Assumption Of Axisymmetry Research Articles

Numerical investigation of laminar Rayleigh–Bénard convection of power-law fluids in square cross-sectional cylindrical annular enclosures

Steady-state laminar Rayleigh–Bénard convection (i.e. differentially heated horizontal walls heated from below) of power-law fluids in square cross-sectional cylindrical annular enclosures has been numerically investigated under the assumption of axisymmetry. The numerical simulations have been conducted for a range of different values of nominal Rayleigh number Ra, nominal Prandtl number Pr, power-law index n, and internal radius to enclosure height ratio ri/L (i.e. 103≤Ra≤105; 10≤Pr≤104; 0.6≤n≤1.8; 0≤ri/L≤24) for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for differentially heated horizontal walls. It has been found that convective transport is stronger for CWT boundary condition than for CWHF boundary condition for large (small) values of Ra (n) for a given set of values of n (Ra), Pr, and ri/L, but an opposite trend is observed for small (large) values of Ra (n). The mean Nusselt number Nu−cy does not show a monotonic increase with increasing (decreasing) Ra (n) especially for small values of ri/L for a given value of Pr due to changes in flow patterns (i.e. number of convection cells). However, the mean Nusselt number Nu−cy and flow patterns for large values of ri/L approach those for square enclosures (ri/L→∞) for both CWT and CWHF boundary conditions. Additionally, the critical Rayleigh number Racrit for the onset of convection has been found to be mostly insensitive to the value of ri/L for both CWT and CWHF boundary conditions.

Morphology and kinematics of the gas envelope of protostar L1527 as obtained from ALMA observations of the C18O(2–1) line emission

Using ALMA observations of the C$^{18}$O(2-1) line emission of the gas envelope of protostar L1527, we have reconstructed its morphology and kinematics under the assumption of axisymmetry about the west-east axis. The main original contribution to our understanding of the formation process of L1527 is the presentation of a simple 3D parameterisation based solely on regions that are not dominated by absorption. In the explored range ($\sim$0.7 to 5 arcsec from the star) the model reproduces observations better than earlier attempts. The main results include: a measurement of the rotation velocity that confirms its evolution to Keplerian toward short distances; a measurement of the mean in-fall velocity, 0.43$\pm$0.10 kms$^{-1}$, lower than free fall velocity, with no evidence for the significant $r$-dependence suggested by an earlier analysis; a measurement of the central mass, 0.23$\pm$0.06 M$_{\odot}$ within a distance of 1.5 arcsec from the star, in agreement with earlier estimates obtained from a different range of distances; evidence for a strong disc plane depression of the in-falling flux resulting in an $X$ shaped flow possibly caused by the freeze-out of CO molecules on dust grains; a measurement of the accretion rate, 3.5$\pm$1.0 10$^{-7}$ M$_{\odot}$yr$^{-1}$ at a distance of 1 arcsec (140 au) from the star; evidence for a 10$^\circ$ tilt of the symmetry plane of the envelope about the line of sight, cancelling below $\sim$3 arcsec from the star, but matching infrared observations and being also apparent on the sky map of the mean Doppler velocity.

Numerical investigation of laminar Rayleigh-Bénard convection of Bingham fluids in square cross-sectioned cylindrical enclosures

Numerical simulations have been conducted under the assumption of axisymmetry to analyse steady-state laminar natural convection of yield stress fluids obeying Bingham model in square cross-sectioned cylindrical annular enclosures heated from below (i.e. Rayleigh-Bénard configuration). The simulations have been carried out for a representative value of nominal Prandtl number (i.e. Pr = 500) for different internal cylinder radius (0≤ri/L≤16 where ri and L are the inner radius and the cylinder height respectively) for a nominal Rayleigh number range 103≤Ra≤105. Both constant wall temperature and constant wall heat flux boundary conditions have been imposed for differentially heated horizontal walls to analyse the effects of wall boundary condition. Although the buoyancy-driven transport strengthens with increasing Ra, the mean Nusselt number Nu¯cy does not show a monotonic increase with increasing Ra for small values of ri/L because of the change in flow pattern (i.e. number of convection rolls/cells). By contrast, Nu¯cy monotonically increases with increasing Ra, and only one cell flow pattern is obtained for large values of ri/L. Furthermore, Nu¯cy has been found to increase with increasing ri/L but asymptotically approaches the corresponding value obtained for square enclosures (ri→∞) for both CWT and CWHF boundary conditions for large values of ri/L. It has also been found that both the flow pattern and the mean Nusselt number Nu¯cy are dependent on the initial conditions for Bingham fluid cases since hysteresis is evident for small values of ri/L for both CWT and CWHF boundary conditions. It has been found that convection could be sustained up to a higher value of Bingham number due to stronger convection arising from higher temperature difference between horizontal walls in the case of CWT boundary condition than in the corresponding CWHF configuration. Finally, the numerical findings have been used to propose a correlation for Nu¯cy in the range of 2≤ri/L≤16 (0.25≤ri/L≤16) and 103≤Ra≤105 for the CWT (CWHF) boundary condition.

대체천연가스 화염 이미지 역변환에서 전처리 효과

Abstract A preprocessing scheme utilizing multi-division of the ROI (region of interest) in a chemiluminescence image duringinversion is proposed. The resulting inverted image shows the flame’s structure, which can be useful for studying combustioninstability. The flame structure is often quantitatively visualized with PLIF (planar laser-induced fluorescence) images as well. The chemiluminescence image, which is a line-integral of the flame, needs to be preprocessed before inversion, mainlydue to the inherent noise and the assumption of axisymmetry during the inversion. The feasibility of the multi-division preprocessing technique has been tested with experimentally-obtained OH PLIF and OH * chemiluminescence images of jetand swirl-stabilized flames burning substitute natural gas (SNG). It turns out that the technique outperforms two conventionalmethods, specifically, the technique without preprocessing and the one with uni-division, reconstructing the SNG flame structures much better than its two counterparts when compared using corresponding OH PLIF images. The characteristicsof the optimum degree of polynomials to be applied for curve-fitting of the flame region data for the multi-division methodinvolving two flames has also been investigated.

Unsteady High-Order Simulation of a Liquid Oxygen/Gaseous Hydrogen Rocket Combustor

Coupled Euler–Lagrange simulations are performed for a subcritically operated model rocket combustor at 10 bar pressure (MASCOTTE A-10 test case). A Lagrangian spray model is used to simulate the liquid phase. This liquid oxygen/gaseous hydrogen single element combustor experiment has been the focus of many numerical studies. In contrast to previous investigations, time-accurate unsteady Reynolds-averaged Navier–Stokes simulations are performed. A good spatial resolution is achieved by using a fifth-order multidimensional limiting process scheme to discretize the inviscid fluxes. Instead of assuming axisymmetry, the three-dimensional geometry of the rectangular combustor is taken into account. However, only a quarter of the combustor is simulated, to limit the computational cost. Presented results indicate that three-dimensional effects are important, questioning the assumption of axisymmetry. A second important finding is that time-averaged unsteady Reynolds-averaged Navier–Stokes results agree much better with experimental data than those of a comparable steady-state simulation. Close to the injector, results show a strong unsteadiness of the turbulent flame, which has been observed in the experiment, too. Finally, pressure fluctuations are monitored at several positions in the combustor and analyzed by fast Fourier transform. The peak amplitudes in the pressure spectra could successfully be assigned to the first longitudinal acoustic mode and its higher harmonics.

Numerical investigations of drop solidification on a cold plate in the presence of volume change

We present a front-tracking/finite difference method for simulation of drop solidification on a cold plate. The problem includes temporal evolution of three interfaces, i.e. solid–liquid, solid–gas, and liquid–gas, that are explicitly tracked under the assumption of axisymmetry. Method validation is carried out by comparing computational results with exact solutions for a two-dimensional Stefan problem, and with related experiments. We then use the method to investigate a drop solidifying on a cold plate in which there exists volume change due to density difference between the solid and liquid phases. Numerical results show that the shape of the solidified drop is profoundly different from the initial liquid one due to the effects of volume change and the tri-junction in terms of growth angles ϕgr on the solidification process. A decrease in the density ratio of solid to liquid ρsl or an increase in the growth angle results in an increase in the height of the solidified drop. The solidification process is also affected by the Stefan number St, the Bond number Bo, the Prandtl number Pr, the Weber number We, the ratios of the thermal properties of the solid to liquid phases ksl and Cpsl. Increasing St, Bo, Pr, We, or ksl decreases the solidified drop height and the time to complete solidification. Moreover, the solidification growth rate is strongly affected by St, ksl and Cpsl. An increase in any of these parameters hastens the growth rate of the solidification interface. Contrarily, increasing ρsl decreases the growth rate. However, other parameters such as ϕgr, Bo, Pr and We have minor effects on the solidification growth rate.

SNG 선회 안정화 화염구조 가시화를 위한 OH<sup>*</sup> 자발광 이미지 역변환에서 전처리 효과

ABSTRACTFlame structure, which contains a useful information for studying combustion instability of the flame, is often quantitatively visualized with PLIF (planar laser-induced fluorescence) and/or chemiluminescence images. The latter, a line-integral of a flame property, needs to be preprocessed before being inverted, mainly due to its inherent noise and the axisymmetry assumption of the inversion. A preprocessing scheme utilizing multi- division of ROI (region of interest) of the chemiluminescence image is proposed. Its feasibility has been tested with OH PLIF and OH* chemiluminescence images of SNG (synthetic natural gas) swirl-stabilized flames taken from a model gas turbine combustor. It turns out that the multi-division technique outperforms two conventional ones: those are, one without preprocessing and the other with uni-division preprocessing, re-constructing the SNG flame structure much better than its two counterparts, when compared with the corres-ponding OH PLIF images. It is also found that the Canny edge detection algorithm used for detecting edges in the multi-division method works better than the Sobel algorithm does.

The ATLAS 3D project – XXIV. The intrinsic shape distribution of early-type galaxies

We use the ATLAS3D sample to perform a study of the intrinsic shapes of early-type galaxies, taking advantage of the available combined photometric and kinematic data. Based on our ellipticity measurements from the Sloan Digital Sky Survey Data Release 7, and additional imaging from the Isaac Newton Telescope, we first invert the shape distribution of fast and slow rotators under the assumption of axisymmetry. The so-obtained intrinsic shape distribution for the fast rotators can be described with a Gaussian with a mean flattening of q = 0.25 and standard deviation σq = 0.14, and an additional tail towards rounder shapes. The slow rotators are much rounder, and are well described with a Gaussian with mean q = 0.63 and σq = 0.09. We then checked that our results were consistent when applying a different and independent method to obtain intrinsic shape distributions, by fitting the observed ellipticity distributions directly using Gaussian parametrizations for the intrinsic axis ratios. Although both fast and slow rotators are identified as early-type galaxies in morphological studies, and in many previous shape studies are therefore grouped together, their shape distributions are significantly different, hinting at different formation scenarios. The intrinsic shape distribution of the fast rotators shows similarities with the spiral galaxy population. Including the observed kinematic misalignment in our intrinsic shape study shows that the fast rotators are predominantly axisymmetric, with only very little room for triaxiality. For the slow rotators though there are very strong indications that they are (mildly) triaxial.

An efficient time‐domain perfectly matched layers formulation for elastodynamics on spherical domains

SUMMARYMany practical applications require the analysis of elastic wave propagation in a homogeneous isotropic media in an unbounded domain. One widely used approach for truncating the infinite domain is the so‐called method of perfectly matched layers (PMLs). Most existing PML formulations are developed for finite difference methods based on the first‐order velocity‐stress form of the elasticity equations, and they are not straight‐forward to implement using standard finite element methods (FEMs) on unstructured meshes. Some of the problems with these formulations include the application of boundary conditions in half‐space problems and in the treatment of edges and/or corners for time‐domain problems. Several PML formulations, which do work with FEMs have been proposed, although most of them still have some of these problems and/or they require a large number of auxiliary nodal history/memory variables. In this work, we develop a new PML formulation for time‐domain elastodynamics on a spherical domain, which reduces to a two‐dimensional formulation under the assumption of axisymmetry. Our formulation is well‐suited for implementation using FEMs, where it requires lower memory than existing formulations, and it allows for natural application of boundary conditions. We solve example problems on two‐dimensional and three‐dimensional domains using a high‐order discontinuous Galerkin (DG) discretization on unstructured meshes and explicit time‐stepping. We also study an approach for stabilization of the discrete equations, and we show several practical applications for quality factor predictions of micromechanical resonators along with verifying the accuracy and versatility of our formulation. Copyright © 2014 John Wiley & Sons, Ltd.

3D simulations of disc winds extending radially self-similar MHD models

Disc-winds originating from the inner parts of accretion discs are considered as the basic component of magnetically collimated outflows. The only available analytical MHD solutions to describe disc-driven jets are those characterized by the symmetry of radial self-similarity. However, radially self-similar MHD jet models, in general, have three geometrical shortcomings, (i) a singularity at the jet axis, (ii) the necessary assumption of axisymmetry, and (iii) the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis, by solving the full three-dimensional equations of MHD and impose a termination radius at finite radial distance. We focus here on studying the effects of relaxing the (ii) assumption of axisymmetry, i.e. of performing full 3D numerical simulations of a disc-wind crossing all magnetohydrodynamic critical surfaces. We compare the results of these runs with previous axisymmetric 2.5D simulations. The structure of the flow in all simulations shows strong similarities. The 3D runs reach a steady state and stay close to axisymmetry for most of the physical quantities, except for the poloidal magnetic field and the toroidal velocity which slightly deviate from axisymmetry. The latter quantities show signs of instabilities, which, however, are confined to the region inside the fast magnetosonic separatrix surface. The forces present in the flow, both of collimating and accelerating nature, are in good agreement in both the 2.5D and the 3D runs. We conclude that the analytical solution behaves well also after relaxing the basic assumption of axisymmetry.

Experimental Investigation of Ion Mass Dependency of Magnetic Reconnection Outflow by using High Precision Ion Doppler Spectroscopy

Doppler spectroscopy diagnostics with a new reconstruction method has been developed to evaluate local ion velocity profile of magnetic reconnection outflow. The multi-chord ion Doppler diagnostic can simultaneously measure spectral profiles of line-integrated emission from 90 chords across the plasma using three monochromators and three intensified CCD cameras. Under an assumption of axisymmetry, 2-dimensional profiles of reconnection outflow ion velocity are achieved with satisfactory accuracy by a vector-based tomography technic for the first time.

Constraining the Galactic potential via action-based distribution functions for mono-abundance stellar populations

We present a rigorous and practical way of constraining the Galactic potential based on the phase-space information for many individual stars. Such an approach is needed to dynamically model the data from ongoing spectroscopic surveys of the Galaxy and in the future Gaia. This approach describes the orbit distribution of stars by a family of parametrized distribution function (DF) proposed by McMillan and Binney, which are based on actions. We find that these parametrized DFs are flexible enough to capture well the observed phase-space distributions of individual abundance-selected Galactic subpopulations of stars (`mono-abundance populations') for a disc-like gravitational potential, which enables independent dynamical constraints from each of the Galactic mono-abundance populations. We lay out a statistically rigorous way to constrain the Galactic potential parameters by constructing the joint likelihood of potential and DF parameters, and subsequently marginalizing over the DF parameters. This approach explicitly incorporates the spatial selection function inherent to all Galactic surveys, and can account for the uncertainties of the individual position--velocity observations. On that basis, we study the precision of the parameters of the Galactic potential that can be reached with various sample sizes and realistic spatial selection functions. By creating mock samples from the DF, we show that, even under a restrictive and realistic spatial selection function, given a two-parameter gravitational potential, one can recover the true potential parameters to a few per cent with sample sizes of a few thousands. The assumptions of axisymmetry, of DFs that are smooth in the actions and of no time variation remain important limitations in our current study.

An adaptive meshfree method for phase-field models of biomembranes. Part I: Approximation with maximum-entropy basis functions

We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp internal layers in the vicinity of the putative interface, and are nearly constant elsewhere. Thanks to the smoothness of the local maximum-entropy (max-ent) meshfree basis functions, we approximate numerically this high-order phase-field model with a direct Ritz–Galerkin method. The flexibility of the meshfree method allows us to easily adapt the grid to resolve the sharp features of the solutions. Thus, the proposed approach is more efficient than common tensor product methods (e.g. finite differences or spectral methods), and simpler than unstructured C0 finite element methods, applicable by reformulating the model as a system of second-order PDE. The proposed method, implemented here under the assumption of axisymmetry, allows us to show numerical evidence of convergence of the phase-field solutions to the sharp interface limit as the regularization parameter approaches zero. In a companion paper, we present a Lagrangian method based on the approximants analyzed here to study the dynamics of vesicles embedded in a viscous fluid.

Large-Eddy Simulation of combustion instabilities in a variable-length combustor

This article presents a simulation of a model rocket combustor with continuously variable acoustic properties thanks to a variable-length injector tube. Fully compressible Large-Eddy Simulations are conducted using the AVBP code. An original flame stabilization mechanism is uncovered where the recirculation of hot gases in the corner recirculation zone creates a triple flame structure. An unstable operating point is then chosen to investigate the mechanism of the instability. The simulations are compared to experimental results in terms of frequency and mode structure. Two-dimensional axi-symmetric computations are compared to full 3D simulations in order to assess the validity of the axi-symmetry assumption for the prediction of mean and unsteady features of this flow. Despite the inaccuracies inherent to the 2D description of a turbulent flow, for this configuration and the particular operating point investigated, the axi-symmetric simulation qualitatively reproduces some features of the instability.

Oscillatory flow and temperature fields in an open tube with temperature difference across the ends

The oscillating flow and temperature field in an open tube subjected to cryogenic temperature at the cold end and ambient temperature at the hot end is studied numerically. The flow is driven by a time-wise sinusoidally varying pressure at the cold end. The conjugate problem takes into account the interaction of oscillatory flow with the heat conduction in the tube wall. The full set of compressible flow equations with axisymmetry assumption are solved with a pressure correction algorithm. Parametric studies are conducted with frequencies of 5–15 Hz, with one end maintained at 100 K and other end at 300 K. The flow and temperature distributions and the cooldown characteristics are obtained. The frequency and pressure amplitude have negligible effect on the time averaged Nusselt number. Pressure amplitude is an important factor determining the enthalpy flow through the solid wall. The frequency of operation has considerable effect on penetration of temperature into the tube. The density variation has strong influence on property profiles during cooldown. The present study is expected to be of interest in applications such as pulse tube refrigerators and other cryocoolers, where oscillatory flows occur in open tubes.

Kinematic constraints on the stellar and dark matter content of spiral and S0 galaxies

We present mass models of a sample of 14 spiral and 14 S0 galaxies that constrain their stellar and dark matter content. For each galaxy, we derive the stellar mass distribution from near-infrared photometry under the assumptions of axisymmetry and a constant KS-band stellar mass-to-light ratio ⁠. To this we add a dark halo assumed to follow a spherically symmetric Navarro, Frenk and White profile and a correlation between concentration and dark mass within the virial radius, MDM. We solve the Jeans equations for the corresponding potential under the assumption of constant anisotropy in the meridional plane, βz. By comparing the predicted second velocity moment to observed long-slit stellar kinematics, we determine the three best-fitting parameters of the model: and βz. These simple axisymmetric Jeans models are able to accurately reproduce the wide range of observed stellar kinematics, which typically extend to ≈2–3Re or, equivalently, ≈0.5–1R25. Although our sample contains barred galaxies, we argue a posteriori that the assumption of axisymmetry does not significantly bias our results. We find a median stellar mass-to-light ratio at KS-band of with an rms scatter of 0.31. We present preliminary comparisons between this large sample of dynamically determined stellar mass-to-light ratios and the predictions of stellar population models. The stellar population models predict slightly lower mass-to-light ratios than we measure. The mass models contain a median of 15 per cent dark matter by mass within an effective radius Re (defined here as the semimajor axis of the ellipse containing half the KS-band light) and 49 per cent within the optical radius R25. Dark and stellar matter contribute equally to the mass within a sphere of radius 4.1Re or 1.0 R25. There is no evidence of any significant difference in the dark matter content of the spirals and S0s in our sample. Models without dark matter are also able to satisfactorily reproduce the observed kinematics in most cases. The improvement when a halo is added is statistically significant, however, and the stellar mass-to-light ratios of mass models with dark haloes match the independent expectations of stellar population models better.

Stochastic wobble of accretion discs and jets from turbulent rocket torques

Models of accretion discs and their associated outflows often incorporate assumptions of axisymmetry and symmetry across the disc plane. However, for turbulent discs these symmetries only apply to averaged quantities and do not apply locally. The local asymmetries can induce local imbalances in outflow power across the disc mid-plane, which can in turn induce local tilting torques. Here we calculate the effect of the resulting stochastic torques on disc annuli that are a consequence of standard mean field accretion disc models. The torques induce a random walk of the vector perpendicular to the plane of each averaged annulus. This random walk is characterized by a radially dependent diffusion coefficient which we calculate for small angle tilt. We use the coefficient to calculate a radially dependent time scale for annular tilt and associated jet wobble. The wobble time depends on the square of the wander angle so the age of a given system determines the maximum wobble angle. We apply this to examples of blazars, young stellar objects and binary engines of pre-planetary nebulae and microquasars. It is noteworthy that for an averaging time $t_w\sim 3$ days, we estimate a wobble angle for jets in SS433 of $\theta\sim 0.8$ degrees, not inconsistent with observational data. In general the non-periodic nature of the stochastic wobble could distinguish it from faster periodic jet precession.

THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. II. THE RECLOSING OF AN OPENED FIELD

This is a study of the spontaneous formation of current sheets responding to the closing of an opened magnetic field by resistive reconnection in an electrically, highly conducting atmosphere outside a unit sphere. Pairs of initial-final equilibrium states are calculated explicitly, taking the field to be composed of three systems of untwisted flux in both states. In the initial state, two of the three flux systems are closed potential fields whereas the third system contains an equilibrium current sheet that keeps the potential fields on its two sides globally open. The final state is an everywhere potential field, with all three flux systems closed, produced by the resistive dissipation of the current sheet in the initial state. The unit sphere is taken to be a rigid, perfectly conducting wall during reconnection, so that the normal flux distribution is unchanged on the unit sphere. Field solutions subject to this unchanging boundary condition are obtained with and without the assumption of axisymmetry. The mathematical model has been designed to show that the topological changes produced by the current-sheet dissipation are simple under axisymmetry but radically different in the absence of axisymmetry, a fundamental point established in the first paper of this series. In the general case, the topological changes imply that other current sheets must have formed. Some of these current sheets form on the separatrix flux surfaces of the multipolar field. Others form throughout the closed-flux systems induced by volumetric changes. The opening and reclosing of magnetic fields during a solar coronal mass ejection may produce a multitude of current sheets not previously anticipated in the current understanding of this phenomenon. Basic to this study is a general topological property of magnetic flux tubes treated separately in the Appendix.

A 3D Nonlinear Anisotropic Spherical Inflation Model for Intracranial Saccular Aneurysm Elastodynamics

Cerebral aneurysms occur in weakened areas of artery walls resulting in a ballooning out of the wall filled with blood. A major catalyst for mathematical modeling of intracranial saccular aneurysms has been the axisymmetric membrane derivations in Shah and Humphrey (1999, Journal of Biomechanics, 32, 593—599) and David and Humphrey (2003, Journal of Biomechanics, 36, 1143—1150). We expand on the foundational membrane dynamics to develop a blood-aneurysm-cerebrospinal fluid model from the fully three-dimensional nonlinear elastic equations of motion with system coupling at both inner and outer fluid— aneurysm boundaries consistent with Navier-Stokes. We derive the 3D elastodynamics and determine subsequent governing nonlinear ordinary differential equations for the three general material symmetries possible under the classic initial assumption of axisymmetry. We employ biologically motivated strain-energy functions to numerically solve the equations and observe resulting aneurysm cyclic stretches, thickness changes, effects of material and geometric parameters, and through-the-thickness stresses due to biological forcing for each type of material symmetry and constitutive model.

The validity of axisymmetric assumptions when investigating pulsatile biological flows

Computational fluid simulations of biological flows is increasingly popular due to its inexpense and ability to define the flow throughout the entire domain---both common limiting factors for experimental work. A common assumption has been that both the geometry and the flow field through an aneurysm is axisymmetric; however, investigations into non-biological flows have seen that even with an axisymmetric geometry, non-axisymmetric flow may develop. Idealised geometries are used to investigate these biological flows as it simplifies the model to enable an improved understanding of the effect geometry has on the flow. Additionally this simplification allows the implementation of a computationally cheaper axisymmetric code. We test this axisymmetric assumption by applying Floquet stability analysis to investigate the stability of the flow and thus determine when an axisymmetric aneurysmal flow is unstable to non-axisymmetric instabilities. Dimensions of the model are selected to be consistent with a high risk aneurysm in the human abdominal aorta and Reynolds numbers relevant to aneurysms in large arteries are examined. The presence of three dimensional instabilities has a significant impact on the validity of the assumption of axisymmetry. The maximum streamwise vorticity in the perturbation fields is found to occur at the downstream section of the aneurysm, implying that it is in these areas that the results of axisymmetric simulations differ the most from fully three dimensional flow. References Barkley, D. and Henderson, R. D., Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322 (1996), 215--241. doi:10.1017/S0022112096002777 Brown, P. M., Zelt D. T., Sobolev B., The risk of rupture in untreated aneurysms: The impact of size, gender, and expansion rate. J. Vasc. Surg. 37 (2003), 280--284. doi:10.1067/mva.2003.119 Cowling R., Soria J., Flow Visualisation through Model Abdominal Aortic Aneurysm, Fourth Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion , The University of Adelaide, South Australia, Australia, 7--9 December 2005, 33--36. Egelhoff C. J., Budwig R. S., Elger D. F., Khraishi T. A., Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions. J. Biomech , 32 (1999), 1319-1329. doi:10.1016/S0021-9290(99)00134-7 Karniadakis, G. E. and Triantafyllou, G. S., Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199 (1989), 441--469. doi:10.1017/S0022112089000431 Karniadakis, G. E., Israeli, M. and Orszag, S. A., High-order splitting methods for the incompressible Navier-Stokes equations, J. Comp. Phys. 97 (1991), 414--443. doi:10.1016/0021-9991(91)90007-8 Ku, D. N., Blood flow in arteries, Annual review of Fluid Mechanics , 29 (1997), 399--434. doi:10.1146/annurev.fluid.29.1.399 Lasheras J., The Biomechanics of Arterial Aneurysms, Annual Review of Fluid Mechanics , 39 (2007), 293--319 doi:10.1146/annurev.fluid.39.050905.110128 Salsac, A. V., Sparks, S. R., Chomaz, J. M. and Lasheras, J. C., Evolution of the wall shear stresses during the progressive enlargement of symmetric abdominal aortic aneurysms, J. Fluid Mech. , 560 (2006), 19--51. doi:10.1017/S002211200600036X Sheard, G. J., Evans, R. G., Denton, K. M. and Hourigan, K., Undesirable Haemodynamics in Aneurysms, In Proceedings of the IUTAM Symposium on Unsteady Separated Flows and Their Control , Hotel Corfu Chandris, Corfu, Greece, 18--22 June 2007 Sheard, G. J. and Ryan, K., Pressure-driven flow past spheres moving in a circular tube, J. Fluid Mech. 592 (2007), 233--262. doi:10.1017/S0022112007008543 Stedman, 2002, The American HeritageAE Stedmanis Medical Dictionary, Houghton Mifflin Company, Massachusetts. Steinman, D. A., Vorp, D. A. and Ethier, C. R., Computational modelling of arterial biomechanics: Insights into pathogenesis and treatment of vascular disease, J. Vascular Surgery , 37 (2003), 1118--1128. doi:10.1067/mva.2003.122 Waite, L. and Fine, J. (2007). Applied biofluid mechanics . United Stated of America: McGraw-Hill.