Three-dimensional Vortex Flow Research Articles

Theoretical study of the influence of gas phase turbulent disturbances on the kinetics of ultrasonic coagulation of PM2.5

A numerical model of ultrasonic coagulation of PM2.5 aerosol particles in three-dimensional vortex and turbulent acoustic flows is proposed in the article. The model is intended to identify the possibility of increasing the efficiency of the process. A numerical analysis of the model using the example of PM2.5 aerosol made it possible to establish that the presence of three-dimensional turbulent disturbances leads to the fact that the coagulation efficiency of PM2.5 reaches almost 100% at a sound pressure level of no more than 165 dB.

Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models.

A lifting relation connecting the distribution function explicitly with the hydrodynamic variables is necessary for the Boltzmann equation-based mesoscopic approaches in order to correctly initialize a nonuniform hydrodynamic flow. We derive two lifting relations for Guo etal.'s total-energy double-distribution-function (DDF) kinetic model [Z. L. Guo etal., Phys. Rev. E 75, 036704 (2007)1539-375510.1103/PhysRevE.75.036704], one from the Hermite expansion of the conserved and nonconserved moments, and the second from the O(τ) Chapman-Enskog (CE) approximation of the Maxwellian exponential equilibrium. While both forms are consistent to the compressible Navier-Stokes-Fourier system theoretically, we stress that the latter may introduce numerical oscillations under the recently optimized discrete velocity models [Y. M. Qi etal., Phys. Fluids 34, 116101 (2022)10.1063/5.0120490], namely a 27 discrete velocity model of the seventh-order Gauss-Hermite quadrature (GHQ) accuracy (D3V27A7) for the velocity field combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5) for the total energy. It is shown that the Hermite-expansion-based lifting relation can be alternatively derived from the latter approach using the truncated Hermite-polynomial equilibrium. Additionally, a relationship between the order of CE expansions and the truncated order of Hermite equilibria is developed to determine the minimal order of a Hermite equilibria required to recover any multiple-timescale macroscopic system. Next, three-dimensional compressible Taylor-Green vortex flows with different initial conditions and Ma numbers are simulated to demonstrate the effectiveness and potential issues of these lifting relations. The Hermite-expansion-based lifting relation works well in all cases, while the Chapman-Enskog-expansion-based lifting relation may produce numerical oscillations and a theoretical model is developed to predict such oscillations. Furthermore, the corresponding lifting relations for Qi etal.'s total energy DDF model [Y. M. Qi etal., Phys. Fluids 34, 116101 (2022)10.1063/5.0120490] are derived, and additional simulations are performed to illustrate the generality of our approach.

An incompressible flow solver on a GPU/CPU heterogeneous architecture parallel computing platform

A computational fluid dynamics (CFD) solver for a GPU/CPU heterogeneous architecture parallel computing platform is developed to simulate incompressible flows on billion-level grid points. To solve the Poisson equation, the conjugate gradient method is used as a basic solver, and a Chebyshev method in combination with a Jacobi sub-preconditioner is used as a preconditioner. The developed CFD solver shows good performance on parallel efficiency, which exceeds 90% in the weak-scalability test when the number of grid points allocated to each GPU card is greater than 2083. In the acceleration test, it is found that running a simulation with 10403 grid points on 125 GPU cards accelerates by 203.6x over the same number of CPU cores. The developed solver is then tested in the context of a two-dimensional lid-driven cavity flow and three-dimensional Taylor-Green vortex flow. The results are consistent with previous results in the literature.

Three-Dimensional Vortex Flow in a Closed Volume and Some Anomalous Phenomena in the Earth’s Atmosphere

Three-Dimensional Vortex Flow in a Closed Volume and Some Anomalous Phenomena in the Earth’s Atmosphere

Magnetic fluid flow and heat transfer due to a uniform source and vorticity

Abstract The present work investigates the ferrohydrodynamic flow and heat transfer due to a uniform source and irrotational vortex under the influence of a stationary magnetic field. A uniform source generates only a two-dimensional flow. However, in the presence of the vorticity with a uniform source, the flow becomes three-dimensional. The governing equations are expressed as a system of nonlinear coupled differential equations. The transformed differential equations are solved using the finite element approach for both the two-dimensional and three-dimensional flow models. With variations in the strength of the source parameter, Reynolds number, and ferromagnetic interaction numbers, the behavior of two-dimensional and three-dimensional flow is investigated. In three-dimensional flow, the influence of swirling effects on the velocity and temperature profiles are weak as compared to two-dimensional flow. The main role of the three-dimensional vortex flow of ferrofluid is to generate rotational viscosity, and it is not possible in the case of two-dimensional flow case.

Vortex structures around two colliding spheres at high Reynolds number

This study incorporates a hybrid Cartesian/immersed boundary (HCIB) method and the Navier-Stokes equations to simulate three-dimensional vortex flows around spheres swinging and colliding in viscous fluids. The motions of the spheres were prescribed in the model, and the simulated velocities around the spheres were validated by the results of laboratory experiments. The Reynolds number computed by the sphere diameter and the maximum swing velocity was Re = 13,500. The simulation results were examined in detail to elucidate the three-dimensional flows and pressure fields induced by the single swinging sphere and two colliding spheres. The evolution of the vortices can be divided into two parts: (i) Before the collision, the primary vortex ring induced by the swinging sphere grows in size, propagates obliquely downward, and eventually dissipates into turbulent flow. (ii) After the collision, the striking sphere transfers its momentum to the target sphere and another vortex ring is generated in front of the striking sphere owing to its impulsive deceleration. This vortex ring is separated from the sphere's boundary and the vorticity pattern is different from that of a single sphere case. After the collision, the target sphere up-swings with almost no vortical wake behind it, as observed in the experiments.

Aerodynamics of a half-rotating wing in hovering flight: An integrated study

This study introduces a new quasi-flapping wing driving mechanism based on a half-rotating mechanism which is capable of pure rotational flapping rather than the more traditional oscillatory flapping method. Lift models for half-rotating wing (HRW) aircraft in hovering flight are proposed based on the kinematics of a HRW prototype and the flow characteristics near the surface of its wing. Alongside further analytical expressions for lift based on kinematic extractions, computational models and a novel lift validation mechanism are used to reinforce the aerodynamic characteristics of the HRW in hovering flight. The aerodynamics of the HRW are experimentally assessed for different wing layouts and wing materials. Results indicate that the flow field generated by the motion of the wing arranged symmetrically on both sides of the body interfere with each other, causing the average lift coefficient of the paired-wing HRW to be less than that of the single-wing HRW. The average lift coefficient of the flexible wing is larger than that of the rigid wing. In addition, the average lift of the flexible wing increases with increasing flexural compliance within a particular range. Lift forces in different flight conditions are calculated using derived formulas alongside representative computational models, through which the derivation of lift variation for the HRW in hovering flight is validated. The theoretical lift curves show reasonable agreement with numerical simulation results in terms of the time course over one stroke cycle. The mechanisms of the HRW for generation and shedding of vortices in hovering flight are further revealed in computed flow field characteristics results. The velocity vectors of the flow field between the HRW and the symmetrically rotating wing indicate that the HRW with asymmetric rotation can generate lift force effectively. The velocity difference between the wing and the fluid is the key factor influencing the structure of generated vortices. In detailed three-dimensional (3D) vortex flows, our computational fluid dynamics study shows that a horseshoe-shaped vortex is first generated in the early downstroke. The horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring, with a jet stream appearing in its core which forms the downwash. The doughnut-shaped vortex ring eventually elongates into a long arc-shaped wake vortex ring. A large increasing lift force is generated during the upstroke, most likely due to the stable distal attached vortices; and in accordance with this, downwash becomes evident in the vortex ring during the downstroke.

Using the Maximum Pressure Principle for Verification of Calculation of Stationary Subsonic Flow

The principle of maximum pressure for subsonic stationary three-dimensional vortex flows of an ideal gas (author Sizykh G.B., 2018) is applied to verify the calculation method and its implementation on a specific computer technology. The four criteria for solution's verification are proposed. The method for obtaining flow parameters is based on solving of discrete analogs of the Navier --- Stokes system of equations on three-dimensional non-structured computational meshes. For example, there was consider the vortex tear-off flow around the fuselage of a helicopter with an empennage and landing gear at obviously insufficient computing resources. Conclusions of the feasibility of applying the author's criteria for evaluation of a particular calculation and for estimation of reliability of the results have been made.

Vorticity dynamics of the three-dimensional Taylor-Green vortex problem

The three-dimensional (3D) Taylor-Green Vortex (TGV) flow problem has been used to study turbulence from genesis to eventual decay governed by the 3D Navier-Stokes equation. The evolution of the TGV shows that the solution becomes unstable at very early times and eventually becomes turbulent, but a study of this transition has not been advanced so far. The computations are performed using a high accuracy compact scheme on a uniform grid, with the fourth-order Runge-Kutta time integration method. The vector potential-vorticity (Ψ→,ω→)-formulation of the governing equations is solved in a cubic periodic domain with one complete basic unit of a TGV cell in the interior of the domain at t = 0. The TGV problem allows one to study the vorticity dynamics using highly accurate formulation because of periodic boundary conditions. Simulations performed for different Reynolds numbers and grid resolutions reveal that numerical error in computations induce a period-doubling bifurcation, which leads to new spatial symmetries maintained up to intermediate times, followed by simultaneous stretching and fragmentation of vortices resulting in a decaying turbulent flow. The compensated energy spectrum of the 3D TGV flow displays inertial subrange at t = 9, after which the generated turbulence starts decaying. The power law for turbulent kinetic energy decay is analyzed, and the decay exponent is noted to approach unity as time increases.

An error indicator for finite difference methods using spectral techniques with application to aerofoil simulation

This work introduces a new error indicator which can be used to determine areas of insufficient numerical resolution in unfiltered finite difference simulations. The background behind the methodology is that smaller scales (i.e. the flow features with higher wave numbers) are physically characterised by a smaller energy content in comparison with larger scales. This energy should decrease with increasing wavenumber at a minimum rate; if this rate is not attained it likely means that the smaller scales are not being properly resolved on the computational grid of solution points. An approach using spectral techniques is used to formulate two varieties of the error indicator – one integer-valued and one floating point-valued. These values are computed at a finite number of ‘blocks’ which span the domain. The indicator is implemented within the OpenSBLI finite difference-based modelling framework, and evaluated in the context of a three-dimensional Taylor-Green vortex problem and flow past a V2C laminar flow aerofoil.

Three-Dimensional Simulation of Air Entrainment in a Sump Pump

AbstractThe three-dimensional unsteady vortex flow in a sump pump is investigated by the computational fluid dynamics (CFD) method with the shear-stress transport (SST) k−ω model and the volume of ...

Three-dimensional shock wave diffraction off a discontinuous edge

The interaction of three-dimensional vortex flows was investigated through vortex shedding off a discontinuous edge. Two wedges of $$14.5^\circ $$ wedge angle (up and downstream edges) were separated by an offset. The size of the offset (5, 10, and 20 mm) and the Mach number (Mach 1.32, 1.42, and 1.6) were the key parameters investigated. Experimental images were taken and computational simulations were run; a close relation was found between the two. This enabled the three-dimensional effects of the flow to be studied and analysed. It was found, as the offset increased in size, the vortices shed off the up and downstream edges took a longer time to merge and the strength of the interaction was weaker. The vortex topology changed with a larger offset; the downstream vortex was thinner (in terms of cross-sectional diameter) adjacent to the offset, which is an indication of a change in density, than the rest of the vortex along the downstream diffraction edge. This particular feature was more prevalent at lower Mach numbers. The effect of a higher Mach number was to increase the rate of dissipation of the vortices, lengthen the shear layer due to the higher upstream velocity, and make the vortex profile elliptical.

Tonal noise production from a wall-mounted finite airfoil

This study is concerned with the flow-induced noise of a smooth wall-mounted finite airfoil with flat ended tip and natural boundary layer transition. Far-field noise measurements have been taken at a single observer location and with a microphone array in the Virginia Tech Stability Wind Tunnel for a wall-mounted finite airfoil with aspect ratios of L/C=1–3, at a range of Reynolds numbers (ReC=7.9×105–1.6×106, based on chord) and geometric angles of attack (α=0–6°). At these Reynolds numbers, the wall-mounted finite airfoil produces a broadband noise contribution with a number of discrete equispaced tones at non-zero angles of attack. Spectral data are also presented for the noise produced due to three-dimensional vortex flow near the airfoil tip and wall junction to show the contributions of these flow features to airfoil noise generation. Tonal noise production is linked to the presence of a transitional flow state to the trailing edge and an accompanying region of mildly separated flow on the pressure surface. The separated flow region and tonal noise source location shift along the airfoil trailing edge towards the free-end region with increasing geometric angle of attack due to the influence of the tip flow field over the airfoil span. Tonal envelopes defining the operating conditions for tonal noise production from a wall-mounted finite airfoil are derived and show that the domain of tonal noise production differs significantly from that of a two-dimensional airfoil. Tonal noise production shifts to lower Reynolds numbers and higher geometric angles of attack as airfoil aspect ratio is reduced.

Three-Dimensional Vortex Flows of Two–Velocity Incompressible Media in the Case of Constant Volume Saturation

Using scalar functions, we describe flows of incompressible viscous two-velocity fluids in the case of the pressure balance and substances of constant volume saturation. We derive a system of differential equations for these scalar functions an illustrate the method by an example. Bibliography: 5 titles. Illustrations: 1 figure.

Shear Stress Variation at Scour Hole of Circular Pier

The causes of local scour are generally categorized into flow condition, structure, and riverbed material. A three-dimensional vortex flow generated with the influence of the structure is the main factors of the flow conditions, and the size of the particles is assumed to be the main factor of the riverbed case. Various studies about pier local scour have been carried out by researchers since the 1960s, and a large number of experimental formulas have been suggested. Difficulties were encountered by these past studies, however, in terms of considering the influence of various riverbed materials and scour changes (floods, etc.) on time, with the condition of maximum scour depth. In the case of Korea, especially, scour influenced by various riverbed materials and the frequency of floods have been determined to be very important factors. Therefore, the ultimate purpose of this study on pier scour is to suggest the scour examination method that could consider various riverbed materials and the frequency of floods. In this study, the periodic changes in local scour based on the differences in the diameters of four types of bed materials, and on the hydraulic condition of the initial scour, were determined and compared with those in former studies. Using the results of the comparison, this study aims to determine the changes in the shear-stress around piers for various bed materials through the effect of time on scour depth (S, Smax), the shear-stress around piers, and the particles’ critical shear stress (τc).

Electrophoretic Motion of a Liquid Droplet in a Cylindrical Pore

Electrophoretic motion of a liquid droplet in a cylindrical pore is investigated theoretically at arbitrary levels of surface potential and double-layer thickness. The effect of double-layer polarization and the droplet viscosity are taken into account. We found, among other things, that the lower the viscosity of the droplet is, the greater the electrophoretic velocity is. On the other hand, an induced electric field opposite to the direction of the droplet motion slows down the droplet movement in general. This is referred to as the polarization effect here, which manifests itself for highly charged droplets. The presence of a nearby cylindrical pore further complicates this polarization effect both hydrodynamically and electrostatically. An intriguing phenomenon is observed when the fluidic channel becomes very narrow: the lowly charged droplet may move faster than the highly charged one. The reason behind it is thoroughly explained here. Moreover, a three-dimensional axisymmetric vortex flow is observ...

Three-dimensional vortex flow near the endwall of a short cylinder in crossflow: Stepped-diameter circular cylinder

The effect of geometry on the flow around a cylinder in crossflow is investigated in this study. Three different stepped-diameter circular cylinders (SDCC s) with varying step heights are used. Extensive flow visualization using the oil-lampblack and smoke-wire techniques and near wake velocity measurements using a hotwire anemometer reveal complex secondary flows on and around the SDCC. Six vortices are observed in the horseshoe vortex system near the cylinder–endwall junction and six additional vortices are found in the step-induced vortex system on the step surface. Based on these experimental results, new secondary flow models are proposed. The step-induced vortices separate from the step surface at both sides and move toward the endwall, washing down the sides of the top/bottom larger diameter cylinders and interact with the separated shear layer and horseshoe vortices. In this process, they modify the near wake flow significantly: they produce an increase in velocity near the endwall region (below the step) and a decrease in velocity near the mid-span region, even altering the oscillatory behavior of the wake.

Unsteady three-dimensional compressible vortex flows generated during shock wave diffraction

The results of an experimental and numerical investigation into the behaviour of the spiral vortex generated by shock wave diffraction over edges yawed to the incident shock wave are presented. Three-dimensional numerical simulations reveal significant distortion and bending of the free vortex in regions near the boundary of the flow domain, so as to meet it at a right angle. The results of numerical simulations were found to mimic the experimentally obtained photographs very well. The numerical results are used to explain the various features of the resultant flow fields, with particular emphasis placed on the behaviour and properties of the spiral vortex, as it evolves with time. The effects of bending on the structure of the vortex are examined. The rate of circulation production for the three-dimensional shock diffraction cases was calculated, and the trends observed correlated with those for the much published two-dimensional diffraction case.

Three-dimensional vortex flow near the endwall of a short cylinder in crossflow: Uniform-diameter circular cylinder

Flow characteristics, around a short uniform-diameter circular cylinder in crossflow, are investigated experimentally. Extensive flow visualization using oil-lampblack and smoke-wire methods have been performed. Near-wake velocity measurements have been performed using a hotwire anemometer. Complex secondary flows are observed on and around the cylinder in crossflow. Multiple vortices are observed in the horseshoe vortex system near the cylinder–endwall junction. Based on this flow visualization and local mass transfer measurement results, a six-vortex secondary flow model has been proposed.

Numerical investigations of vortex flows and vortex suppression schemes in a large pumping-station sump

This work uses a commercial computational fluid dynamics code to predict three-dimensional (3D) vortex flows in a large centrifugal-pump station under construction in China and proposes relevant vortex-eliminating schemes. Because of the complex nature of the vortex flows in sumps, different turbulence models, namely, standard k–ε, re-normalization group k–ε and realizable k–ε models, are first used to investigate their feasibility in predicting flows in a small physical model of an open pump sump, and various vortex streamlines and strength in the sump are predicted, analysed, and compared with the experimental data. The comparisons show that the realizable k–ε model predicts the position and strength of free-surface, sidewall-attached, and floor-attached vortices more accurately than the other two models. Then, the realizable k–ε model is used here to investigate 3D vortex flows in a large pumping-station sump. All the various vortices, such as free-surface, wall-attached vortices, are successfully predicted. Thus, based on the information of location, shape, size, and strength of the calculated vortices, three types of vortex-eliminating devices are proposed and their corresponding vortex suppression effects are analysed. These results will be used as reference for the safe and stable operation of the Hui–Nan–Zhuang pumping station in the future.