Vortex Axis Research Articles

Analytic solution of in-plane vortex\u2013rotor interactions with arbitrary orientation and its impact on rotor trim

The general aerodynamic problem of arbitrarily oriented in-plane vortex-rotor interaction was investigated in the past only by numerical simulation. Just one special case of in-plane vortex-rotor interaction with the vortex axis in flight direction was recently solved analytically. In this article, the analytical solution for arbitrary in-plane vortex orientation and position relative to the rotor is given for the first time. The solution of the integrals involved as derived here encompasses and simplifies the previous derivation of the special case significantly. Results provide the vortex impact on rotor trim (thrust, aerodynamic rolling and pitching moments about the hub) and the rotor controls required to mitigate these disturbances. For the special case with the vortex axis in flight direction, the results are identical to the former solution and results for the other in-plane vortex orientations and positions agree with the numerical results obtained so far.

Three tailorable optical vortices generated by a modified fractal spiral forked plate

A modified fractal spiral forked plate (MFSFP) is proposed to generate three tailorable coplanar optical vortices at multiple focal planes, which consist of two off-axis vortices and one axial vortex. The axial vortex and one low-intensity off-axis vortex can have equal intensity by designing an appropriate spiral-like filter. In addition, the MFSFP has self-similar axial and off-axis optical vortices. Moreover, the tailorable topological charges of two off-axis vortices are related to those of the fractal spiral zone plate (FSZP) and forked grating and the topological charge of the axial vortex is equal to that of the FSZP. In the experiments, based on the interferometric measurement method, the differences between fingers of forked fingers are used to prove the above topological charge transformation rule. The method of constructing the MFSFP is illustrated. The MFSFP is applicable to rotate particles at multiple positions of the different planes simultaneously, increase optical communication capacities and produce multiple images simultaneously.

Modelling of damage of a liquid-core microcapsule in simple shear flow until rupture.

Capsules, composed of a liquid core protected by a thin deformable membrane, offer high-potential applications in many fields of industry such as bioengineering. One of their limitations comes from the absence of models of capsule damage and/or rupture when they are subjected to an external flow. To assess when rupture is initiated, we develop a fluid-structure interaction (FSI) numerical model of a capsule in Stokes flow that accounts for potential damage of the capsule membrane. We consider the framework of Continuum Damage Mechanics and model the membrane with an isotropic brittle damage model, in which the membrane damage state depends on the history of loading. The FSI problem is solved by coupling the finite element method, to solve for the membrane deformation, with the boundary integral method, to solve for the inner and outer fluid flows. The model is applied to an initially spherical capsule subjected to a simple shear flow. Damage initiates at a critical value of the capillary number, ratio of the fluid viscous forces to the membrane elastic forces, and rupture at a higher capillary number, when it reaches a threshold value. The material parameters introduced in the damage model do not influence the mode of damage but only the values of the critical and threshold capillary numbers. When the capillary number is larger than the critical value, damage develops in the two symmetric central regions containing the vorticity axis. It is indeed in these regions that the internal tensions are the highest on the membrane.

Investigation of the Matching Relation Between Impeller and Flow Channel of Regenerative Flow Pumps

Abstract As a specific radial flow pump, the regenerative flow pump (RFP) usually has a low efficiency. In this study, in order to explore the matching mechanism, three cases with various matching relations were investigated by the methods of theoretical calculation, computational fluids dynamics (CFD) simulation, and experiment test. The results illustrate that the theoretical prediction, numerical simulation, and experimental data are in good agreement. Furthermore, when the matching relation expressed by a ratio of the channel's and blade's radial length is equal to 1, the geometrical profiles of RFP can well guide the circulation flow into the channel at large radii and into the impeller at small radii, forming intense longitudinal vortex. The steady, strong exchange flow is characterized by the inflow and outflow regions approximately half of the isosurface. The axial vortex motion without apparent flow separation and irregular flow is observed in the impeller, a low velocity annulus exists in the medium radii of the impeller without other distinct velocity clouds, and a low velocity strip and a high velocity annulus in the channel are, respectively, performed along the blade's pressure surface and the channel's outer radii. All of this corresponds to the best pump's performance and the largest efficiency of the impeller and channel. This work promotes a systematical understanding of the matching mechanism between impeller and flow channel in the RFP and could provide some reference for the design and performance optimization for RFP.

Large-scale clustering of light small particles in developed turbulence

Small solid particles, droplets, and bubbles can form clusters in turbulent flows by the action of coherent vortices. This phenomenon, sometimes called the preferential concentration, was often thought to be most conspicuous when the velocity relaxation time τp of particles is comparable with the Kolmogorov time τη. However, since high-Reynolds number turbulence consists of coherent eddies with different timescales, particles can form clusters even when τp≫τη. We demonstrate, by direct numerical simulations, that light particles with different τp values form clusters around axes of coherent vortices with different sizes in developed turbulence.

Density and surface tension effects on vortex stability. Part 2. Moore–Saffman–Tsai–Widnall instability

Abstract

A Multiscale Numerical Modeling Investigation on the Significance of Flow Partitioning for the Development of Quartz c‐Axis Fabrics

AbstractQuartz c‐axis fabrics in natural mylonites can vary to such an extent that they apparently give opposite senses of shear in a single thin section. Many hypotheses have been invoked to explain this. Here, we couple our self‐consistent multiscale approach for flow partitioning with the viscoplastic self‐consistent model for c‐axis fabric simulation to investigate quartz c‐axis fabric development. Quartz aggregates are regarded as microscale Eshelby inhomogeneities embedded in a macroscale medium whose effective rheology is represented by a hypothetical homogeneous equivalent medium which is assumed to be rheologically isotropic or has a planar anisotropy. We reproduced the observed quartz c‐axis fabrics. We found that although the microscale flow fields are distinct from one another and from the macroscale flow, the microscale vorticity in every inhomogeneity has the same sense as the macroscale vorticity. This implies that one can use the average of the microscale vorticity axes determined through the crystallographic vorticity axis analysis to obtain the macroscale vorticity axis. However, quartz c‐axis fabrics cannot be used to determine the vorticity number where flow partitioning is significant.

Non-equilibrium behavior of large-scale axial vortex cores

A logical basis for incorporating pressure non-equilibrium and turbulent eddy viscosity in an incompressible vortex model is presented. The infrasonic acoustic source implied in our earlier work has been examined. Finally, this non-equilibrium turbulent vortex core is shown to dissipate mechanical energy more slowly than a Burgers vortex, helping us to explain the persistence of axial vortices in nature. Recent molecular dynamics simulations replicate aspects of this non-equilibrium pressure behavior.

Investigation of the Time Resolution Set Up Used to Compute the Full Load Vortex Rope in a Francis Turbine

The flow in a Francis turbine at full load is characterised by the development of an axial vortex rope in the draft tube. The vortex rope often promotes cavitation if the turbine is operated at a sufficiently low Thoma number. Furthermore, the vortex rope can evolve from a stable to an unstable behaviour. For CFD, such a flow is a challenge since it requires solving an unsteady cavitating flow including rotor/stator interfaces. Usually, the numerical investigations focus on the cavitation model or the turbulence model. In the present works, attention is paid to the strategy used for the time integration. The vortex rope considered is an unstable cavitating one that develops downstream the runner. The vortex rope shows a periodic behaviour characterized by the development of the vortex rope followed by a strong collapse leading to the shedding of bubbles from the runner area. Three unsteady RANS simulations are performed using the ANSYS CFX 17.2 software. The turbulence and cavitation models are, respectively, the SST and Zwart models. Regarding the time integration, a second order backward scheme is used excepted for the transport equation for the liquid volume fraction, for which a first order backward scheme is used. The simulations differ by the time step and the number of internal loops per time step. One simulation is carried out with a time step equal to one degree of revolution per time step and five internal loops. A second simulation used the same time step but 15 internal loops. The third simulations used three internal loops and an adaptive time step computed based on a maximum CFL lower than 2. The results show an influence of the time integration strategy on the cavitation volume time history both in the runner and in the draft tube with a risk of divergence of the solution if a standard set up is used.

Vortex impingement onto an axisymmetric obstacle – subcritical bifurcation to vortex breakdown

Abstract

The Dynamic Modelling of Vortex Axis Blade between Speed? Force and Rotation under Variable Angle & Power in Helicopter

The Dynamic Modelling of Vortex Axis Blade between Speed? Force and Rotation under Variable Angle & Power in Helicopter

Angular momentum of radiation from a charge drifting along a cylindrical channel in a magnetic field

The angular momentum of radiation related to the passage of relativistic particles in a cylindrical channel is studied theoretically. To enhance the angular momentum of radiation, it is proposed to place the channel in a strong magnetic field parallel to the channel axis. The trajectories of the particles in the channel, the conditions for trapping particles in the channeling mode are investigated and equations for calculating the orbital angular momentum of radiation are obtained. It is shown that the angular momentum of radiation of a uniform beam of particles in the channel is not equal to zero only if the particles enter the channel at an angle greater than the critical angle. A significant difference between vortex radiation from a bunch of cylindrical channels (for example bunch of carbon nanotubes) from laser or undulator radiation is that the radiation beam of the latter has only one vortex axis. While the radiation from the beam of cylindrical channels has one vortex axis per each channel. Dependence of the angular momentum of radiation on the value of magnetic field and on the incident angle is studied.

Near-field spray characterization of a spill return atomizer using a PIV laser sheet

The Combustion of liquid fuels is largely dependent on effective ways of atomization. The investigation of flow dynamics and atomization of alternative fuels is essential and supportive for combustion assessment. The current experimental investigation aims at providing a microscopic insight into the spray characteristics of the conventional (light diesel oil) fuel, a renewable fuel (waste cooking oil), and their blend together. A PIV laser measuring technique is used to provide detailed information on the fuel spray: droplets size, pattern, evaporation rate, instantaneous velocity, local cone angle, average axial velocity, penetration, and vorticity. The experiments cover four air to liquid ratios (ALR) of 0.8, 0.78, 0.65, and 0.57. A coaxial spill return atomizer is employed downwards as well as is surrounded by co-flowing air (kg/hr) of 48, 52.2, 55.8, and 60. The spray images are taken in an open atmosphere and the assessment of the fuel droplets velocity and size is obtained through PIV cross-correlation inside a glass room. The maximum evaporation rate is 48.1% for diesel fuel, 37% for waste cooking oil, and 44% for blended fuel at an ALR of 0.57. The application of co-flowing air (kg/hr) of 48 will reduce the local cone angle by 17%, 6%, and 4.3%. The interaction between waste cooking oil droplets with surrounding air is very difficult because of its high viscosity, density, lower evaporation rate, and larger droplets size than diesel fuel.

Influence of aspect ratio on vortex formation in X-junctions: Direct numerical simulations and eigenmode decomposition

We study numerically the appearance and number of axial vortices in the outlets of X-shaped junctions of two perpendicular channels of rectangular sections with facing inlets. We explore the effect of the aspect ratio of the cross section, AR, on the number of vortices created at the center of the junction. Direct numerical simulations (DNSs) performed for different values of the Reynolds number Re and AR demonstrate that vortices with their axis parallel to the outlets, referred to as axial vortices, appear above critical Reynolds numbers Rec. As AR increases from 1 to 11, the number of vortices observed increases from 1 to 4, independently of Re. For AR = 1, the single axial vortex induces an interpenetration of the inlet fluids in the whole section; instead, for larger AR’s for which more vortices appear, the two inlet fluids remain largely segregated in bands, except close to the vortices. The linear stability analysis demonstrates that only one leading eigenmode is unstable for a given set of values of AR and Re. This mode provides a simplified model of the flow field, reproducing its key features such as the number of vortices and their distance. Its determination with this method requires a much smaller computational load than the DNS. This approach is shown to allow one to determine quickly and precisely the critical Reynolds number Rec and the sensitivity function S, which characterizes the influence of variations of the base flow on the unstable one.

Experimental study of coolant flow mixing processes in a pressure chamber model of nuclear reactor

The paper presents results of experimental research, the purpose of which was to simulate the phenomenon of mixing of loop coolant flows inside the model of the pressure chamber of the water-cooled reactor. The study was conducted at the high-pressure aerodynamic test bench of NNSTU n.a. R.E. Alekseev. The scale model consisted of elements characteristic of water-cooled nuclear reactors (lowering annular channel, lower pressure chamber). Experimental studies were carried out in the range of Reynolds numbers from 20,000 to 50,000. The axial velocity field was studied at the entrance to the reactor core simulator, using a pneumometric research probe. The temperature field was simulated using the impurity diffusion method by introducing a contrast tracer into one of the loops of the model. Propane was used as a passive tracer. Tracer concentration at the inlet core simulator allowed to evaluate the degree of flow mixing and thereby studied the direction of coolant flow. As a result of the studies, the spatial distribution of the tracer concentration in the coolant flow in the lower annular channel, as well as in the lower pressure chamber, was determined. It was shown that in the lower pressure chamber, an axial central vortex influences the mixing intensity. The estimation of the parameters of mixing of the passive tracer in the model of reactor pressure was given.

Newtonian and Non-Newtonian Blood Rheology Inside a Model of Stenosis

In order to imitate the atherosclerosis artery disease and determine the key issues, Computational Fluid Dynamics (CFD) is able to play a leading rule in the analysis of flow physics within the clogged arteries, in particular the stenosis artery. The problem of blood flow blockage through the blood vessel has been investigated numerically within a stenosis artery. In this work, a CFD technique was employed to solve the three-dimensional, steady, laminar and non-Newtonian Carreau model blood flow through a stenosis artery using Star-CCM+ software. The shape of stenosis that has been selected is a trapezoidal with two cases (70% and 90% blockage). Shear rate, streamlines, vorticity and importance factor are examined to assess the influence of non-Newtonian model through the test section, the Carreau model was compared with Newtonian model. The clinical significance of the shear rate is reported for the examined cases, observing that the levels of non-Newtonian model are predicted to be higher in the 90% blockage than that observed within the 70%; the same finding as related with the axial velocity and vorticity. The levels of re-circulation areas and vorticity are showed to be enlarged in the Carreau model compared with the case of Newtonian.

Heat transfer scaling in natural convection with shear due to rotation

Axial vortices are ubiquitous in nature and in engineering, and the breakdown of these vortices can have far-reaching consequences. In the presence of a temperature gradient, topological behavior dramatically changes depending on the various flow parameters. Quantities such as heat transport, scalar mixing, and turbulent correlations are influenced immensely by the interplay between rotation and convection.

Numerical Analysis for the Assessment of Factors Influencing the Breakdown of Swirl Flow in a Cylinder Driven by a Rotating End Wall

Abstract Finite element solution for the classical problem of swirl flow in a cylinder with a rotating lid has been used to study the characteristic features of the stream-tube and identify the factors contributing to axial vortex breakdown. An increase of rotational Reynolds number has been found to result in (i) a decrease of total flow rate; (ii) an increase of flow rate through the boundary layer over the stationary walls; (iii) an increase of the throat area of the stream-tube, with the upstream axial vortex flow in some cases having a deficit in momentum flux needed to overcome the pressure and viscous forces; and (iv) an increase of distance for the axial flow to sustain deceleration in the diverging passage. Based on the analysis, it is hypothesized that “flow with particles in axial vortex motion having a deficit of momentum flux for axial flow when subjecting to a fluctuating radial force undergoes axial vortex breakdown.” This explanation has been able to justify the disappearance of vortex breakdown at larger Re of laminar regime and the absence of vortex breakdown in small aspect ratio cylinders. We report novel results pertaining to total flow rate and its distribution within the vessel. The momentum flux of axial vortex, a main determinant of bubble breakdown, is found to be governed by the total flow rate, distribution of flow through the boundary layers, and the Reynolds number. The proposed hypothesis has been verified by analyzing two cases, one involving a passive and the other involving an active mechanism for regulating the axial momentum.

Extrusion kinematics of UHP terrane in a collisional orogen: EBSD and microstructure-based approach from the Tso Morari Crystallines (Ladakh Himalaya)

Several extrusion mechanisms have been proposed to explain the occurrences of ultra-high pressure (UHP) rocks at collisional margins. Here we assess the suitability of the channel flow model of extrusion for the Tso Morari Crystallines (TMC) by investigating the syn-extrusion deformation kinematics of the UHP eclogite-bearing gneiss that dominates the TMC. Samples collected from the two transects viz. Sumdo-Karzok and Sumdo-Debring, have been examined. The channel flow model predicts high simple shear component at the channel margins during extrusion. Gneisses near the upper margin of the subduction channel – also the northern margin of the TMC on map – support this claim and exhibit closely spaced shear planes, and elevated fluid activity as revealed by X-ray diffraction results. Quartz grain parameters e.g. Feret diameter, aspect ratio, and vector mean strength measured from oriented thin-sections of the gneiss do not exhibit distinct pattern of variation of deformation intensity across the TMC. EBSD-based low-angle intragranular 'neighbor to neighbor' misorientation analysis and micro-textural evidences of incipient partial melting in the gneiss reflect temperatures >600 °C. We propose that return flow and buoyancy of the subducted continental crust triggered the extrusion, which was then facilitated by the Indo-Eurasia collision. The mechanism could thus be a combination of both channel flow and ductile wedge extrusion. Continued convergence possibly promoted non-planar triclinic transpression – also evident from the crystallographic vorticity axis (CVA) analysis – such that the extrusion direction varied spatially, producing the diverse shear senses observed at both meso- and micro-scales.

Numerical Simulation of Axial Vortex in a Centrifugal Pump as Turbine with S-Blade Impeller

Pump as turbines (PATs) are widely applied for recovering the dissipated energy of high-pressure fluids in several hydraulic energy resources. When a centrifugal pump operates as turbine, the large axial vortex occurs usually within the impeller flow passages. In view of the structure and evolution of the vortex, and its effect on pressure fluctuation and energy conversion of the machine, a PAT with specific-speed 9.1 was analyzed based on detached eddy simulation (DES), and the results showed that vortices generated at the impeller inlet region, and the size and position of detected vortices, were fixed as the impeller rotated. However, the swirling strength of vortex cores changed periodically with double rotational frequency. The influence of vortices on pressure fluctuation of PAT was relatively obvious, deteriorating the operating stability of the machine evidently. In addition, the power loss near impeller inlet region was obviously heavy as the impact of large axial vortices, which was much more serious in low flow rate conditions. The results are helpful to realize the flow field of PAT and are instructive for blade optimization design.