Axisymmetric Configuration Research Articles

Design and analysis of non-axisymmetric installed aero-engine exhaust systems

In order to increase propulsive efficiency, and hence reduce fuel consumption, future aero-engines are expected to operate with higher bypass ratios and larger fan diameters relative to current in-service engines. As such, propulsion systems are likely to be more closely-coupled with the airframe which is expected to accentuate detrimental aerodynamic interference effects between the engine and airframe. It is therefore crucial that the design of future aero-engine exhaust systems is considered as part of an engine-airframe configuration in order to ensure that the expected benefits of high BPR engines are realised. This work presents the aerodynamic performance and evaluation of a set of novel exhaust systems within complete engine-airframe configurations. The introduction of non-axisymmetric exhaust systems was shown to mitigate the aerodynamic penalties associated with closely-coupled propulsion systems at cruise conditions. Relative to an axisymmetric baseline configuration, the introduction of non-axisymmetric bypass and core nozzles were found to increase the net vehicle force of the engine-airframe configuration by 0.8% and 0.6% respectively. As a result of this work, it can be concluded that non-axisymmetric exhaust systems represent a viable method for reducing aircraft cruise fuel burn.

Enhanced mechanical properties in cellular solids using axisymmetric configurations

Cellular solids, as a class of materials, are known for a high strength to weight ratio. Their design into non-stochastic configurations is known to be beneficial for the tailor and control of their mechanical properties. The current developments on additive manufacturing allow a successful route to manufacture these scaffolds and gives a novel freedom in their design process. This study explores the deformation behavior of axisymmetric non-stochastic cellular solids, allowing the understanding of the mechanisms that enhance their mechanical properties relatively to regular extruded lattices. It is shown that axisymmetric samples display a circumferential deformation effect that distributed loads along the volume of the material. This effect, however, is more prominent in axisymmetric samples with auxetic behavior. The coupling of circumferential deformation and the dynamic density changes in auxetic samples generate an overall increase in modulus, collapse stress and energy absorption.

Numerical description of axisymmetric blue whirls over liquid-fuel pools

This numerical investigation is focused on determining the structures of blue whirls, recently found to occur in laboratory investigations of fire whirls when the circulation becomes sufficiently large to produce a vortex breakdown that drastically shortens the fire whirl and correspondingly reduces residence times, so that the yellow flames turn blue. The computations address axisymmetric configurations for round pools of liquid fuels flush with and at the center of a larger solid horizontal disc, at the outer edge of which vanes of adjustable angles cause the entrained air to enter with a controllable azimuthal component of velocity. The nondimensionlized conservation equations employed include realistic Lewis numbers with temperature-dependent transport coefficients and a one-step chemical-kinetic approximation that correctly reproduces laminar burning velocities. Buoyancy and radiant energy transport from the flames to the liquid surface are both taken into account, the latter being found to be essential for the blue whirl. Along with the vaporization-equilibrium and energy-conservation boundary conditions at the fuel surface, inflow boundary conditions are provided by a recently developed solution for the boundary-layer flow over the solid disc, while zero-gradient outflow conditions are applied above the whirl. Controlling nondimensional parameters, besides Reynolds, Damköhler, and Froude numbers, are a ratio of radiant to convective energy flux and a ratio of azimuthal to inward radial flow velocity in the boundary layer at the edge of the disc. The computed conditions for the onset of the blue whirl, as well as the computed structure of the whirl itself, bear close resemblance to what was found experimentally.

Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone

Context. The interactions between magnetic fields and differential rotation in stellar radiative interiors could play a major role in achieving an understanding of the magnetism of intermediate-mass and massive stars and of the differential rotation profile observed in red-giant stars. Aims. The present study is aimed at studying the flow and field produced by a stellar radiative zone which is initially made to rotate differentially in the presence of a large-scale poloidal magnetic field threading the whole domain. We focus both on the axisymmetric configurations produced by the initial winding-up of the magnetic field lines and on the possible instabilities of those configurations. We investigate in detail the effects of the stable stratification and thermal diffusion and we aim, in particular, to assess the role of the stratification at stabilising the system. Methods. We performed 2D and 3D global Boussinesq numerical simulations started from an initial radial or cylindrical differential rotation and a large-scale poloidal magnetic field. Under the conditions of a large rotation frequency compared to the Alfvén frequency, we built a magnetic configuration strongly dominated by its toroidal component. We then perturbed this configuration to observe the development of non-axisymmetric instabilities. Results. The parameters of the simulations were chosen to respect the ordering of time scales of a typical stellar radiative zone. In this framework, the axisymmetric evolution is studied by varying the relative effects of the thermal diffusion, the Brunt-Väisälä frequency, the rotation, and the initial poloidal field strength. After a transient time and using a suitable adimensionalisation, we find that the axisymmetric state only depends on tes/tAp the ratio between the Eddington–Sweet circulation time scale and the Alfvén time scale. A scale analysis of the Boussinesq magnetohydrodynamical equations allows us to recover this result. In the cylindrical case, a magneto-rotational instability develops when the thermal diffusivity is sufficiently high to enable the favored wavenumbers to be insensitive to the effects of the stable stratification. In the radial case, the magneto-rotational instability is driven by the latitudinal shear created by the back-reaction of the Lorentz force on the flow. Increasing the level of stratification then leaves the growth rate of the instability mainly unaffected while its horizontal length scale grows. Conclusions. Non-axisymmetric instabilities are likely to exist in stellar radiative zones despite the stable stratification. They could be at the origin of the magnetic dichotomy observed in intermediate-mass and massive stars. They are also unavoidable candidates for the transport of angular momentum in red giant stars.

Effects of resonant magnetic perturbations on the loss of energetic ions in tokamak pedestal

Resonant magnetic perturbations (RMPs) are extensively applied to mitigate or suppress the edge localized mode in tokamak plasmas, but will break the axisymmetric magnetic field configuration and increase the loss of energetic ions. The mechanism of RMPs induced energetic ion loss has been extensively studied, and is mainly attributed to resonant effects. In this paper, in the perturbed non-axisymmetric tokamak pedestal, we analytically derive the equations of guiding center motion for energetic ions including the bounce/transit averaged radial drift velocity and the toroidal precession frequency modified by strong radial electric field. The loss time of energetic ions is numerically solved and its parametric dependence is analyzed in detail. We find that passing energetic ions cannot escape from the plasma, while deeply trapped energetic ions can escape from the plasma. The strong radial electric field plays an important role in modifying the toroidal precession frequency and resulting in the drift loss of trapped energetic ions. The loss time of trapped energetic ions is much smaller than the corresponding slowdown time in DIII-D pedestal. This indicates that the loss of trapped energetic ions in the perturbed non-axisymmetric pedestal is important, especially for the trapped energetic ions generated by perpendicular neutral beam injection.

Spinning behavior of flow-acoustic resonant fields inside a cavity: Vortex-shedding modes and diametral acoustic modes

The spinning behavior of flow-acoustic resonant fields inside an axisymmetric cavity configuration was numerically investigated in four flow conditions containing different resonances between vortex-shedding modes and diametral acoustic modes. Zonal large-eddy simulations (ZLESs) were conducted to determine the aeroacoustic and aerodynamic fields simultaneously. In the ZLESs, a shear stress transport turbulence model was used to model the relatively steady flow field inside the inlet and outlet sections. Simultaneously, the wall-modeled LES formulation was used in the cavity section to resolve the highly complex flow-acoustic resonant fields. The ZLES results were well validated by the experimental results in the literature in terms of the frequency, amplitude, and spatial features of the acoustic pressure pulsations. Subsequently, the spinning behavior and mechanism of the excited diametral acoustic modes and the resonant vortex-shedding modes were comprehensively illustrated. The results showed that the excited diametral acoustic mode span anticlockwise along the cavity circumference, resulting in intense acoustic-pressure fluctuations several times greater than at the inlet dynamic-pressure head, together with longitudinal pressure propagations. Using proper orthogonal decomposition analysis, the spinning mechanism was found to be closely related to the interaction between the α-mode and the β-mode, which had fixed temporal and spatial phase lags. Thereafter, the first vortex-shedding mode gave rise to a strong spinning motion of the resonant flow field, while the second vortex-shedding mode created a slight spinning motion. The corresponding phase-dependent flow fields at consecutive planes along the cavity circumference revealed the spatiotemporal evolution of the velocity variations, surface streamlines, and vorticity variations of the shedding vortices. Large-scale helical vortex tubes were formed within the cavity volume due to the strong spinning behavior.

Anisotropic disclination cores in nematic liquid crystals modeled by a self-consistent molecular field theory.

Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known divergences in the Landau-de Gennes formulation. Our results agree with the asymptotic results of Dzyaloshinskii for the Frank-Oseen energy far from the defect core, but reveal biaxial order at intermediate distances from the core, crossing over to uniaxial but axisymmetric configurations as the core is approached. The elastic terms considered in our energy allow for the separate control of surface tension, anchoring, and elasticity contrast, and are used to analyze recent results for lyotropic chromonic liquid crystals. The latter display unusually large defect cores (on the order of tens of microns) which can be used for a quantitative comparison with the theory. Both ±1/2 disclination configurations are well reproduced by our calculations. Elastic anisotropy is also shown to lead to qualitative changes in the disclination polarization, a quantity that is proportional to the active stress in models of active matter.

Thermodynamics of two aligned Kerr black holes

We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and for thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length $\ell$ is defined by the formula $\ell=L\exp(\gamma_0)$, where $L$ is the coordinate length of the strut, and $\gamma_0$ is the value of the metric function $\gamma$ on the strut.

Core magnetic field imprint in the non-radial oscillations of red giant stars

ABSTRACT Magnetic fields in red giant stars remain a poorly understood topic, particularly in what concerns their intensity in regions far below the surface. In this work, we propose that gravity-dominated mixed modes of high absolute radial order and low angular degree can be used to probe the magnetic field in their radiative cores. Using two poloidal, axisymmetric configurations for the field in the core and the classical perturbative approach, we derive an analytical expression for the magnetic frequency splitting of these oscillation modes. Considering three distinct red giant models, with masses of 1.3, 1.6, and 2.0 M⊙, we find that a field strength of 105 G is necessary in the core of these stars to induce a frequency splitting of the order of a μHz in dipole and quadrupole oscillation modes. Moreover, taking into account observational limits, we estimate that magnetic fields in the cores of red giants that do not present observable magnetic splittings cannot exceed 104 G. Given the general absence of observable splittings in the oscillation spectra of these stars, and assuming that present mode suppression mechanisms are not biased towards certain azimuthal orders and retain all peaks in each multiplet, our results lead us to conclude that internal fields with the considered configurations and strengths above 104 G are not prevalent in red giants.

Diblock copolymer architecture and complex viscosity

General rigid bead-rod theory [O. Hassager, J. Chem. Phys. 60, 4001 (1974)] explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead-rod theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric macromolecules. In this paper, we explore the complex viscosities of different axisymmetric diblock copolymer configurations. When nondimensionalized with the zero-shear viscosity, the diblock copolymer complex viscosity depends on the dimensionless frequency and the sole dimensionless architectural parameter, the macromolecular lopsidedness. In this paper, through this way, we thus compare the dimensionless relaxation time of different diblock macromolecular chains. We explore the effects of linear density, macromolecular length, and bead number ratio.

Viability of basic heterogeneous nucleation studies with thermally diffusive condensation particle counters

HypothesisWhile the lack of efficient tools yielding controllable uniform supersaturations (S) has delayed basic experimental heterogeneous nucleation studies, common diffusive condensation particle counters (DCPCs) would fill this gap if their present substantial S-variation could be minimized. AnalysisFor an initially saturated vapor in two-dimensional (2D) parabolic flow, with discontinuous wall temperature change from Ts to Tc, we calculate the spatial S(x,y) distribution, including the curve Smax(Ψ) of maximal supersaturations versus streamline Ψ. Activation probability curves P(Ts,Tc) are also calculated assuming that nucleation goes from zero to 100% at a critical supersaturation S*. FindingsTwo new approaches to achieve a nearly constant Smax(Ψ) are discovered. (i) Sampling only the central 50% of the flow is most effective because the [dSmax(Ψ)/Dψ]Ψ=0 = 0. This advantage is lost in the more common axisymmetric configuration. (ii) When the ratio Le = α/D between gas–vapor heat and mass diffusivities is unity, we find the quite general property that Smax(Ψ) is exactly constant. This singular condition may be achieved in special vapor/gas mixtures (ethanol/CO2; methanol/CO2; H2O/air, all seeded with lighter or heavier gases). With greater generality, Le = 1 also in turbulent flows. Therefore, basic heterogeneous nucleation studies with newly available seed particles of fixed size and composition are viable in DCPCs.

Nanofluid Heat Transfer in Wavy-Wall Channels with Different Geometries: A Finite-Volume Lattice Boltzmann Study

In this work, we perform an extensive numerical investigation of the heat transfer behavior of nanofluid laminar flows, in wavy-wall channels. The adopted computational approach is based on a finite-volume formulation of the lattice Boltzmann method constructed on a fully-unstructured mesh. We show the validity and effectiveness of this numerical approach to deal with realistic problems involving nanofluid flows, and we employ it to analyze the effects of the wavy-wall channel geometry on the rate of heat transfer, thus providing useful information to the design of efficient heat transfer devices. Results show that an increasing of the wavy surface amplitude has a positive effect on the heat transfer rate, while a phase shift between the wavy walls leads to a decreasing of the mean Nusselt number along the channel. The addition of solid nanoparticles within a base liquid significantly contributes to increase the rate of heat transfer, especially when a relatively high value of nanoparticles volume fraction is employed. The present analysis then suggests that the use of nanofluids within an axis-symmetric configuration of the wavy-wall channel, with high wavy surface amplitude, may represent an optimal solution to enhance the thermal performances of heat transfer devices.

Numerical study of conjugate mass transfer from a spherical droplet at moderate Reynolds number

Hydrodynamics and conjugate mass transfer from a spherical droplet at low to moderate Reynolds number have been investigated by direct numerical simulation. The study particularly focuses on the coupling between the internal and external flows, and their respective effects on the resulting mass transfer of a solute under 2D axi-symmetric configuration. The influence of the viscosity, density, and diffusivity ratios (μ*, ρ* and D* respectively) between the two phases, as well as that of the equilibrium constant k (or Henry’s number) characterizing thermodynamic equilibrium at the interface, has been studied in a range of flow Reynolds numbers relevant for solvent extraction processes (up to Reynolds number 100).The temporal evolution of the Sherwood number has been analyzed and a general correlation is proposed for its steady state regime. Interestingly, simulation results show that correlations available in the literature in the limiting cases kD*≪1 and kD*≫1, referred to as internal and external mass transfer regimes, are not always appropriate in the context of conjugate mass transfer. This limits the use of the addition rule of transfer resistances, which reflects the flux continuity in the double stagnant film model. Indeed, a significant discrepancy is observed under specific configurations, especially at low Péclet number (Pe ≤ 500) where non uniform interface concentration prevails.

Streamlined bodies drag force estimation using wake integration technique

In this paper, the drag force calculation around the SUBOFF submarine in axisymmetric configuration was investigated using the “Wake Integration Technique.” This method is usually used in wind tunnels as an auxiliary method instead of the common “surface integral technique” for flow around complex geometries or shock wave flows. The results of this method are dependent on data collection vertex space, distance, and section size, where practical suggestions were made for each parameter in this research. Furthermore, the contribution of the pressure, momentum, and fluctuation terms in the total drag force were also evaluated at different cross sections. These findings can be implemented in wind tunnels with small test section length and also to compare the results obtained by the common surface integral method. Simulations were carried out at different aspect ratios at zero angles of attack, and the capabilities of this method at inclined flows were also discussed. The obtained results were also compared against the common method, and the results show only 4% deviation at zero angle.

Polymer branching and first normal stress differences in small‐amplitude oscillatory shear flow

AbstractGeneral rigid bead‐rod theory explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead‐rod theory, we relate the normal stress differences of polymeric liquids to the branch position on a backbone branched macromolecule. In this work, we explore the first normal stress differences coefficients of different axisymmetric polymer configurations. When non‐dimensionalized with the zero‐shear first normal stress difference coefficient, the normal stress differences depend solely on the dimensionless frequency. In this work, in this way, we compare and contrast the normal stress differences of macromolecular chains that are branched. We explore the effects of branch position, length, functionality, spacing, and multiplicity, along a straight chain, in addition to rings and star‐shaped macromolecules in small‐amplitude oscillatory shear flow.

The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses

In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A complete description of the problem is given by providing both the coordinates and masses of the bodies. We show furthermore how the three-equal-mass solutions are related to the general case in the coordinate space. The physical aspects of the configurations are also studied and discussed.

Optical Textures and Orientational Structures in Cholesteric Droplets with Conical Boundary Conditions.

Cholesteric droplets dispersed in polymer with conical boundary conditions have been studied. The director configurations are identified by the polarising microscopy technique. The axisymmetric twisted axial-bipolar configuration with the surface circular defect at the droplet’s equator is formed at the relative chirality parameter . The intermediate director configuration with the deformed circular defect is realised at , and the layer-like structure with the twisted surface defect loop is observed at . The cholesteric layers in the layer-like structure are slightly distorted although the cholesteric helix is untwisted.

Simulation of Primary Film Atomization in Prefilming Air-assisted Atomizer Using Volume-of-Fluid Method

We studied fuel atomization in an air-assisted atomizer of aircraft engine with volume-of-fluid method in microgravitation approximation under the conditions closer to the ones of the operating cruise mode. The problem was looked upon in a two-dimensional axisymmetric configuration, including the simulation of the swirl velocity and in a three-dimensional configuration. We found a drop-size distribution function and spatial distribution of kerosene in an atomizer, which was designed by the engineers from UEC-Aviadvigatel JSC. We have hypothesized the formula connecting the drop-size distribution function obtained in the three-dimensional configuration with the distribution function obtained in the two-dimensional configuration. Along with that, the spray half angles found in these configurations appeared to be the same, although, generally, there is a difference in spatial distribution of kerosene drops.

Microscopic description of axisymmetric vortices in P23 superfluids

We study quantized vortices in ${}^{3}P_{2}$ superfluids using a microscopic theory for the first time. The theory is based on the Eilenberger equation to determine the order parameters and the Bogoliubov-de Gennes (BdG) equation to obtain the eigenenergies and the core magnetization. Within axisymmetric vortex configurations, we find several stable and metastable vortex configurations which depend on the strength of a magnetic field, similar to a $v$ vortex and $o$ vortex in $^3$He superfluids. We demonstrate that the $o$ vortex is the most stable axisymmetric vortex in the presence of a strong magnetic field, and we find two zero-energy Majorana fermion bound states in the $o$-vortex core. We show that the profiles of the core magnetization calculated using the BdG equation are drastically different from those calculated using only the order parameter profiles known before.

Overview and comparison of approaches towards the planar restricted five-body problem with primaries forming an axisymmetric four-body central configuration

The aim of this paper is to present recent results on the restricted five-body problem where the primaries are located at a known central configuration having the $x$-axis as symmetry axis, so that two bodies with equal masses are situated symmetrically with respect to this axis. We firstly give an overview of the axisymmetric central configurations computed by Erdi and Czirjak (2016), as well as that where three bodies with equal masses are situated at the vertices of an equilateral triangle, while the fourth body lies at the center of the triangle. This last one bridges the gap between convex and concave four-body central configurations. After that, the characterization of the geometry of the restricted five-body problem families with these configurations are described, and the number and the evolution positions of equilibrium points, which depend on the mass parameters of the primaries, are compared.