Non-uniform Velocity Research Articles

Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation

This paper reports multiple slip effects on MHD unsteady flow heat and mass transfer over a stretching sheet with Soret effect; suction/injection and thermal radiation are numerically analyzed. We consider a time-dependent applied magnetic field and stretching sheet which moves with nonuniform velocity. Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved numerically by applying an implicit finite difference method with quasi-linearization technique. The influences of the various parameters on the velocity temperature and concentration profiles as well as on the skin friction coefficient and Sherwood and Nusselt numbers are discussed by the aid of graphs and tables.

Numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid

PurposeThe purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids.Design/methodology/approachConsidering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated.FindingsThe results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory.Originality/valueThis paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.

Kinetic Alfvén waves generated by ion beam and velocity shear in the Earth's magnetosphere

Generation of Kinetic Alfvén Waves (KAWs) in a generalized three component plasma model consisting of the background cold ions, hot electrons, and hot ion beams, where all the three species have non-uniform streaming and velocity shear, is discussed. First, the role played by the ion beam solely in exciting KAWs is analyzed. Next, how this behavior gets modified when the velocity shear is present along with the streaming ion beam is discussed. The effects of other parameters such as temperature, number density, and propagation angle on the growth of KAWs are explored. It is found that when shear is positive and ions are streaming along the ambient magnetic field, KAWs are stabilized. On the other hand, with positive shear and an anti-parallel ion beam or vice-versa, KAWs with a larger growth rate are excited as compared to the case of waves excited by the ion beam alone. Also, for the first time, we have shown the combined effect of the ion beam and velocity shear on the generation of KAWs. The theoretical model can generate ultra-low frequency waves with frequencies up to ≈60 mHz for the plasma parameters relevant to auroral/polar cusp field lines.

Impingement jet hydrogen, air and Cu[sbnd]H2O nanofluid cooling of a hot surface covered by porous media with non-uniform input jet velocity

In this paper, a numerical investigation is performed on the flow and thermal performance of a heat sink, covered with an open cell metal foam, under the influences of uniform and non-uniform velocity impinging jets. Hydrogen, air and Cu-water nanofluid are considered as the cooling fluids. Navier-Stokes PDEs including the porous drag induced terms – represented by Darcy-Brinkman-Forchheimer relation – in line with the energy equation, are transformed to a system of ordinary differential equations (ODE) through definition of non-dimensional parameter and similarity variables. The system of non-linear ODEs has been solved numerically and results are validated by comparison with those of a commercial software. Afterward, the influences of hydrodynamic variables, porous medium properties and nanofluid volume fraction on flow and heat transfer performance of the heat sink, have been scrutinized. Results presented in terms of non-dimensional velocity and temperature profiles, as well as the stream function, velocity and temperature contours. Results indicate that increasing the volume fraction of nanofluid have increased the heat transfer rate. In addition, under the constant heat sink inlet mass flow rate, the use of non-uniform impingement jet with decreasing velocity distribution improves the thermal performance of the heat sink.

Wind farm interference and terrain interaction simulation by means of an adaptive actuator disc

Wind turbine wake interference is a relevant phenomenon that involves speed losses and turbulence increments which greatly affect downstream turbines, and power efficiency of wind farms. To precisely simulate wake interaction, the most common simplified wind turbine model, the Actuator Disc (AD) model, is improved adding the capability to adapt the thrust force distribution to a non-uniform velocity field over the disc, and the orientation to different local wind directions. These situations are typically found in wind farm situation where turbines interact with wakes of upstream turbines and the terrain. This development is based on the OpenFOAM open source finite volume parallel software. The improved AD model is first validated against wind tunnel experiments. Then, an onshore wind farm case is presented, in which the complex interaction of the turbines and terrain is studied. Comparing with power efficiency of field measurements, the simulations succeed to capture the characteristic values for low and high wake impact situations, with differences of 2.5% and 1.3%, respectively. Results show that this improved AD model produces a better solution for wake interaction cases. Its usefulness to predict the wind farm power output at feasible computational cost is also evidenced.

Compressible Fanno flows in micro-channels: An enhanced quasi-2D numerical model for laminar flows

Micro-scale fluid systems are becoming common in many applications ranging from electronic cooling to refrigeration systems and more. One-dimensional numerical models represent a simple and fast tool for the design of such devices, yet they struggle to accurately predict the flow characteristics in compressible micro-flows. Under the adiabatic assumption, the elegant theory developed by Fanno allows models for the viscous compressible flow in constant cross-section channels to be easily built. Although reasonably accurate, these models suffer from drawbacks inherent to their being one-dimensional, as such they cannot take into account the local profiles of quantities like the velocity and the temperature. In cascade, this results into incorrect evaluations of other dependent quantities, such as the dynamic pressure and the fluid thermophysical properties. The mismatch turns large when the fluid compressibility becomes important. As the Mach number grows, the velocity profile changes, and so the friction factor, even though a reliable model for predicting this change is still missing. In fact, a constant friction factor throughout the channel is generally assumed, following the incompressible flow theory. Here, a set of correlations is proposed improving the 1D theory accuracy by taking into account the effects of the non-uniform velocity and temperature profiles in a quasi-2D fashion. A detailed analysis of the velocity profiles at different Mach numbers coming from a large set of CFD simulations results in a model for assessing the impact of compressibility on friction and other quantities. The numerical model proposed, being able to properly account for the compressibility effects, offers an improved tool for the design of micro-scale fluid systems. Extending the analysis to include heat transfer is not difficult as the effect of heat flux will be analogous to the effect of pressure drop due to friction.

Analysis of the influence of non-uniformity of air flow velocity on the trajectory of grain particles motion in a pneumatic inertial separator

Purpose. Determination of influence of non-uniform velocity field of air in horizontal channel of pneumatic inertial separator on efficiency of separation of components of grain material into fractions by aerodynamic properties. Methods. The specificity of the issue under consideration determines the analytical method of study based on the compilation and analysis of kinetic equations of motion of a particle, in the form of a ball in the air flow of a horizontal channel with uneven distribution of air flow velocity over the height of the pneumatic channel. Results. The mathematical description of the motion of particles of the grain mixture in the chamber of the gravitational-air separator under the action of air flow of variable speed air is given. The trajectories of motion of particles of different size were obtained. The obtained equation of motion of a particle under the action of air flow allows to determine the dependence of the speed of movement of the material in the layer of grain material on a number of factors: geometric parameters of the separator, the angle of feed of the material, the initial kinematic mode of the material, as well as the coefficient of sail of the particle. The technological possibilities of the proposed method of grain separation under the action of air flow are theoretically substantiated and the influence on the technological parameters of the basic parameters: air velocity, coefficient of live section taking into account the layer thickness of the material entering the channel is established. Conclusions 1.On the basis of the analysis of the force interaction of the grain material particle with the air stream, an advanced mathematical model of particle motion in a non-uniform field of air flow velocity in the horizontal channel was obtained. 2.The real possibility of controlling the process of separation of components of grain material by aerodynamic properties by changing the plot of the air flow velocity along the height of the horizontal channel is determined. Keywords: variable air velocity, trajectory, resistance of forces, fractions, air flow, wind factor, fractionation process, grain mixture, air separator.

ALMA observations of the “fresh” carbon-rich AGB star TX Piscium

Aims. The carbon-rich asymptotic giant branch (AGB) star TX Piscium (TX Psc) has been observed multiple times during multiple epochs and at different wavelengths and resolutions, showing a complex molecular CO line profile and a ring-like structure in thermal dust emission. We investigate the molecular counterpart in high resolution, aiming to resolve the ring-like structure and identify its origin. Methods. Atacama Large Millimeter/submillimeter Array (ALMA) observations have been carried out to map the circumstellar envelope (CSE) of TX Psc in CO(2–1) emission and investigate the counterpart to the ring-like dust structure. Results. We report the detection of a thin, irregular, and elliptical detached molecular shell around TX Psc, which coincides with the dust emission. This is the first discovery of a non-spherically symmetric detached shell, raising questions about the shaping of detached shells. Conclusions. We investigate possible shaping mechanisms for elliptical detached shells and find that in the case of TX Psc, stellar rotation of 2 km s−1 can lead to a non-uniform mass-loss rate and velocity distribution from stellar pole to equator, recreating the elliptical CSE. We discuss the possible scenarios for increased stellar momentum, enabling the rotation rates needed to reproduce the ellipticity of our observations, and come to the conclusion that momentum transfer of an orbiting object with the mass of a brown dwarf would be sufficient.

Nonlinear isobaric flow of a viscous incompressible fluid in a thin layer with permeable boundaries

A new exact solution of the Navier-Stokes equations system is investigated. This solution describes an isobaric three-dimensional nonlinear flow of a viscous incompressible fluid in an infinite horizontal layer with permeable boundaries. Permeable layer boundaries allow one to realize fluid suction or injection in a vertical direction. Thus, a generalization of the non-uniform layered Couette-type flow to the three-dimensional case is obtained. The announced exact solution belongs to the Lin class. The velocity field is a linear form with respect to two spatial horizontal coordinates with coefficients depending on the third (transverse) coordinate in this class. The obtained exact solution describes a three-dimensional flow of a vertically vortex fluid, which can be used to describe large-scale processes in oceanology and in atmospheric physics. The obtained exact solution describes a large-scale flow of a vertical vortex fluid in the thin layer approximation. Vertical twist in a non-rotating fluid arises due to the inclusion of inertial forces in the motion equations and the velocities inhomogeneous distribution on the upper non-deformable permeable boundary of the layer. A non-uniform velocity field is studied using the Navier slip condition on the lower boundary. Additionally, the case of equality to zero of the slip length (sticking condition) is analyzed. The velocity field is studied for an arbitrary value of the Navier parameter. The obtained exact solution allows one to describe the counterflows of a viscous incompressible fluid. The obtained solution is analyzed and the existence of stagnation points in the vertical vortex fluid flow in an infinite layer with permeable boundaries is shown. Only one stagnation point is recorded in the fluid flow, when the no-slip and Navier slip conditions at the lower boundary are realized. Thus, the obtained exact solutions of the Navier-Stokes equations describe a new angular momentum transfer mechanism in a fluid. This exact solution illustrates the existence of vertical vorticity in a non-rotating fluid. Vertical twist is induced by a non-uniform velocity field at the boundaries of the fluid layer.

Design of a high-specific speed turbine with non-uniform blade cascade

This paper presents the hydraulic design of Kaplan type turbine in fully axial configuration. The turbine model consists of a straight pipe intake, a rib which covers the shaft, five axial guide vanes, a six blade runner and a 10,6°-full angle draft tube. Due to the presence of non-uniform velocity field behind the rib and interaction between stator and rotor, the pressure pulsations occur and cause some excitation forces acting on the runner. To reduce these negative phenomena the six non-uniform blade runner has been designed using computational fluid dynamics modelling (CFD). The runner blades are placed in various axial distances from the guide vanes. This new design should reduce the pressure pulsations caused by interaction between the rib and the runner, which is the main negative effect by the current design. The forces and torque which are acting on the runner blades as well as the pressure inside the turbine are observed in time domain. The amplitudes and frequencies are analysed using Fast Fourier Transform (FFT). The frequencies are compared to the modal analysis results of the runner submerged in water. This hydraulic design is based on previous axial turbine, which was designed for small hydro power plant located at Lužnice River. The design point is defined by head H = 1,5 m, volumetric flow rate Q = 2,1 m3/s and RPM n = 260 min-1. This turbine was designed using six runner blades to reduce the pressure, force and torque pulsations caused mainly by wakes, which were observed behind the rib.

Two-stage velocity distribution measurement from multiple projections by tunable diode laser absorption spectrum

A novel approach to using tunable diode laser absorption spectrum (TDLAS) is developed for nonuniform velocity distribution measurement by Doppler effect. An analysis of the energy in direct absorption spectrum at low frequencies is made by Fourier transform, because the TDLAS method offers the advantages in using Beer law to deal with coupling relations between velocity distribution and corresponding length of velocity region. By comparing with traditional TDLAS-Doppler velocity measurement, advantages of this approach to the more exact solution of core flow velocity by signal process without using extra lasers and detectors are explored. Following the published theory, between velocity regions at multiple projections the absorbance about average in frequency offsets and the absorbance about difference in frequency offsets are incorporated into an improved fitting model. A solution to obtaining changes of absorbance energy at low frequencies by Fourier transform is used to demonstrate the ability to recover minor change in absorbance under different conditions, inferring a better method to realize the simultaneous measurement of velocity distribution. The influences of these parameters, such as projection angles and noise during absorption, are investigated by the multiple projection simulations at rovibrational transitions of H<sub>2</sub>O near 7185.6 cm<sup>–1</sup> from three projections. This approach is validated in a two-stage velocity distribution model, demonstrating the ability to exactly measure core flow, with a precision of 0.9% RMS (root mean square). The high velocity in the core flow is less influenced by the random noise in absorption due to nearly linear relationship between the difference in frequency offsets and the ratio of length of velocity region. Some satisfied results can be obtained when larger angles of projection are arranged. The combination of 0°, 30°, and 60° will be a reasonable optic design considering the limitation of spatial resolution. In conclusion, the novel approach to velocity distribution measurement based on TDLAS-Doppler from multiple projections has great potential applications in engine diagnosis and gas dynamic research.

Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation

Обсуждается разрешимость переопределенной системы уравнений тепловой конвекции в приближении Буссинеска. Система уравнений Обербека-Буссинеска, дополненная уравнением несжимаемости, является переопределенной. Количество уравнений превосходит количество неизвестных функций, поскольку изучаются неоднородные слоистые потоки вязкой несжимаемой жидкости (одна из компонент вектора скорости тождественно равна нулю). Проведено исследование разрешимости нелинейной системы уравнений Обербека-Буссинеска. Исследование разрешимости переопределенной системы нелинейных уравнений в частных производных Обербека-Буссинеска осуществлялось при помощи построения нескольких частных точных решений. Приведен новый класс точных решений для описания трехмерных нелинейных слоистых течений вертикальной завихренной вязкой несжимаемой жидкости. Вертикальная компонента завихренности в невращающейся жидкости генерируется неоднородным полем скоростей на нижней границе бесконечного горизонтального слоя жидкости. Конвекция в вязкой несжимаемой жидкости индуцируется линейными источниками тепла. Основное внимание уделено исследованию свойств поля скоростей течения. Исследована зависимость структуры этого поля от величины вертикальной закрутки. Показано, что одна из компонент вектора скорости при ненулевой вертикальной закрутке допускает расслоение на пять зон по толщине рассматриваемого слоя (четыре застойные точки). Анализ поля скоростей показал, что кинетическая энергия жидкости может дважды принимать нулевой значение по толщине слоя.

Instability analysis of the cone–jet flow in liquid-driven flow focusing

The instability behaviors of a liquid jet issuing from a cone in liquid-driven flow focusing for droplet generation are studied. The experiment, numerical simulation by solving the Navier–Stokes equation coupled with a diffuse interface method, and linear spatio-temporal instability analysis based on non-uniform velocity profiles are performed. Typical flow modes and transitions are obtained by adjusting the flow rates of focused and focusing phases. The cone instability is examined and the flow patterns in the vicinity of the cone are presented numerically. The result shows that the liquid cone can be always stable in a wide range of process parameters when the viscous shear stress overcomes the interfacial tension stress and a scaling law is given. In addition, the spatial evolution of velocity profiles of the flow is numerically investigated. Finally, the jetting–dripping (J–D) transition is studied through the dimensional analysis and the linear instability theory in comparison with experiments and good agreements among them are achieved. It is also indicated that the J–D transition boundary can be approximately given by the scaling law of $$We_{\mathrm{i}}+Ca_{\mathrm{o}}\approx 1,$$ where $$We_{\mathrm{i}}$$ and $$Ca_{\mathrm{o}}$$ reflect the competitions of inertia force and viscous shear stress to the interfacial tension along the jet, respectively.

Non-uniform filtration velocity of process gas passing through a long bag filter.

Filtration velocity is one of the dominant parameters that determine the pressure drop through a bag filter. Experimental investigation of the air flow pattern around a bag filter inside a bag house is very difficult because of the complexity of the 3-D air flow. For this reason, we numerically investigated flow characteristics along a bag filter in detail. We newly found that the filtration velocity is non-uniform along the axial direction of a long bag filter when the height of the filter is greater than 10 m. The filtration velocity is very small at the bottom of the bag filter but very large at the top. For bag filter lengths of over 10 m, 70% of total inlet flow is filtered in just the top 30% of the long bag filter. This indicates that the top section of the long bag filter could deteriorate faster than the bottom section, making it necessary to develop a new method to avoid the problem. We developed an equation that can help predict the initial pressure drop across long bag filters with different heights, but identical filtration characteristics.

An improved viscous/acoustic splitting method by analyzing source effects

The origin and effect of each term in the equations of the viscous/acoustic splitting (VAS) method are studied in this paper. With its rigorous mathematical derivation, the VAS method could be an improved version of Lighthill’s acoustic analogy method (referred to here as the ILAA method). The ILAA method contains a new monopole acoustic source due to the time derivative of the incompressible pressure and a modified quadrupole acoustic source due to the increment in momentum flux and viscous stress from the compressible/incompressible flow. Based on the incompressible Navier–Stokes equations, the VAS method is also considered as an ILAA method in which the quadrupole acoustic source is due to the compressible momentum flux, compressible viscous stress and the incompressible pressure. A source decomposition method is proposed by which the sound waves are sorted by the source terms. We analyze the effects of each source in the VAS method and propose an improved VAS (IVAS) method by distinguishing between an unstable source and acoustic radiation sources. Using the IVAS method suppresses the pseudo-sound waves that are excited by the additional unstable source that is generated by the waves spreading in a non-uniform velocity field, and the radiating quadrupole source in the ILAA method (VAS method) is retained to the utmost extent.

Solitary waves in a long structure of charged particles confined in the linear Paul trap

This paper demonstrates the possibility of generation of density waves in the form of individual humps in a long structure of the one-component Coulomb system of dust particles confined in the linear Paul traps in air under normal conditions Our numerical simulations by particle-in-cell method support this possibility. Physical possibility of analogous the hump density waves (caustics) is discussed by V.I. Arnold in his book ‘Catastrophe Theory’ and is caused by the nonuniform velocity distribution of dust particles.

Mixing layer instability and vorticity amplification in a creeping viscoelastic flow

We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at $Re\ll1$ and $Wi\gg1$. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatio-temporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with $Wi$, and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e. $Wi\gg1$ and $Re\ll1$, and oppose the current view of suppression of vorticity solely by polymer additives.

Nonequilibrium phases and segregation for skyrmions on periodic pinning arrays

Using particle-based simulations, we examine the collective dynamics of skyrmions interacting with periodic pinning arrays, focusing on the impact of the Magnus force on the sliding phases. As a function of increasing pinning strength, we find a series of distinct dynamical phases, including an interstitial flow phase, a moving disordered state, a moving crystal, and a segregated cluster state. The transitions between these states produce signatures in the skyrmion lattice structure, the skyrmion Hall angle, the velocity fluctuation distributions, and the velocity-force curves. The moving clustered state is similar to the segregated state recently observed in continuum-based simulations with strong quenched disorder. The segregation arises from the drive dependence of the skyrmion Hall angle, and appears in the strong pinning limit when the skyrmions have nonuniform velocities, causing different portions of the sample to have different effective skyrmion Hall angles. We map the evolution of the dynamic phases as a function of the system density, the ratio of the Magnus force to the dissipative term, and the ratio of the number of skyrmions to the number of pinning sites.

Energy efficient design of high depth raceway pond using computational fluid dynamics

Abstract Open Raceway Ponds (RWP) are at present the most used large-scale reactors for microalgae culture. RWPs are extensively applied technology for algae mass cultivation although the scientific design of these ponds remains a major hurdle in this field. An erroneous design result in the presence of dead zones where the fluid flow is sluggish and non-uniform velocity throughout the pond actualized negative impact on algae growth, further these designs are energy inefficient. A dominant component of energy loss is the energy required to circulate the fluid around the raceway, particularly at the 180° bends. This paper investigates effects of various ratio of channel length to width (L/W) and position of side entry axial flow impeller (distance from the bottom of the tank) on the hydrodynamics in RWP. To curtail the dead zone, power consumption, shear stress and enhance surface renewal, the different designs of RWPs with flow deflectors and different types of central baffles were investigated by using Computational Fluid Dynamics (CFD). The CFD model was validated through Particle Image Velocimetry (PIV) tests. A feasible move headed for energy optimization and thus reduction in operational cost can be established through a better understanding of the mixing phenomena by CFD simulations.

Experimental validation of analytical wake and downstream turbine performance modelling

Wake effects in wind farms can cause significant power losses. In order to reduce these losses layout and control optimization can be applied. For this purpose, simple and fast prediction tools for the wake flow are needed. In the first part of this work, five analytical wind turbine wake models are compared to small-scale turbine wind tunnel measurements. The measurements are conducted at several downstream distances, varying the ambient turbulence intensity and upstream turbine blade pitch angle. Furthermore, an adjustment of a recently developed wake model is proposed. Subsequently, the adjusted model is found to perform best throughout all test cases. In the second part, the performance of an aligned downstream turbine is modelled based on the predicted wake flow using a Blade Element Momentum method with guaranteed convergence. In order to consider the non-uniform inflow velocity a mean-blade-element-velocity method is developed. Moreover, a blockage effect correction is applied. A comparison to wind tunnel measurement data shows that the wake velocity as well as the combined power of two aligned turbines are fairly well predicted. Additionally, the presented analytical framework of wake and downstream turbine performance modelling proposes several model improvements for state-of-the art wind farm simulation tools.