Fluids, Volume 6, Issue 10 (October 2021) – 34 articles

In the design practices of many engineering applications, gross information about the flow field may suffice to provide magnitudes of the parameters that are essential to complete the design with reasonable accuracy. If such design parameters can be estimated following simpler steps, it may be possible to abandon the need to conduct expensive numerical and/or experimental works to produce them. In this work, we are interested in providing a generalized power law that depicts the velocity profile for fully developed turbulent flows. This law incorporates two fitting parameters m and n that represent the exponents of (1) a nondimensional length scale and (2) an overall exponent, respectively. These two parameters may be determined by fitting the experimental and/or computational data. In this work, fitting benchmark experimental and computational fluid dynamics (CFD) data found in the literature reveals that the parameter m changes over a relatively smaller range (between 1 and 2), while the parameter n changes over a wider range (between 1 and 12 for the range of Reynolds number considered). These two parameters (m and n) are, generally, not universal, and they depend on the Reynolds number (Re). A correlation was also developed to correlate n and Re in the turbulent flow region. In order to preserve the continuity of the derivative of the velocity profile at the centerline, a value of m equals 2 over the whole range of Re is recommended. Apart from the near wall area, the new law fits the velocity profile reasonably well. This generalized law abides to a number of favorable stipulations for the velocity profile, namely the continuity of derivatives and reduction to the laminar flow velocity profile for lower values of Re. Full article

A detailed study of solar wind turbulence throughout the heliosphere in both the upwind and downwind directions is presented. We use an incompressible magnetohydrodynamic (MHD) turbulence model that includes the effects of electrons, the separation of turbulence energy into proton and electron heating, the electron heat flux, and Coulomb collisions between protons and electrons. We derive expressions for the turbulence cascade rate corresponding to the energy in forward and backward propagating modes, the fluctuating kinetic and magnetic energy, the normalized cross-helicity, and the normalized residual energy, and calculate the turbulence cascade rate from 0.17 to 75 au in the upwind and downwind directions. Finally, we use the turbulence transport models to derive cosmic ray (CR) parallel and perpendicular mean free paths (mfps) in the upwind and downwind heliocentric directions. We find that turbulence in the upwind and downwind directions is different, in part because of the asymmetric distribution of new born pickup ions in the two directions, which results in the CR mfps being different in the two directions. This is important for models that describe the modulation of cosmic rays by the solar wind. Full article

We present the results of a combined experimental and numerical study of the free-surface flow behind a finite height rigid vertical cylinder. The experiments measure the drag and the wake angle on cylinders of different diameters for a range of velocities corresponding to 30,000 $<Re<$ 200,000 and $0.2<Fr<2$ where the Reynolds and Froude numbers are based on the diameter. The three-dimensional large eddy simulations use a conservative level-set method for the air-water interface, thus predicting the pressure, the vorticity, the free-surface elevation and the onset of air entrainment. The deep flow looks like single phase turbulent flow past a cylinder, but close to the free-surface, the interaction between the wall, the free-surface and the flow is taking place, leading to a reduced cylinder drag and the appearance of V-shaped surface wave patterns. For large velocities, vortex shedding is suppressed in a layer region behind the cylinder below the free surface. The wave patterns mostly follow the capillary-gravity theory, which predicts the crest lines cusps. Interestingly, it also indicates the regions of strong elevation fluctuations and the location of air entrainment observed in the experiments. Overall, these new simulation results, drag, wake angle and onset of air entrainment, compare quantitatively with experiments. Full article

The use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil the strict conservative form. If one is willing to work in three dimensions, these fictitious forces can be eliminated by solving for rectangular (Cartesian) momentum components on a curvilinear mesh. A thoroughly geometric approach to fluid dynamics on spacetime demonstrates this transparently, while also giving insight into a greater unity of the relativistic and nonrelativistic cases than is usually appreciated. Full article

To reduce aerodynamic drag of a minivan, non-smooth surfaces are applied to the minivan’s roof panel design. A steady computational fluid dynamics (CFD) method is used to investigate the aerodynamic drag characteristics. The accuracy of the numerical method is validated by wind tunnel test. The drag reduction effects of rectangle, rhombus and arithmetic progression arrangement for circular concaves are investigated numerically, and then the aerodynamic drag coefficient of the rectangle arrangement with a better drag reduction effect is chosen as the optimization objective. Three parameters, that is, the diameter D of the circular concave, the width W and the longitudinal distance L among the circular concaves, are selected as design variables. A 20-level design of an experimental study using a Latin Hypercube scheme is conducted. The responses of 20 groups of sample points are obtained by CFD simulation, based on which a Kriging model is chosen to create the surrogate-model. The multi-island genetic algorithm is employed to find the optimum solution. The result shows that maximum drag reduction effects up to 7.71% can be achieved with a rectangle circular concaves arrangement. The reduction mechanism of the roof with the circular concaves was discussed. The circular concaves decrease friction resistance of the roof and change the flow characteristics of the recirculation area in the wake of the minivan. The roof with the circular concaves reduces the differential pressure drag of the front and rear of the minivan. Full article

Large-eddy simulations have been conducted for two-phase flow (water and air) in a hydrocyclone using Two-Fluid (Euler–Euler) and Volume-of-Fluid (VOF) models. Subgrid stresses are modeled using a dynamic eddy–viscosity model, and results are compared to those using the Smagorinsky model. The effects of grid resolutions on the mean flow and turbulence statistics have been thoroughly investigated. Five block-structured grids of 0.72, 1.47, 2.4, 3.81, and 7.38 million elements have been used for the simulations of Hsieh’s 75 mm hydrocyclone Mean velocity profiles and normal Reynolds stresses have been compared with experimental data. Results of the two-fluid model are in good agreement with those of the VOF model. A fine mesh in the axial and radial directions is necessary for capturing the turbulent vortical structure. Turbulence structures in the hydrocyclone are dominated by helical vortices around the air core. Energy spectra are analyzed at different points in the hydrocyclone, and regions of low turbulent kinetic energy are identified and attributed to stabilizing effects of the swirling velocity component. Full article

The operating conditions during the braking process in an automobile affect the tribological contact between the pad and disc brake, thus, influencing the times and distances of braking and, in a more significant way, the safety of the braking process. This mathematical work aimed to provide a general visualization of the disc brake’s mechanical, dynamic, and thermal behavior under different operating conditions through 2D maps of the power dissipated, braking time, and braking distance of a disc brake with a ventilation blade N- 38 type. However, the dissipated energy on the disc brake in terms of temperature was analyzed considering Newton’s cooling law and mathematical calculations through classical theories of the dynamic and mechanical behavior of the disc brakes. For this purpose, the Response Surface Methodology (RSM) and Distance Weighted Least Squares (DWLS) fitting model considered different operating conditions of the disc brake. The results demonstrate that the disc brakes can be used effectively in severe operational requirements with a speed of 100 km/h and an ambient temperature of 27 °C, without affecting the occupant’s safety or the braking system and the pad. For the different conditions evaluated, the instantaneous temperature reaches values of 182.48 and 82.94 °C, where the high value was found for a total deceleration to 100 km/h to 0, which represent a total braking distance of around 44.20 to 114.96 m depending on the inclination angle (θ). Furthermore, the energy dissipation in the disc brakes depends strongly on the disc, blades and pad geometry, the type of material, parameters, and the vehicle operating conditions, as can be verified with mathematical calculation to validate the contribution of the effectiveness of the braking process during its real operation. Full article

With the availability of more and more efficient and sophisticated Computational Fluid Dynamics (CFD) tools, engineering designs are also becoming more and more software driven. Yet, the insights in temporal and spatial scaling issues are still with us and very often imbedded in complexity and many design aspects. In this paper, with a revisit to a so-called leakage issue in sucker rod pumps prevalent in petroleum industries, the author would like to demonstrate the need to use perturbation approaches to circumvent the multi-scale challenges in CFD with extreme spatial aspect ratios and temporal scales. In this study, the gap size between the outer surface of the plunger and the inner surface of the barrel is measured with a mill (one thousandth of an inch) whereas the plunger axial length is measured with inches or even feet. The temporal scales, namely relaxation times, are estimated with both expansions in Bessel functions for the annulus flow region and expansions in Fourier series when such a narrow circular flow region is approximated with a rectangular one. These engineering insights derived from the perturbation approaches have been confirmed with the use of full-fledged CFD analyses with sophisticated computational tools as well as experimental measurements. With these confirmations, new perturbation studies on the sucker rod leakage issue with eccentricities have been presented. The volume flow rate or rather leakage due to the pressure difference is calculated as a quadratic function with respect to the eccentricity, which matches with the early prediction and publication with comprehensive CFD studies. In short, a healthy combination of ever more powerful modeling tools along with the physics, mathematics, and engineering insights with dimensionless numbers and classical perturbation approaches may provide a balanced and more flexible and efficient strategy in complex engineering designs with the consideration of parametric and phase spaces. Full article

Flapping wing micro-air-vehicles (FWMAVs) animate the small-space dexterous flight, hovering, and energy-saving characteristics of birds and insects, and are believed to have enlightenment for the development of bionic flight in the future. When designing FWMAVs, detailed unsteady aerodynamic information is required. Besides the computational fluid mechanics (CFD) technology study, the flow visualization is also needed to assist this research. This article innovatively used soap film visualization with high-speed photography to record two kinds of the 2D flow fields laterally and longitudinally, respectively, generated by a flapping wing of 10 cm span. Different from the qualitative comparison of soap film imaging with the conventional smoke tracing method, the subsequent processing of the soap film images was demonstrated. This work explains how to quantify the soap film imaging into lift and thrust forces, and the corresponding results are compared with the wind tunnel force measurement data preliminarily. Full article

Ocean convection is a key mechanism that regulates heat uptake, water-mass transformation, CO₂ exchange, and nutrient transport with crucial implications for ocean dynamics and climate change. Both cooling to the atmosphere and salinification, from evaporation or sea-ice formation, cause surface waters to become dense and down-well as turbulent convective plumes. The upper mixed layer in the ocean is significantly deepened and sustained by convection. In the tropics and subtropics, night-time cooling is a main driver of mixed layer convection, while in the mid- and high-latitude regions, winter cooling is key to mixed layer convection. Additionally, at higher latitudes, and particularly in the sub-polar North Atlantic Ocean, the extensive surface heat loss during winter drives open-ocean convection that can reach thousands of meters in depth. On the Antarctic continental shelf, polynya convection regulates the formation of dense bottom slope currents. These strong convection events help to drive the immense water-mass transport of the globally-spanning meridional overturning circulation (MOC). However, convection is often highly localised in time and space, making it extremely difficult to accurately measure in field observations. Ocean models such as global circulation models (GCMs) are unable to resolve convection and turbulence and, instead, rely on simple convective parameterizations that result in a poor representation of convective processes and their impact on ocean circulation, air–sea exchange, and ocean biology. In the past few decades there has been markedly more observations, advancements in high-resolution numerical simulations, continued innovation in laboratory experiments and improvement of theory for ocean convection. The impacts of anthropogenic climate change on ocean convection are beginning to be observed, but key questions remain regarding future climate scenarios. Here, we review the current knowledge and future direction of ocean convection arising from sea–surface interactions, with a focus on mixed layer, open-ocean, and polynya convection. Full article

Vertical air curtains are often used to separate two different zones to reduce contaminant transfer or even to provide aerodynamic sealing from one zone to the other. In this isothermal full-size experimental research work, the contaminant transfer between zones is reduced using an air extraction from the “contaminated” compartment and an air curtain. This work correlates the minimum exhaust air flow rate required to reach the aerodynamic sealing at the opening connecting two different zones with the jet nozzle velocity for small nozzle thicknesses (5 mm, 10 mm and 16 mm), particularly for Reynolds numbers below 3800. Following the experimental study, a general physical law that relates the jet parameters (angle, nozzle thickness and jet velocity at the nozzle) with the average velocity through the opening (for the condition of acceptable contaminant tightness) was obtained. The results showed that the average velocity of the flow across a door protected by an air curtain required to keep the aerodynamic sealing varies linearly with Re. The slope, however, is different below and above Re = 3820. Full article

Fluid flow and transport processes in fractured porous media are of particular interest for geologists and in the material sciences. Here a systematic investigation is presented, dealing with a generic geometric set-up of a porous matrix with a crack. In such a combined porous medium/free fluid system flow patterns have been examined frequently, while the resulting transport patterns have attracted less attention. Using numerical modeling with finite elements the problem is approached using a dimensionless formulation. With a reduced number of dimensionless parameter combinations (Darcy-, Peclet- and Reynolds-numbers) solution dependencies are examined in parametric sweeps. Breakthrough curves are fitted in comparison to those of 1D model approaches, yielding effective diffusivities and velocities. The computations reveal highest sensitivity concerning the angle between crack axis and flow direction, followed by the Peclet number and the crack axes ratio. As a dimensionless representation is used the results are scale independent. Thus, they deliver estimations concerning effective heat and solute transport parameters that can be relevant in all application fields. Full article

This paper studies the species separation of a binary fluid in a porous cavity between two horizontal concentric cylinders, submitted to a temperature gradient. The thickness of the cavity is $e=R_o-R_i$, where $R_i$ and $R_o$ are the internal and external radius, respectively. The numerous previous experiments performed in thermogravitational vertical columns (TGCs) showed that in order to obtain a significant separation, the thickness of the cell must be very small, compared with its height. Therefore, in our configuration, we considered $e\ll R_i$. The solution is assumed to be axisymmetric. Under the assumptions of parallel flow and forgotten effect, an analytical solution is obtained using Maple software, and the results are compared with those found numerically using Comsol Multiphysics. In natural convection, our results are in very good agreement with those evaluated with a regular perturbation method in powers of the dimensionless gap width $\epsilon =\frac{e}{R_i}$ of order 15, and with the Galerkin method. The species separation calculated for our configuration is very close to the one obtained in a TGC column of height: $H=\pi R_i.$ One of the main interests of the analytical solution presented here is that it can be used as a basic solution for a stability study analysis. Full article

Widely used for modeling biological fluids flows—in particular, blood vessel flows—a Casson flow is studied in a symmetric channel for which the aspect ratio enables one to use the lubrication approximation. Two flow driving conditions are prescribed: inlet–outlet pressure difference and peristaltic oscillations of the vessel walls. In both cases, starting from mass and momentum balance and using lubrication approximation, we investigate the conditions to be imposed on the driving mechanisms so that the inner plug does not come in touch with the walls. The study of the peristaltic flow is of great importance in view of its applications in physiology (including microcirculation applications). Full article

Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed the one-dimensional problem of multicomponent fluid flow in a porous medium and solved the system of the algebraic equation with the Newton-GMRES method. We calculated the linear equations with the GMRES, the GMRES with restarts after every m steps—GMRES (m) and preconditioned with Incomplete Lower-Upper factorization, where the factors L and U have the same sparsity pattern as the original matrix—the ILU(0)-GMRES algorithms, respectively, and compared the computation time and convergence. In the course of the research, the influence of the preconditioner and restarts of the GMRES (m) algorithm on the computation time was revealed; in particular, they were able to speed up the program. Full article

In this manuscript, a function is derived that allows the interactions between the atoms/molecules in nanoparticles, nanodrops, and macroscopic liquid phases to be modeled. One goal of molecular theories is the development of expressions to predict specific physical properties of liquids for which no experimental data are available. A big limitation of reliable applications of known expressions is that they are based on the interactions between pairs of molecules. There is no reason to suppose that the energy of interaction of three or more molecules is the sum of the pairwise interaction energies alone. Here, an interaction function with the limit value w = e^2π/e is presented, which allows for the derivation of the atomic mass unit and acts as a bridge between properties of elementary particles and emergent properties of macroscopic systems. The following properties of liquids are presented using the introduced interaction function: melting temperatures of n-alkanes, nanocrystals of polyethylene, melting temperatures of metal nanoparticles, solid–liquid phase transition temperatures for water in nanopores, critical temperatures and critical pressures of n-alkanes, vapor pressures in liquids and liquid droplets, self-diffusion coefficients of compounds in liquids, binary liquid diffusion coefficients, diffusion coefficients in liquids at infinite dilution, diffusion in polymers, and viscosities in liquids. Full article

Sperm have thin structures known as flagella whose motion must be regulated in order to reach the egg for fertilization. Large numbers of sperm are typically needed in this process and some species have sperm that exhibit collective or aggregate motion when swimming in groups. The purpose of this study is to model planar motion of flagella in groups to explore how collective motion may arise in three-dimensional fluid environments. We use the method of regularized Stokeslets and a three-dimensional preferred curvature model to simulate groups of undulating flagella, where flagellar waveforms are modulated via hydrodynamic coupling with other flagella and surfaces. We find that collective motion of free-swimming flagella is an unstable phenomenon in long-term simulations unless there is an external mechanism to keep flagella near each other. However, there is evidence that collective swimming can result in significant gains in velocity and efficiency. With the addition of an ability for sperm to attach and swim together as a group, velocities and efficiencies can be increased even further, which may indicate why some species have evolved mechanisms that enable collective swimming and cooperative behavior in sperm. Full article

In marine engineering, the dynamics of fixed offshore structures (for oil and gas production or for wind turbines) are normally found by modelling of the motion by a classical mass-spring damped system. On slender offshore structures, the loading due to waves is normally calculated by applying a force which consists of two parts: a linear “inertia/mass force” and a non-linear “drag force” that is proportional to the square of the velocity of the particles in the wave, multiplied by the direction of the wave particle motion. This is the so-called Morison load model. The loading function can be expanded in a Fourier series, and the drag force contribution exhibits higher order harmonic loading terms, potentially in resonance with the natural frequencies of the system. Currents are implemented as constant velocity terms in the loading function. The paper highlights the motion of structures due to non-linear resonant motion in an offshore environment with high wave intensity. It is shown that “burst”/“ringing” type motions could be triggered by the drag force during resonance situations. Full article

Braking time in a moving train at standard speeds has become a critical variable that increasingly concerns the industry. The present paper discusses the possible option of temperature variation to cut down the response time of the whole pneumatic braking system in a train installation. A pneumatic system, considered equivalent to the system existing in a real train, was experimentally analyzed to account for the time and characteristics of a sonic pressure wave moving in the pipes. The available system behavior was compared for two different air temperatures. The obtained results point to a relevant temperature effect on the pressure wave transmission, which may promote time or distance shortening in a standard braking process. Although in the experimental campaign only two initial temperatures could be set, the study shows a possible research path for future improvements. A parallel theoretical calculation corrected by the effect of the relevant elements in the pipes was performed to allow a comparison with the experiments. Full article

An advanced numerical model is presented for the simulation of wave-induced free-surface flow, utilizing an efficient hybrid parallel implementation. The model is based on the solution of the Navier–Stokes equations using large-eddy simulation of large-scale coastal free-surface flows. The three-dimensional immersed boundary method was used for the enforcement of the no-slip boundary condition on the bed surface. The water-air interface was tracked using the level-set method. The numerical model was effectively validated against laboratory measurements involving wave propagation over a flatbed with an elliptical shoal, whose presence induces combined wave refraction and diffraction phenomena. The parallel implementation of the model enabled the efficient simulation of depth-resolved, wave-induced, three-dimensional, free-surface flow; the model parallel efficiency and strong scaling are quantitatively demonstrated. Full article

The food industry has increased its interest in using natural and consumer-friendly ingredients to produce food products. In the case of hydrocolloids of natural origin, the materials are biodegradable and environmentally friendly. This study aimed to isolate hydrocolloids from Pereskia bleo leaves and evaluate their proximal composition, technological and rheological properties. High-carbohydrate Pereskia bleo with high water holding capacity and emulsifying stability were obtained. The samples showed a shear-thinning behavior adjusted to the Cross model (R² > 0.93) and a high dependence on temperature corroborating with the higher activation energy value (11.78 kJ/mol, R² = 0.99) as an indicator of a rapid change in viscosity and microstructure. The viscoelastic properties are shown with a storage modulus higher than the loss modulus, presenting a gel structure. The isolation of hydrocolloids from leaves is a major challenge for commercializing natural ingredients with technological properties. Therefore, this study suggests that these hydrocolloids from Pereskia bleo leaves can be good ingredients in microstructure and texturizing products, improving the stability as thickener agents. Full article

The finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here, we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second-order velocity structure function. Full article

The nonlinear transformation of waves in the coastal zone over the sloping bottom is considered on the base of field, laboratory, and numerical experiments by methods of spectral and wavelet analyses. The nonlinearity leads to substantial changes of wave shape during its propagation to the shore. Since these changes occur rapidly, the wave movement is non-periodical in space, and the application of linear theory concepts of wavenumber or wavelength results in some paradoxical phenomena. When analyzing the spatial evolution of waves in the frequency domain, the effect of periodic energy exchange and changes in the phase shift between the first and second wave harmonics are observed. When considering the wavenumber domain, the free and bound waves of both the first and second harmonics with constant in space amplitudes appear, and all spatial fluctuations of the wave parameters are caused by interference of these four harmonics. Practically important consequences such as the wave energy spatial fluctuations and of anomalous dispersion of the second harmonic are shown and discussed. Full article

This paper confronts the numerical simulation of steady flows of fluid layers through channels of varying bed and width. The fluid consists of two immiscible fluid layers with constant density, and it is assumed to be of a one-dimensional shallow flow. The governing equation is a coupled system of two-layer shallow water models. In this paper, we apply a direct extension of the momentum conserving scheme previously used for solving the one layer shallow water equations. Computations of various steady-state solutions are used to demonstrate the performance of the proposed numerical scheme. Under the influence of a given flow rate, the numerical steady interface is generated in a channel topography with a hump. The results obtained confirm the analytic steady interface of the two-layer rigid-lid model. Furthermore, the same scheme was used with an additional artificial damping to simulate the maximal exchange flow in channels of varying width. The numerical steady interface agreed well with the analytical steady solutions. Full article

Many methods to produce hydrate reservoirs have been proposed in the last three decades. Thermal stimulation and injection of thermodynamic hydrate inhibitors are just two examples of methods which have seen reduced attention due to their high cost. However, different methods for producing hydrates are not evaluated thermodynamically prior to planning expensive experiments or pilot tests. This can be due to lack of a thermodynamic toolbox for the purpose. Another challenge is the lack of focus on the limitations of the hydrate phase transition itself. The interface between hydrate and liquid water is a kinetic bottle neck. Reducing pressure does not address this problem. An injection of CO₂ will lead to the formation of a new CO₂ hydrate. This hydrate formation is an efficient heat source for dissociating hydrate since heating breaks the hydrogen bonds, directly addressing the problem of nano scale kinetic limitation. Adding limited amounts of N₂ increases the permeability of the injection gas. The addition of surfactant increases gas/water interface dynamics and promotes heterogeneous hydrate formation. In this work we demonstrate a residual thermodynamic scheme that allows thermodynamic analysis of different routes for hydrate formation and dissociation. We demonstrate that 20 moles per N₂ added to the CO₂ is thermodynamically feasible for generating a new hydrate into the pores. When N₂ is added, the available hydrate formation enthalpy is reduced as compared to pure CO₂, but is still considered sufficient. Up to 3 mole percent ethanol in the free pore water is also thermodynamically feasible. The addition of alcohol will not greatly disturb the ability to form new hydrate from the injection gas. Homogeneous hydrate formation from dissolved CH₄ and/or CO₂ is limited in amount and not important. However, the hydrate stability limits related to concentration of hydrate former in surrounding water are important. Mineral surfaces can act as hydrate promotors through direct adsorption, or adsorption in water that is structured by mineral surface charges. These aspects will be quantified in a follow-up paper, along with kinetic modelling based on thermodynamic modelling in this work. Full article

Improving heat transfer from surface to airflow is a current research concern for enhancing energy efficiency. The use of vortex generators for improving heat transfer from the surface to the airflow is very effective. Therefore, this study focuses on applying flat and concave vortex generators with and without holes in order to improve heat transfer. In this study, the number of pairs of vortex generators was varied from one to three pairs at a certain angle of attack for various forms of vortex generators. The airflow velocity through the duct was varied in the range of 0.4 to 2.0 m/s at 0.2 m/s intervals. From the investigation results, we observed that the highest thermal performance was found with the use of concave delta winglets without holes for various pairs of vortex generators in terms of the overall Reynolds number. The highest thermal enhancement factor was found to be around 1.42 at a Reynolds number of approximately 9000. From this study, it was also shown that the lowest cost–benefit ratio was about 1.75 at a Reynolds number of approximately 3500 for three pairs of vortex generators. Full article

Bayesian methods were studied in this paper using deep neural networks. We are interested in variational autoencoders, where an encoder approaches the true posterior and the decoder approaches the direct probability. Specifically, we applied these autoencoders for unsteady and compressible fluid flows in aircraft engines. We used inferential methods to compute a sharp approximation of the posterior probability of these parameters with the transient dynamics of the training velocity fields and to generate plausible velocity fields. An important application is the initialization of transient numerical simulations of unsteady fluid flows and large eddy simulations in fluid dynamics. It is known by the Bayes theorem that the choice of the prior distribution is very important for the computation of the posterior probability, proportional to the product of likelihood with the prior probability. Hence, we propose a new inference model based on a new prior defined by the density estimate with the realizations of the kernel proper orthogonal decomposition coefficients of the available training data. We numerically show that this inference model improves the results obtained with the usual standard normal prior distribution. This inference model was constructed using a new algorithm improving the convergence of the parametric optimization of the encoder probability distribution that approaches the posterior. This latter probability distribution is data-targeted, similarly to the prior distribution. This new generative approach can also be seen as an improvement of the kernel proper orthogonal decomposition method, for which we do not usually have a robust technique for expressing the pre-image in the input physical space of the stochastic reduced field in the feature high-dimensional space with a kernel inner product. Full article

Linear stability analysis of a steady convective flow in a tall vertical annulus caused by nonlinear heat sources is conducted in the paper. Heat sources are generated as a result of a chemical reaction. The effect of radial cross-flow through permeable porous walls of the annulus is analyzed. The problem is relevant to biomass thermal conversion. The base flow solution is obtained by solving nonlinear boundary value problem. Linear stability analysis is performed, using collocation method. The calculations show that radial inward or outward flow has a stabilizing effect on the flow, while the increase in the Frank–Kamenetskii parameter (proportional to the intensity of the chemical reaction) destabilizes the flow. The increase in the Reynolds number based on the radial velocity leads to the appearance of the second minimum on the marginal stability curves. The rate of increase in the critical Grashof number with respect to the Reynolds number is different for inward and outward radial flows. Full article

Subsurface multiphase flow in porous media simulation is extensively used in many disciplines. Large meshes with non-orthogonalities (e.g., corner point geometries) and full tensor highly anisotropy ratios are usually required for subsurface flow applications. Nonetheless, simulations using two-point flux approximations (TPFA) fail to accurately calculate fluxes in these types of meshes. Several simulators account for non-orthogonal meshes, but their discretization method is usually non-conservative. In this work, we propose a semi-implicit procedure for general compositional flow simulation in highly anisotropic porous media as an extension of TPFA. This procedure accounts for non-orthogonalities by adding corrections to residual in the Newton-Raphson method. Our semi-implicit formulation poses the guideline for FlowTraM (Flow and Transport Modeller) implementation for research and industry subsurface purposes. We validated FlowTraM with a non-orthogonal variation of the Third SPE Comparative Solution Project case. Our model is used to successfully simulating a real Colombian oil field. Full article

In the early 1980s it was well established that Leray solutions of the unforced Navier–Stokes equations in ${\mathbb{R}}^n$ decay in energy norm for large t. With the works of T. Miyakawa, M. Schonbek and others it is now known that the energy decay rate cannot in general be any faster than $t^{-(n+2)/4}$ and is typically much slower. In contrast, we show in this note that, given an arbitrary Leray solution $\mathit{u}(·,t)$, the difference of any two Stokes approximations to the Navier–Stokes flow $\mathit{u}(·,t)$ will always decay at least as fast as $t^{-(n+2)/4}$, no matter how slow the decay of ${\parallel \mathit{u}(·,t)\parallel }_{L^2\left({\mathbb{R}}^n\right)}$ might be. Full article