Axisymmetric Fluid Research Articles

Zonal flow induced by longitudinal librations of a rotating cylindrical cavity

Longitudinal librations represent oscillations about the axis of a rotating axisymmetric fluid filled cavity. An analytical theory is developed for the case of a cylindrical cavity in the limit when the libration frequency is small in comparison with the rotation rate, but large in comparison with the inverse of the spin-up time. It is shown that through the nonlinear advection in the Ekman layers the librations cause the fluid to rotate more slowly.

The Shapes of Splash-Form Tektites: Their Geometrical Analysis, Classification and Mechanics of Formation

Splash-form tektites are found with a wide range of sizes and in an intriguing array of shapes ranging from spheres to flat discs to dumbbells. Despite the considerable interest that exists in tektites, there has been relatively little effort to develop rational shape descriptors and to understand the origin of their shapes based on basic physics. Tektites represent a natural laboratory experiment that can be analyzed to better understand the physics of rotating fluid drops. In this paper, we propose a classification scheme based on the axial ratios of ellipsoids, and we analyze the frequency of tektite shapes using a database of over 1,000 measured tektites. We show that the shape distribution for tektites from Thailand and Vietnam are very similar and that the most common tektites are moderately deformed discs but there exist also a significant number of moderately deformed dumbbells, and we argue that this distribution comes about because fluid drops first deform as oblate forms and then undergo a non-axisymmetric instability to become prolate. We also find that the largest tektites are most likely to be weakly deformed oblate objects while the most strongly deformed and most highly prolate forms are considerably smaller. A numerical model for the evolution of an axisymmetric fluid drop, such as a tektite in its molten early stage, is presented which demonstrates that drops that deform relatively slowly over a longer period of time are likely to develop central thinning while those that deform more rapidly are more likely to retain the shape of an ellipsoid. For the numerical parameters used the characteristic time scale for deformation was less than 1 s.

On the effects of sliding velocity and operating pressure differential in rotary O-ring seals

An experimental study is conducted to investigate the effect of sliding velocity and pressure differential across an O-ring seal. Of specific interest are the power loss, friction torque and temperatures at the interface between the O-ring and rotating shaft. Nitrile butadiene rubber of circular cross-section with 70 Shore A hardness is used as a test specimen. The O-ring power loss and temperatures at a distance of 0.61 mm away from the O-ring tip are measured during the tests. In order to analyze the temperature at the interface, a two-dimensional axisymmetric computational fluid dynamics (CFD) model is preprocessed in GAMBIT and thermal heat transfer analysis is carried out using a commercial CFD package, FLUENT. Variations of frictional torque, O-ring friction power loss and interfacial temperatures with changes in sliding velocity and operating pressure differential are presented. Results reveal that the O-ring power loss increases in an approximately linear fashion with sliding velocity. Further, it is found that the friction power significantly increases with relatively higher pressure differentials across an O-ring. Friction torque is found to drop with an increase in shaft speed and it rises at relatively higher pressure differentials. Moreover, the interfacial temperatures are found to increase with increase in sliding speed and operating pressure differentials. The physical and practical usefulness of these results are discussed.

Hydrodynamics and global embeddings of Taub-NUT spacetime

On Taub-NUT spacetime, we investigate the hydrodynamic properties of perfect fluid spiraling inward toward the spacetime along a conical surface. On the equatorial plane of the Taub-NUT spacetime, we derive the radial equations of motion with eective potentials and the Euler equation for steady-state axisymmetric fluid. Higher dimensional global embeddings are constructed inside and outside the event horizons of the Taub-NUT spacetime. We also study the eective potentials of particles on the Taub-NUT spacetime in terms of the gravitational magnetic monopole strength of the source, the total energy, and the angular momentum per unit rest mass of the particle.

Stability of black holes from hydrodynamics

It has been well known from old days as a "membrane paradigm" that black holes exhibit laws analogous to laws of fluids. Recent development of AdS/CFT correspondence enhances this similarity into an exact duality, according to which the fluid lumps solving Navier-Stokes equations corresponds holographically to black holes in Scherk-Schwarz (SS) AdS spacetime solving Einstein's equations in the bulk. Black rings in SS-AdS5 are considered to be gravitational duals of stationary and axisymmetric fluid annuli found by Lahiri and Minwalla. We will present a study on the stability of higher dimensional black holes via this dual configurations and further discuss new multiple plasma configurations.

Comparison of different turbulence models in predicting the temperature separation in a Ranque–Hilsch vortex tube

An axisymmetric computational fluid dynamics (CFD) model is used to compare the influence of different Reynolds Averaged Navier–Stokes (RANS) based turbulence models in predicting the temperature separation in a Ranque–Hilsch vortex tube. The standard κ– ɛ, RNG κ– ɛ, standard κ– ω and SST κ– ω turbulence models are used in this study. The performance curves (hot and cold outlet temperatures versus hot outlet mass fraction) obtained by using these turbulence models are compared with the experimental results. The objective is to select an appropriate turbulence model for the simulation of the flow phenomena in a vortex tube with optimum computational expense. The performance analysis shows that among all the turbulence models investigated in this study, temperature separation predicted by the standard κ– ɛ turbulence model is closer to the experimental results.

Vibrational Modeling of CO2 in High-Enthalpy Nozzle Flows

A state-specific vibrational model for CO 2 , CO, O 2 , and O systems is devised by taking into account the first few vibrational states of each species. All vibrational states with energies at or below 1 eV are included in the present work. Of the three modes of vibration in CO 2 , the antisymmetric mode is considered separately from the symmetric stretching mode and the doubly degenerate bending modes. The symmetric and bending modes are grouped together because the energy transfer rates between the two modes are very large due to Fermi resonance. The symmetric and bending modes are assumed to be in equilibrium with the translational and rotational modes. The kinetic rates for the vibrational-translation energy exchange reactions and the intermolecular and intramolecular vibrational-vibrational energy exchange reactions are based on experimental data to the maximum extent possible. Extrapolation methods are employed when necessary. This vibrational model is then coupled with an axisymmetric computational fluid dynamics code to study the expansion of CO 2 in a nozzle.

Multigrid Method for Numerical Simulation of Faraday Probe Measurements

An axisymmetric hybrid electron fluid particle-in-cell computational method is used extensively to simulate Faraday probe measurements for a range of plasma conditions and probe techniques. A new multigrid (MG) method is developed and implemented to speed up the simulations and allow larger domains to be simulated in a practical amount of time. The first study considers how different flowing ion distributions affect the current measurements at a planar Faraday probe surface. The second study considers variations of the standard probe technique and includes varying a uniform bias voltage and varying the guard-ring bias relative to the collecting surface bias. These studies indicate that the standard Faraday probe technique is very robust, and measurements accurately reflect the ion current for a broad range of conditions. The new MG method obtains an overall speedup slightly better than a factor of two, enabling a study of a reversed Faraday probe configuration. This study indicates that the plasma flow behind a reversed probe has strong gradients and complex structure. It is recommended that the probe-body potential should be allowed to float, in order to minimize the focusing effects of sheaths along the side of the probe.

Assessment of Computational Fluid Dynamics for Supersonic Shock Containing Jets

This paper describes a combined experimental and computational investigation of supersonic jets operating off design. Axisymmetric steady-state computational fluid dynamics simulations were performed with a Reynolds-averaged Navier―Stokes solver using a two-equation turbulence model. These results were compared directly with experimental results for two differen t axisymmetric nozzles operating at over- and underexpanded conditions. Pitot and static pressure probes were used to measure the Mach number and local static pressure at various downstream locations. A comparison of both experimental and numerically predicted schlieren visualizations were performed for a qualitative assessment of the accuracy of the flowfield predictions. Quantitative comparisons of pitot and static pressures were made between the experiments and simulations. This provides an assessment of the quality of the numerical simulations as well as an indication of the errors associated with any interference between the pressure probes and the flow in the experiments.

Heat transfer in unsteady axisymmetric second grade fluid

This work looks at the heat transfer effects on the flow of a second grade fluid over a radially stretching sheet. The axisymmetric flow of a second grade fluid is induced due to linear stretching of a sheet. Mathematical analysis has been carried out for two heating processes, namely ( i) with prescribed surface temperature (PST case) and ( ii) prescribed surface heat flux (PHF case). The modelled non-linear partial differential equations in two dependent variables are reduced into a partial differential equation with one dependent variable. The resulting non-linear partial differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence is properly discussed. The series solutions and graphs of velocity and temperature are constructed. Particular attention is given to the variations of emerging parameters such as second grade parameter, Prandtl and Eckert numbers.

Evaluation of models for numerical simulation of the non-neutral region of sheath plasma

Four different electron models are used to simulate the nonequilibrium plasma flow around a representative cylindrical Faraday probe geometry. Each model is implemented in a two-dimensional axisymmetric hybrid electron fluid and particle in cell method. The geometric shadowing model is derived from kinetic theory on the basis that physical obstruction of part of the velocity distribution leads to many of the expected sheath features. The Boltzmann electron fluid model relates the electron density to the plasma potential through the Boltzmann relation. The non-neutral detailed electron fluid model is derived from the electron conservation equations under the assumption of neutrality, and then modified to include non-neutral effects through the electrostatic Poisson equation. The Poisson-consistent detailed electron fluid model is also derived from the conservation equations and the electrostatic Poisson equation, but uses an alternative method that is inherently non-neutral from the outset. Simulations using the geometric shadowing and non-neutral detailed models do not yield satisfactory sheath structures, indicating that these models are not appropriate for sheath simulations. Simulations using the Boltzmann and Poisson-consistent models produce sheath structures that are in excellent agreement with the planar Bohm sheath solution near the centerline of the probe. The computational time requirement for the Poisson-consistent model is much higher than for the Boltzmann model and becomes prohibitive for larger domains.

Fluid Modeling and Analysis of the Constriction of the DC Positive Column in Argon

The glow-to-arc transition of the positive column of a dc discharge in argon in the course of constriction has been investigated on the basis of a self-consistent 1-D axisymmetric fluid model. The model adopts the nonlocal moment method, i.e., the system of balance equations resulting from the moments of the radially dependent Boltzmann equation is solved. The electron transport and rate coefficients are applied in dependence on the mean energy of the electrons, the gas temperature, and the ionization degree. Investigations have been performed for currents from 0.6 to 70 mA and pressures from 100 to 500 torr. The model predictions are compared with experimental and other available modeling results, and they show good agreement with these data in general. The pronounced nonlocal features of the mean electron energy balance are found, and their influence on the constricted argon positive column is analyzed. Different assumptions concerning the electron velocity distribution function have been considered in the present model. In particular, the impact of using a Maxwellian distribution instead of solutions of the steady-state spatially homogeneous electron Boltzmann equation is discussed where the assumption of a Maxwellian distribution for the electrons was found to be inappropriate for describing the constriction effect.

A transient analysis of a micro-tubular solid oxide fuel cell (SOFC)

A two-dimensional, axisymmetric transient computational fluid dynamics model is developed for an intermediate temperature micro-tubular solid oxide fuel cell (SOFC), which incorporates mass, species, momentum, energy, ionic and electronic charge conservation. In our model we also take into account internal current leak which is a common problem with ceria based electrolytes. The current density response of the SOFC as a result of step changes in voltage is investigated. Time scales associated with mass transfer and heat transfer are distinguished in our analysis while discussing the effect of each phenomenon on the overall dynamic response. It is found that the dynamic response is controlled by the heat transfer. Dynamic behavior of the SOFC as a result of failure in fuel supply is also investigated, and it is found that the external current drops to zero in less than 1 s.

Inviscid limit for axisymmetric flows without swirl in a critical Besov space

In this paper, we study the inviscid limit for the 3-D axisymmetric incompressible fluid flows without swirl and prove the convergence rate. We will also prove the uniform persistence of the initial regularity for 3-D axisymmetric Navier-Stokes equations in a critical Besov space.

Numerical implementation of Aristov–Pukhnachev's formulation for axisymmetric viscous incompressible flows

AbstractIn the present work a finite‐difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49(2):112–115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross‐flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross‐flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions.The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in‐depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd.

Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow

The method of associated matrices is used to obtain Galerkin type representations. Fundamental solutions are then obtained for the cases of a point body couple and a point microstretch force. A formula for calculating the total couple acting on a rigid body rotating axi-symmetrically in a microstretch fluid is deduced. A generalized reciprocal theorem is deduced. An application for a rigid sphere rotating in a microstretch fluid is discussed. The results of the application are represented graphically.

Temporal behaviour of global perturbations in compressible axisymmetric flows with free boundaries

AbstractThe dynamics of small global perturbations in the form of a linear combination of a finite number of non‐axisymmetric eigenmodes is studied in the two‐dimensional approximation. The background flow is assumed to be an axisymmetric perfect fluid with adiabatic index γ = 5/3 rotating with a power law angular velocity distribution Γ ∝ r–q , 1.5 < q < 2.0, confined by free boundaries in the radial direction. The substantial transient growth of acoustic energy of optimized perturbations is discovered. An optimal energy growth G is calculated numerically for a variety of parameters. Its value depends essentially on the perturbation azimuthal wavenumber m and increases for higher values of m. The closer the rotation profile to the Keplerian law, the larger growth factors can be obtained but over a longer time. The highest acoustic energy increase found numerically is of order ∼102 over ∼6 typical Keplerian periods. Slow neutral eigenmodes with corotation radius beyond the outer boundary mostly contribute to the transient growth. The revealed linear temporal behaviour of perturbations may play an important role in angular momentum transfer in toroidal flows near compact relativistic objects (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of dilated cardiomyopathy and a left ventricular assist device on vortex dynamics in the left ventricle

Together with new developments in mechanical cardiac support, the analysis of vortex dynamics in the left ventricle has become an increasingly important topic in literature. The aim of this study was to develop a method to investigate the influence of a left ventricular assist device (LVAD) on vortex dynamics in a failing ventricle. An axisymmetric fluid dynamics model of the left ventricle was developed and coupled to a lumped parameter model of the complete circulation. Simulations were performed for healthy conditions and dilated cardiomyopathy (DCM). Vortex structures in these simulations were analysed by means of automated detection. Results show that the strength of the leading vortex ring is lower in a DCM ventricle than in a healthy ventricle. The LVAD further influences the maximum strength of the vortex and also causes the vortex to disappear earlier in time with increasing LVAD flows. Understanding these phenomena by means of the method proposed in this study will contribute to enhanced diagnostics and monitoring during cardiac support.

Stochastic Earthquake Analysis of Underwater Storage Tanks

In this paper, the problem and analysis method of underwater storage tanks resting on a horizontal seabed is presented under stochastic earthquake loading. The tank is axisymmetrical and has a flexible wall/roof. The finite element method is used for the response solution. A solid axisymmetrical finite element has been formulated to idealize the tank whereas an axisymmetrical fluid element is used for the idealization of the fluid domain. The Eulerian formulation of the fluid system is used to calculate the interactive water pressure acting on the tank during the free motion of the tank and earthquake motion. For the response calculation, the modal analysis technique is used with a special algorithm to obtain natural frequencies of the water-structure coupled system. For the stochastic description of the earthquake loading, the modified Kanai–Tajimi earthquake spectrum is used. Finally, the analysis method presented in the paper is demonstrated by an example.

An explicit series solution of the squeezing flow between two infinite plates by means of the homotopy analysis method

In this paper, we investigated an axisymmetric Newtonian fluid squeezed between two parallel plates. The steady nonlinear governing equations are reduced to a single differential equation using integrability condition. Homotopy analysis method (HAM) is used to solve the nonlinear differential equation analytically. Numerical solutions indicate this method is satisfactory.