Axisymmetric Fluid Research Articles

Steady Flow Generated by a Core Oscillating in a Rotating Spherical Cavity

Steady flow generated by oscillations of an inner solid core in a fluid-filled rotating spherical cavity is experimentally studied. The core with density less than the fluid density is located near the center of the cavity and is acted upon by a centrifugal force. The gravity field directed perpendicular to the rotation axis leads to a stationary displacement of the core from the rotation axis. As a result, in the frame of reference attached to the cavity, the core performs circular oscillation with frequency equal to the rotation frequency, and its center moves along a circular trajectory in the equatorial plane around the center of the cavity. For the differential rotation of the core to be absent, one of the poles of the core is connected to the nearest pole of the cavity with a torsionally elastic, flexible fishing line. It is found that the oscillation of the core generates axisymmetric azimuthal fluid flow in the cavity which has the form of nested liquid columns rotating with different angular velocities. Comparison with the case of a free oscillating core which performs mean differential rotation suggests the existence of two mechanisms of flow generation (due to the differential rotation of the core in the Ekman layer and due to the oscillation of the core in the oscillating boundary layers).

INVESTIGATING THE USE OF PHASE-CHANGE MATERIALS FOR TEMPERATURE CONTROL DURING FAST FILLING OF HYDROGEN CYLINDERS

This paper explores the use of phase-change materials in the process of fast filling of hydrogen cylinders in order to limit the rise in the gas temperature by enhancing heat transfer from the gas. It is necessary to limit the temperature rise because the structural performance of the cylinder materials can be degraded at higher temperatures. Initially, two computational approaches for modeling the fast filling of hydrogen cylinders are presented and validated; the first is an axisymmetric computational fluid dynamics simulation and the second is a single-zone approach with one-dimensional conjugate heat transfer through the cylinder walls. The models are applied to study fast filling of a hydrogen-powered passenger car. The predictions show that the minimum safe fill time for Type III cylinders with aluminum liners is generally shorter than for Type IV cylinders with plastic liners, for given ambient and precooling temperatures. Alternatively, Type III cylinders require less precooling for a given fill time. Introduction of a phase-change material heat sink is assessed as a means of reducing the fill time for Type IV cylinders. Paraffin-based phase-change materials are considered. The predictions show that the use of pure paraffin wax does not help in reducing the gas temperature due to its low thermal conductivity, however materials with improved thermal conductivity, for example, mixtures of paraffin wax and graphite, can facilitate reduced fill times. Without use of phase-change material it is not possible to reduce the fill time of Type IV cylinders below three minutes unless the gas supply is precooled. While the fill time can be reduced by precooling the gas supply, the phase-change material reduces the degree of precooling required for a given fill time by 10–20 K, and reduces the minimum theoretical power consumption of the cooler by 50–100%, depending on the ambient temperature.

Fluid modeling of radical species generation mechanism in dense methane-air mixture streamer discharge

Atmospheric dielectric barrier discharge (DBD) was found to be promising in the context of plasma chemistry, plasma medicine, and plasma-assisted combustion. In this paper, we present a detailed fluid modeling study of abundant radical species produced by a positive streamer in atmospheric dense methane-air DBD. A two-dimensional axisymmetric fluid model is constructed, in which 82 plasma chemical reactions and 30 different species are considered. Spatial and temporal density distributions of dominant radicals and ions are presented. We lay our emphasis on the effect of varying relative permittivity (εr = 2, 4.5, and 9) on the streamer dynamics in the plasma column, such as electric field behavior, production, and destruction pathways of dominant radical species. We find that higher relative permittivity promotes propagation of electric field and formation of conduction channel in the plasma column. The streamer discharge is sustained by the direct electron-impact ionization of methane molecule. Furthermore, the electron-impact dissociation of methane (e + CH4 = >e + H+CH3) is found to be the dominant reaction pathway to produce CH3 and H radicals. Similarly, the electron-impact dissociations of oxygen (e + O2 = >e + O+O(1D), e + O2 = >e + O+O) are the major routes for O production.

A two-dimensional numerical study of peristaltic contractions in obstructed ureter flows

The flow of urine from the kidneys to the bladder is accomplished via peristaltic contractions in the ureters. The peristalsis of urine through the ureter can sometimes be accompanied, more specifically, obstructed to a certain degree, by entities such as kidney stones. In this paper, 2D axisymmetric computational fluid dynamics simulations are carried out using the commercial code ANSYS FLUENT, to model the peristaltic movement of the ureter with and without stone. The peristaltic movement was assumed to be a sinusoidal wave on the boundary of the ureter with a specific physiological velocity. While the first part of the study considers flow in the ureter with prescribed peristaltic contractions in absence of any obstruction, the second part compares the effect of varying obstructions (0, 5, 15, and 35%) in terms of spherical stones of different sizes. Pressure contours, velocity vectors, and profiles of pressure gradient magnitudes and wall shear stresses are presented along one bolus of the ureter, during contraction and expansion of the ureteral wall, in order to understand backflow, trapping and reflux phenomena, as well as monitor the health of the ureteral wall in the presence of any obstruction. The 35% ureteral obstruction case resulted in a significant backflow at the inlet in comparison to the other cases, and also a wall shear stress that was up to 20x larger than the case without any obstruction.

DETERMINATION OF AVERAGED AXISYMMETRIC FLOW SURFACES AND MERIDIAN STREAMLINES IN THE CENTRIFUGAL PUMP USING NUMERICAL SIMULATION RESULTS

One of the most important aims in the turbo pump design is to achieve an optimal design of the pump impeller. The basic assumption in the design procedure of the impeller is that of the axisymmetric fluid flow. It can be confirmed or disputed by using the method presented in the paper, which uses the results of numerical simulation of fluid flow in the pump impeller. The method is actually a procedure for determining averaged axisymmetric flow surfaces and meridian streamlines. Furthermore, according to the obtained streamlines, a correction of the impeller blade geometry can be made (if the streamlines deviate significantly from the assumed axisymmetric ones). It is also possible to calculate the specific works of the elementary stages and compare them with the previous assumptions. The pump impeller torque can be calculated as well.

Analytical and numerical performance models of a Heisenberg Vortex Tube

Analytical and numerical investigations of a Heisenberg Vortex Tube (HVT) are performed to estimate the cooling potential with cryogenic hydrogen. The Ranque-Hilsch Vortex Tube (RHVT) is a device that tangentially injects a compressed fluid stream into a cylindrical geometry to promote enthalpy streaming and temperature separation between inner and outer flows. The HVT is the result of lining the inside of a RHVT with a hydrogen catalyst. This is the first concept to utilize the endothermic heat of para-orthohydrogen conversion to aid primary cooling. A review of 1st order vortex tube models available in the literature is presented and adapted to accommodate cryogenic hydrogen properties. These first order model predictions are compared with 2-D axisymmetric Computational Fluid Dynamics (CFD) simulations.

A numerical simulation study on active species production in dense methane-air plasma discharge

Recently, low-temperature atmospheric pressure plasmas have been proposed as a potential type of ‘reaction carrier’ for the conversion of methane into value-added chemicals. In this paper, the multi-physics field coupling software of COMSOL is used to simulate the detailed discharge characteristics of atmospheric pressure methane-air plasma. A two-dimensional axisymmetric fluid model is constructed, in which 77 plasma chemical reactions and 32 different species are taken into account. The spatial density distributions of dominant charged ions and reactive radical species, such as H, O, CH3, and CH2, are presented, which is due to plasma chemical reactions of methane/air dissociation (or ionization) and reforming of small fragment radical species. The physicochemical mechanisms of methane dissociation and radical species recombination are also discussed and analyzed.

Earth Reentry Flow over a Phenolic Aeroshell in the X2 Expansion Tube

The effects of phenolic decomposition on shock layer radiation in air were investigated in the X2 expansion tube. By subjecting a carbon phenolic aeroshell to a flow with a velocity of , decomposing resin on the model surface was allowed to react with the boundary-layer gases. Emission spectroscopy was used to measure radiation emitted by the gas in parts of the ultraviolet, visible, and near-infrared spectrum and then compared with control measurements taken with a steel model. With the composite model in place, measured spectral radiance was seen to increase for CN violet band radiation but remained unchanged for atomic emissions in the visible and near-infrared spectrum. Recorded data were then compared with spectra produced by two-dimensional axisymmetric computational fluid dynamics simulations parsed to the NEQAIR radiation solver. Both the applied chemistry models overpredicted CN violet band radiation, but excellent comparison was found for the band. Good comparisons were also achieved for the O triplet (777 nm) and atomic N line intensities, between 740 and 750 nm. However, peak intensities were underestimated by the numerical simulations in the visible spectrum. Background radiation and broadening of the spectral wings were not accurately accounted for by simulations.

Venus Entry Flow over a Decomposing Aeroshell in X2 Expansion Tube

The effects of phenolic decomposition on shock-layer radiation were investigated experimentally in X2 expansion tube for a Venus entry flow. A carbon–phenolic composite aeroshell was subjected to a flow with a flight equivalent velocity of . Emission spectroscopy was used to measure boundary-layer radiation in parts of the ultraviolet (380–480 nm) and visible (620–700 nm) spectrum, and it was compared to control measurements taken with a cold steel model. With the composite model in place, the calibrated spectral radiance measured was seen to increase for the O (645.598 nm) atomic line and the (391.22 nm) band head, but it decreased for the Swan band (420–480 nm). The recorded data were then compared to numerical spectra produced by two-dimensional axisymmetric computational fluid dynamic simulations coupled to a radiation solver. Both of the applied chemistry models overpredicted CN violet band radiation, which demonstrated strong self-absorption at these conditions. Better comparisons were achieved for the Swan band radiation. At visible wavelengths, peak intensities were underestimated by the numerical simulations. Several possible reasons were hypothesized for these discrepancies.

Effects of the wall boundary conditions of a showerhead plasma reactor on the uniformity control of RF plasma deposition

Technical difficulties hinder the formation of uniform deposition profiles near the electrode edge during a deposition in a showerhead capacitively coupled plasma (CCP) reactor. The discharge structure, gas flow, and radial distribution of the source gas outward from the electrode edge are subject to change significantly, which in turn affects the spatial distributions of the radical fluxes toward the electrode. To control the local non-uniformity of deposition profiles in the SiH4/NH3/N2/He CCP discharges for a hydrogenated silicon nitride (SiNxHy) film, the effects of the reactor components―including the sidewall boundary condition, electrode spacing, and showerhead design―were investigated using an axisymmetric fluid model. When the sidewall is electrically grounded, the deposition rate profiles of the SiNxHy film remain consistently convex (in which the deposition rate at the reactor center is locally much higher than that near the electrode edge), regardless of electrode spacing. However, when the sidewall surface is dielectric, the deposition rate profile can be transformed between a convex and a concave shape (in which the deposition rate at the reactor center is locally much lower than that near the electrode edge) by varying electrode spacing. The showerhead design also enables the modification of edge deposition profiles by redistribution of the local depletion rate of radicals. The simulation results agree very well with the experimental measurement.

Simulation of a Bubble Column by Computational Fluid Dynamics and Population Balance Equation Using the Cell Average Method

AbstractAn axisymmetric computational fluid dynamics (CFD) simulation coupled with a population balance equation (PBE) has been applied in simulating the gas‐liquid flow in a bubble column with an in‐house code. The novel feature of this simulation is the application of the cell average method in a CFD‐PBE coupled model for the first time. The predicted results by this method are compared with those by the traditional fixed pivot method and experimental data. For both methods, the simulated results are in reasonable agreement with the reported experimentally measured values. However, the bubble size distributions determined by the cell average method are slightly better than those found by means of the fixed pivot method, i.e., the latter provides a smaller peak value and a wider bubble size distribution, and the probability density function of large bubbles is higher.

On the swirling Trkalian mean flow field in solid rocket motors

In this work, an exact Euler solution is derived under the fundamental contingencies of axisymmetric, steady, rotational, incompressible, single-phase, non-reactive and inviscid fluid, which also stand behind the ubiquitously used mean flow profile named ‘Taylor–Culick.’ In comparison with the latter, which proves to be complex lamellar, the present model is derived in the context of a Trkalian flow field, and hence is capable of generating a non-zero swirl component that increases linearly in the streamwise direction. This enables us to provide an essential mathematical representation that is appropriate for flow configurations where the bulk gaseous motion is driven to swirl. From a procedural standpoint, the new Trkalian solution is deduced directly from the Bragg–Hawthorne equation, which has been repeatedly shown to possess sufficient latitude to reproduce several existing profiles such as Taylor–Culick’s as special cases. Throughout this study, the fundamental properties of the present model are considered and discussed in the light of existing flow approximations. Consistent with the original Taylor–Culick mean flow motion, the Trkalian velocity is seen to exhibit both axial and tangential components that increase linearly with the distance from the headwall, and a radial component that remains axially invariant. Furthermore, the Trkalian model is shown to form a subset of the Beltramian class of solutions for which the velocity and vorticity vectors are not only parallel but also directly proportional. This characteristic feature is interesting, as it stands in sharp contrast to the complex-lamellar nature of the Taylor–Culick motion, where the velocity and vorticity vectors remain orthogonal. By way of verification, a numerical simulation is carried out using a finite-volume solver, thus leading to a favourable agreement between theoretical and numerical predictions.

Well-posedness of a nonstationary axisymmetric hydrodynamic problem with free surface

On assuming that the fluid motion is potential, we prove a local existence and uniqueness theorem for a time-analytic solution in an exact mathematical statement. We obtain a rigorous description of the initial stage of the nonstationary motion of an axisymmetric fluid droplet preceding the moment of evolutionary destruction (blow-up) of the free boundary.

Analytical and numerical study on the fast refill of compressed natural gas with active heat removal

Heavy-duty vehicles powered by compressed natural gas (CNG) store the fuel in large onboard cylinders. Fast fill of depleted CNG cylinders is a common refueling method because it achieves refueling time comparable to liquid fuels. However, under-filling of CNG cylinders occurs during fast fill due to the recompression work of CNG in the cylinder that heats the fuel during the fill. The heated fuel has a lower density at the rated pressure, and thus less mass of CNG can be stored than if it was at ambient temperature. To increase the mass of dispensed CNG during fast fill, an active heat removal method is proposed. In this study, analytical and numerical models of the filling process of CNG into a Type-III cylinder with and without active heat removal are developed. In the analytical study, mass and energy conservation equations are coupled with an ideal-gas equation of state and orifice flow equations to predict the heat generation rates during fast fill. The influence of heat removal via a cooling coil inserted into the cylinder during fill on the dispensed mass and fill time is quantified. The analytical study is compared to numerical simulations employing a two-dimensional axisymmetric computational fluid dynamics (CFD) model for unsteady, compressible turbulent flow in a Type-III cylinder with and without active heat removal. Dynamic average temperature, pressure and mass curves as well as the local temperature distribution in the cylinder are obtained at different time instances during the fill. The effect of the location of the heat removal coils is also investigated. The results of the analytical/numerical study illustrate the benefit of heat removal from the cylinder as a means of improving fast-fill efficiency in natural gas fueled heavy-duty vehicles.

On the compressible bidirectional vortex in a cyclonically driven Trkalian flow field

In this study, the Bragg–Hawthorne equation (BHE) is extended in the context of a steady, inviscid and compressible fluid, thus leading to an assortment of partial differential equations that must be solved simultaneously. A solution is pursued by implementing a Rayleigh–Janzen expansion in the square of the reference Mach number. The corresponding formulation is subsequently used to derive a compressible approximation for the Trkalian model of the bidirectional vortex. The approximate solution is compared to a representative computational fluid dynamics simulation in order to validate the modelling assumptions under realistic conditions. The latter is found to exhibit an appreciable steepening of the axial velocity profile, which is accompanied by an axial dependence in the mantle location that is somewhat reminiscent of the radial shifting of mantles reported in some experimental trials and simulations. In this context, flows with a strong swirl intensity do not seem to be significantly affected by the introduction of compressibility. Rather, as the swirl intensity is reduced the effects of compressibility become more noticeable, especially in the axial and radial velocity components. It may also be realized that imparting a progressively larger swirl component stands to promote the axisymmetric distribution of flow field properties, and these include an implicit resistance to dilatational effects in the tangential direction. From a broader perspective, this study provides a viable approximation to the Trkalian motion associated with cyclonic flows, while serving as a limited proof of concept for the compressible Bragg–Hawthorne procedure applied to a steady, axisymmetric and inviscid fluid.

Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

Relativistic formulation of Helmholtz’s vorticity transport equation is presented on the basis of Maxwell-like version of Euler’s equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg’s theory of spacelike congruence of vortex lines and \(1+1+(2)\) decomposition of the gradient of fluid’s 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid’s angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid’s angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid’s rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.

Counterexamples to Moffatt's statements on vortex knots.

One of the well-known problems of hydrodynamics is studied: the problem of classification of vortex knots for ideal fluid flows. In the literature there are known Moffatt statements that all torus knots K_{m,n} for all rational numbers m/n (0<m/n<∞) are realized as vortex knots for each one of the considered axisymmetric fluid flows. We prove that actually such a uniformity does not exist because it does not correspond to the facts. Namely, we derive a complete classification of all vortex knots realized for the fluid flows studied by Moffatt and demonstrate that the real structure of vortex knots is much more rich because the sets of mutually nonisotopic vortex knots realized for different axisymmetric fluid flows are all different. An exact formula for the limit of the hydrodynamic safety factor q_{h} at a vortex axis is derived for arbitrary axisymmetric fluid equilibria. Another exact formula is obtained for the limit of the magnetohydrodynamics safety factor q at a magnetic axis for the general axisymmetric plasma equilibria.

Hollow cathode modeling: I. A coupled plasma thermal two-dimensional model

A two-dimensional axisymmetric quasi-neutral fluid model of an emissive hollow cathode that includes neutral xenon, single charge ions and electrons has been developed. The gas discharge is coupled with a thermal model of the cathode into a self-consistent generic model applicable to any hollow cathode design. An exhaustive description of the model assumptions and governing equations is given. Boundary conditions for both the gas discharge and thermal model are clearly specified as well. A new emissive sheath model that is valid for any emissive material and in both space charge and thermionic emission limited regimes is introduced. Then, setting the emitter temperature to an experimentally measured profile, we compare simulation results of the plasma model to measurements available in the literature for NASA NSTAR barium oxide cathode. Qualitative discrepancies between simulation results and measurements are noted in the cathode plume regarding the simulated plasma potential. Motivated by experimental evidence supporting the occurrence of ion acoustic instabilities in the cathode plume, an enhanced model of electron transport in the plume is presented and its consequences analyzed. Using the obtained plasma model, simulated quantities in the plume are qualitatively comparable with measurements. Inside the cathode, the simulated plasma density agrees well with measurements and is within the experimental uncertainty associated with these measurements. A comparison of simulation results of the full coupled cathode model for the NASA NSTAR cathode with experimental measurements is presented in a companion paper, as well as a physical analysis of the cathode behavior and a parametric study of the influence of the operating point and key design choices.

The influence of the area ratio on ejector efficiencies in the MED-TVC desalination system

In this paper, an axi-symmetric computational fluid dynamics (CFD) model is used to investigate the effect of the area ratio on ejector component efficiencies. The geometrical parameters and operating conditions are designed for thermal vapor compression (TVC) used in multi-effect distillation (MED) desalination system. By changing the primary nozzle throat diameter and ejector throat diameter, two groups of ejectors are tested under different operating conditions. The results show that the mixing efficiency plays a more important role in ejector performance than other efficiencies such as primary nozzle efficiency, suction efficiency and diffuser efficiency with the changing of the area ratio. The mixing efficiency can be improved as much as 200% by adjusting the area ratio, and the entrainment ratio is increased from 0.025 to 0.8. Finally empirical correlations are summarized to estimate ejector component efficiencies.

Photoacoustic field calculation for nonspherical axisymmetric fluid particles

The photoacoustic (PA) field calculation using a Green's function approach for nonspherical axisymmetric fluid particles is discussed. The PA fields have been computed for spheroidal droplets, Chebyshev particles and normal and pathological red blood cells (RBCs) over a large frequency band (10–1000 MHz). Theoretically constructed RBC contours have been fitted using the Legendre polynomial expansion for parametrization of cell shapes. It is shown that first minimum of the PA spectrum appears at a lower frequency as the width of the particle along the direction of measurement increases. The spectra for higher order (n = 6, 8) Chebyshev particles resembled that of an equivalent sphere up to first minimum. The first minimum for a stomatocyte appeared (420 MHz) much earlier compared to that (640 MHz) of normal RBC when measured along the direction of the symmetry axis; whereas the locations were 310 and 240 MHz, respectively from a perpendicular direction. The evaluation of cellular morphology might be feasible by analyzing the single particle PA spectrum.