enhance the productivity in the fractured reservoirs. During this process, the interaction between HF and natural fracture (NF) plays a critical role by making it possible to predict fracture geometry and reservoir production. In this paper, interaction modes between HF and NF are simulated using the discrete element method (DEM) and effective parameters on the interaction mechanisms are investigated. The numerical results also are compared with different analytical methods and experimental results. The results showed that HF generally tends to cross the NF at an angle of more than 45&deg; and a moderate differential stress (greater than 5 MPa), and the opening mode is dominated at an angle of fewer than 45&deg;. Two effects of changing in the interaction mode and NF opening were also found by changing the strength parameters of NF. Interaction mode was changed by increasing the friction coefficient, while by increasing the cohesion of NF it was less opened under a constant injection pressure.

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