Axisymmetric Shape Research Articles

Numerical model and analysis of heat transfer during microjets array impingement

In this paper heat and fluid flow characteristics during impingement of an array of microjets was numerically investigated. The numerical model which was based on the compressible steady-state Navier-Stokes equations and SST k-ω turbulence model was developed. Then an array of 8 × 8 microjets which impinged on a hot surface was analyzed. The influence of both a ratio of a distance between a nozzle and hot plate (H/d) as well as a microjet diameter-based Reynolds number (Red) on both the local and average temperature and heat transfer coefficient (HTC) on the surface of the hot plate were numerically studied. During simulations the ratio of the distance between the nozzle and hot plate to the microjet diameter was H/d = 3.125, 25 and 50, while the microjet diameter-based Reynolds number was equal to Red = 690, 1100 and 1510. It was found that the H/d ratio and Red significantly influenced flow patterns in the gap between the nozzle and hot plate as well as the temperature and HTC on the surface of the hot plate. With increase of the H/d ratio a more uniform distributions of the plate temperature and HTC were observed. Moreover, differences between extreme values of these parameters decreased. The optimal ratio of the distance between the nozzle and hot plate to the microjet diameter was calculated to be H/d = 25. Increasing or decreasing of this ratio resulted in the higher average temperatures and lower average values of the HTC on the hot plate. For the small value of the H/d ratio (i.e., H/d = 3.125) the influence of the microjet flow on adjacent microjets was vestigial. The area of the hot plate which was influenced by impinging microjets was small and degradation of the microjet velocity profile was negligible, i.e., high-speed microjets impinged the plate. Air from the microjet flowed above the hot plate and left the zone through spaces between adjacent microjets. For higher values of the H/d ratio influence of the microjet flow on adjacent microjets was observed. The microjet left the nozzle and greatly expanded, while its velocity profile was degraded. The area of the hot plate which was influenced by impinging microjets was large and the microjet velocity was low. Due to significant enlargement of the size of the microjet, it interacted with adjacent microjets, which resulted in the lost of their axisymmetric shape. Moreover, air from the microjet flowed above the hot plate and affected adjacent microjets. The rise in the Red intensified mentioned effects as well as heat transfer intensity on the hot plate. Moreover, the increase of the Red resulted in the decrease of the average temperature of the heater surface as well as the increase of the average HTC regardless the height of the microjet. Calculated average hot plate temperatures were also compered with experimentally measured temperatures and the good matching was found. However, much slower degradation of microjet profiles was observed in experiments than predicted numerically.

Deformation Dynamics of Giant Unilamellar Vesicles in the Large Surface-to-Volume Ratio Regime: The Emergence of Neuron-like Morphology.

Deformation of liposomes, or lipid vesicles, has been investigated extensively in terms of the thermodynamic equilibrium of the bending energy of the lipid bilayer membrane. However, the range of such deformation in previous literature has been limited within the moderate surface-to-volume ratio of the vesicles, in which axisymmetric shapes are dominant. Here, we show that neuron-like morphology, in which many lipid tubes extend radially from the mother vesicle, becomes dominant upon the slow osmotic shrinkage of giant unilamellar vesicles (GUVs) initially larger than several tens of micrometers. We show that, in the time-lapse confocal imaging, the emergence of lipid tubes is initiated from the instability that appeared along the annular rim of the flat stomatocyte shape. Since these deformation dynamics into the neuron-like morphology resemble that of the milk-crown formation in liquid splashing, we discuss that the Rayleigh-Plateau capillary instability drives this transformation into a nonaxisymmetric shape.

The Shape of Mercury's Magnetopause: The Picture From MESSENGER Magnetometer Observations and Future Prospects for BepiColombo

AbstractThe MErcury Surface, Space Environment, GEochemistry, and Ranging (MESSENGER) spacecraft orbited Mercury between March 2011 and April 2015, typically passing through the magnetosphere, magnetosheath, and interplanetary magnetic field, on each orbit. Using data from the Magnetometer, we identify magnetopause crossings for the complete orbital mission and model the average boundary shape. We find that Mercury's average magnetopause is well modeled by both an axisymmetric shape and a three‐dimensional shape containing indentations in the cusp regions and a magnetotail that is wider in the north‐south versus east‐west direction. Examination of MESSENGER data and the use of simulated crossings show that coverage is very limited in the cusp region. Parameters describing the indentation are poorly constrained, and model fits may be biased due to the combination of orbital geometry and magnetospheric dynamics. The distribution of MESSENGER data inside the magnetopause, together with minimum variance analysis of a representative subset of magnetopause crossings, hints at the presence of a cusp indentation, though likely shallower than that estimated from the observed crossing positions. The BepiColombo spacecraft will arrive at Mercury in 2025. We simulate expected data coverage and magnetopause crossings using both axisymmetric and three‐dimensional magnetopause models. BepiColombo will improve our understanding of the magnetopause shape by providing data over the southern hemisphere and regions of the northern cusp indentation not covered by MESSENGER. There is also the potential for simultaneous measurements of the interplanetary magnetic field and magnetopause position.

An ALE method for simulations of axisymmetric elastic surfaces in flow

SummaryThe dynamics of membranes, shells, and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface, which exhibits an elastic response to in‐plane stretching and out‐of‐plane bending, possibly accompanied by a surface tension force. In this work, we present a novel arbitrary Lagrangian‐Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier‐Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can, therefore, be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions, which are present in a wide range of biophysical problems. We formulate axisymmetric elastic surface forces and propose a discretization with surface finite‐differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. We show in several numerical test cases that accurate results can be achieved at computational times on the order of minutes on a single core CPU. We demonstrate two state‐of‐the‐art applications which to our knowledge cannot be simulated with any other numerical method so far: we present first simulations of the observed shape oscillations of novel microswimming shells and the uniaxial compression of the cortex of a biological cell during an AFM experiment.

Influence of Geometric Features of the Peripheral Part of the Thin-Walled Spherical Segment on the Explosive Throwing Process

The main factors controlling the formation of the stern of explosively formed projectiles are investigated using numerical calculations in a three-dimensional formulation of a problem. To form folds in the stern, it is proposed to use thin-walled spherical segments with a peripheral thickness deviation in terms of decreasing or increasing with respect to the thickness in the central part. The configurations of explosively formed projectiles with inclined folds in the stern are shown, and it is proposed to describe the fold inclination by two angles of its position. The effect of folds in the stern on the change in aerodynamic coefficients for a wide range of angle of attack is numerically studied. The angular velocity of the axial rotation of explosively formed projectiles with inclined folds in the stern is estimated based on the Newton method and considering the angles of its position. The results obtained are of interest to specialists working in the field of physics of explosion and high-speed impact, as well as those dealing with aerodynamics of aircrafts, mainly of axisymmetric shape

Asymmetric spinning for offset blanks

Various approaches have been attempted by researchers to break through the limitation of axisymmetric shape in metal spinning. In this study, a synchronous multipass spinning method for offset blanks is proposed. The motion of the roller and the rotation of the mandrel are synchronized to achieve asymmetric shapes. The roller trajectory is represented by a set of scattered data which contains the axial position of the roller, the radial position of the roller, and the rotational angle of the mandrel. Conventional spinning for offset blanks is also conducted in comparison with synchronous spinning. The geometries of the products with different offset values λ are examined. The axial distribution of wall thickness varies at different circumferential positions of the product due to the oblique shape. The thickness increases from the short side to the long side of the product. A larger offset value λ results in a larger product diameter due to the springback of the material. Forming limits in terms of roller feed ratio f, offset value λ, blank thickness t0, blank diameter D, and the number of passes are investigated. Both fracture and wrinkling occur in the experiments. Due to the oblique shape, wrinkling tends to occur during the first several passes on the long side of the flange, and fracture tends to occur during the last several passes on the long side of the product. The experiments are more likely to succeed when a small offset ratio λ, a small blank diameter D, a small feed ratio f, or a large blank thickness t0 is used. Compared with synchronous spinning, the difference between the axial thickness distributions on both sides of the product is smaller in conventional spinning due to the uniform feed ratio. In terms of forming limits, conventional spinning has a slightly better performance.

Experimental and numerical investigation on the shape approximation of rice particle by multi-sphere particle models

In this study experimental and numerical investigations on the mechanical and flow behavior of the multi-sphere (MS) rice particles with different degrees of shape approximation are conducted. This work aims to provide a better understanding of the adaptability of the degree of the shape approximation. The results indicated that rice particles can be approximated using the MS models with axi-symmetric ellipsoid shape. Furthermore, the angularity factor, AF, can be used to quantify the degree of shape approximation. As AF decreases, the degree of shape approximation increases. Finally, selection of the shape approximation scheme depends on the application of granular materials. Specifically, for the static and dynamic mechanical behavior of the single particle, the degree of shape approximation should not be strictly accurate, but should be appropriately rough. However, for the static and dynamic flow behavior of the particle assembly, the degree of shape approximation should be accurate.

A Study of Secular Perturbations of Translational-Rotational Motion in a Nonstationary Two-Body Problem Using Computer Algebra

A nonstationary two-body problem is considered such that one of the bodies has a spherically symmetric density distribution and is central, while the other one is a satellite with axisymmetric dynamical structure, shape, and variable oblateness. Newton’s interaction force is characterized by an approximate expression of the force function up to the second harmonic. The body masses vary isotropically at different rates. Equations of motion of the satellite in a relative system of coordinates are derived. The problem is studied by the methods of perturbation theory. Equations of secular perturbations of the translational-rotational motion of the satellite in analogues of Delaunay–Andoyer osculating elements are deduced. All necessary symbolic computations are performed using the Wolfram Mathematica computer algebra system.

Raising by spinning

Industrial metal spinning depends on costly trial-and-error when introducing new products. However, a recently developed flexible spinning setup allows a new form of process operation similar to raising by hammering: two rollers on either side of the rotating workpiece apply a couple to deform it locally whilst moving towards its edge. This paper presents this configuration for the first time and develops and verifies an upper bound yield-line model to design stable tool-paths that avoid wrinkling. Raising by spinning is shown to be feasible and more stable than conventional spinning, paving the way for automatic production of deep axisymmetric shapes.

Constrained multiobjective shape optimization of superconducting rf cavities considering robustness against geometric perturbations

High current storage rings, such as the Z-pole operating mode of the FCC-ee, require accelerating cavities that are optimized with respect to both the fundamental mode and the higher order modes. Furthermore, the cavity shape needs to be robust against geometric perturbations which could, for example, arise from manufacturing inaccuracies or harsh operating conditions at cryogenic temperatures. This leads to a constrained multi-objective shape optimization problem which is computationally expensive even for axisymmetric cavity shapes. In order to decrease the computation cost, a global sensitivity analysis is performed and its results are used to reduce the search space and redefine the objective functions. A massively parallel implementation of an evolutionary algorithm, combined with a fast axisymmetric Maxwell eigensolver and a frequency-tuning method is used to find an approximation of the Pareto front. The computed Pareto front approximation and a cavity shape with desired properties are shown. Further, the approach is generalized and applied to another type of cavity.

Shape and maximum volume of static holdup in between two vertical spheres: A modeling study

Static liquid holdup is one of the important parameters in packed bed operations. Packed bed can be fundamentally imagined as an aggregate of two-sphere contacts and liquid is potentially held at the contact points. Between two vertical spheres, existing literature report maximum volume of films either as the geometric limit while solving Young-Laplace equation or the stability limit of static liquid holdup in the presence of asymmetric perturbation. However, it is of fundamental interest to find out the maximum limit of stability of the liquid without any asymmetric perturbation. This work shows a limit, below the geometrical limit of the system, beyond which liquid cannot be stable due to the gravitational force. Axisymmetric film shapes of a given volume, derived using Young- Laplace equation with different boundary conditions, are tested with total energy minimization principle to define the stability limit. Further, a correlation for maximum static liquid holdup is reported with respect to a modified Bond number.

In-Vitro Simulation of the Blood Flow in an Axisymmetric Abdominal Aortic Aneurysm

We investigated the blood flow patterns and the hemodynamics associated with an abdominal aortic aneurysm detected in an in vitro measurement campaign performed in a laboratory model of an aneurysm with rigid walls and an axisymmetric shape. Experiments were run in steady flow conditions and by varying the Reynolds number in the range 410 < Re < 2650. High spatial and temporal resolution 2D optical measurements of the velocity field were obtained through a particle tracking technique known as Hybrid Lagrangian Particle Tracking. Conversely to classical Particle Image Velocimetry, both the fluid particle trajectories and the instantaneous and time-averaged velocity fields are provided without constraints on the grid size and very close to the vessel boundary. All the most relevant quantities needed to investigate the flow features were evaluated, and in particular, we focused on the wall shear stress distribution both in the healthy aortic portion and within the aneurysm. Results show that the recirculation zone in correspondence of the cavity moves downstream, and this displacement is found to increase with Re. Very low wall shear stress values are recovered in correspondence of the aneurysmal cavity, while a sharp peak occurs in correspondence of the reattachment point. In agreement with the literature data, the peak value is found to decrease with Re and to be about equal to twice the upstream value.

Global stability analysis of axisymmetric boundary layer: Effect of axisymmetric forebody shapes

This paper presents the effect of axisymmetric forebody shapes on the global stability characteristics of axisymmetric boundary layer developed on a circular cylinder. Axisymmetric forebodies like sharp-cone, ellipsoid, and paraboloid with a fineness ratio (FR) of 2.5, 5.0 and 7.5 are considered. The boundary layer starts to develop at a stagnation point on the forebody geometry and grows in spatial directions. The inflow velocity component is parallel to the axis of the cylinder, and hence the angle of attack is zero. The base flow is axisymmetric, non-parallel and non-similar. The linearised Navier–Stokes equations are derived in the cylindrical polar coordinates for the disturbance flow components. The discretised linearised Navier–Stokes equations along with appropriate boundary conditions form a general eigenvalue problem and it has been solved using Arnoldi’s algorithm. The global temporal modes have been computed by solving the two-dimensional eigenvalue problem. The extent of a favourable pressure gradient developed in streamwise direction depends on the shape of axisymmetric forebody. The temporal and spatial growth of the disturbances has been computed for axisymmetric ($$N = 0$$) mode for different Reynolds numbers (Re). The forebody shapes have a significant effect on the base flow and stability characteristics at low Re.

Measurement of the microlayer characteristics in the whole range of nucleate boiling for water by laser interferometry

During nucleate boiling, a thin liquid film (microlayer) is formed beneath a boiling bubble when the bubble undergoes rapid growth/expansion. The linear distribution of the microlayer has been previously confirmed, and its crest shape has been observed in the isolated bubble region of nucleate boiling. However, the microlayer behavior in larger heat flux regions up to critical heat flux has not yet been elucidated. In this study, to further understand the microlayer structure in the whole heat flux range of nucleate boiling, microlayer configuration was measured using laser interferometry. Water was adopted as the test fluid, and it is confirmed that the microlayer can be observed over a whole range of nucleate boiling containing the critical heat flux point. It is also confirmed that the deformation of the microlayer from axisymmetric shape was caused by complicated, irregular bubble motions such as bubble coalescence, which was observed for relatively higher heat flux. The crest shape of the microlayer, which appears near the periphery of its maximum diameter under relatively smaller heat flux, was not observed at a relatively higher heat flux. Finally, it is confirmed that heat flux does not obviously influence the thickness distribution of the initial microlayer.

Parametric Method Applicable in Calculating Breakout Force and Time for Lifting Axisymmetric Objects from Seabed

Abstract The issue of calculating parameters for lifting objects of axisymmetric shapes from the seabed is studied. The article presents the results of numerical simulation examination of the equation formulated by Foda for the force needed to extricate the object from the seabed depending on soil and water parameters, extrication speed, and object diameter. The simulations were performed within the range of parameters characteristic for real applications, and their results were used for deriving approximate algebraic formulas applicable in engineering practice of lifting objects resting on seabed.

Assessment of deformation of human red blood cells in flow cytometry: measurement and simulation of bimodal forward scatter distributions.

Light scattering by single cells is widely applied for flow cytometric differentiation of cells. However, even for human red blood cells (RBCs), which can be modeled as homogeneous dielectric particles, the potential of light scattering is not yet fully exploited. We developed a dedicated flow cytometer to simultaneously observe the forward scattering cross section (FSC) of RBCs for orthogonal laser beams with incident wave vectors and . At a wavelength , bimodal distributions are observed in two-dimensional dot plots of FSC( ) vs. FSC( ), which result from the RBCs' random orientation around the direction of flow, as well as from the distributions of their size and their optical properties. Typically, signals of RBCs were analyzed. We actively oriented the cells in the cytometer to prove that orientation is the main cause of bimodality. In addition, we studied the wavelength dependence of FSC( ) using and 632.8 nm, covering both weak and strong light absorption by the RBCs. Simulations of the light scattering by single RBCs were performed using the discrete dipole approximation (DDA) for a range of sizes, orientations and optical properties to obtain FSC distributions from RBC ensembles. Using the axisymmetric biconcave equilibrium shape of native RBCs, the experimentally observed distributions cannot be reproduced. If, however, an elongated shape model is employed that accounts for the stretching of the cell by hydrodynamic forces in the cytometer, the features of the strongly bimodal measured frequency distributions are reproduced by the simulation. Elongation ratios significantly greater than 1 in the range of 1.5 to 2.5 yield the best agreement between experiments and simulated data.

Raindrop shapes and fall velocities in “turbulent times”

Abstract. Raindrop shapes and fall velocities measured by 2-dimensional video disdrometer are presented for 2 high-wind/turbulent events. The shapes were reconstructed using a relatively new technique. 10 m height wind sensor data are used to derive proxy-indicators for turbulent intensities. Our results show strong gusts, directional wind shifts (i.e. shear) and/or inferred high turbulence intensity are correlated with reduced fall speeds, reaching values ∼25 %–30 % less than the expected values, i.e. sub-terminal fall speeds. Significant percentage (20 %–35 %) of asymmetric drops (> 2 mm) deviating from the most probable axisymmetric shapes were also detected for some events with high turbulent intensities.

An Enhanced Axisymmetric Solid Element for Rotor Dynamic Model Improvement

Abstract The authors present an improved formulation for the axisymmetric solid harmonic finite element (FE) modeling of a flexible, spinning rotor. A thorough comparison of beam-type FE and axisymmetric solid FE rotor models is presented, indicating the errors that result from beam FE usage for various nondimensional rotor topologies. The axisymmetric rotor is meshed in only two dimensions: axial and radial, with both displacement fields being represented with Fourier series expansions. Centrifugal stress-stiffening and spin-softening effects are included in all elements and most importantly in modeling flexible disks. Beam FE and axisymmetric FE natural frequencies, mode shapes, and critical speeds are compared to identify shaft geometries where the beam model yields a significant error. Finally, limitations of beam FE models and guidance for utilizing axisymmetric solid FE models in rotor dynamic simulations are provided.

Solution to a three-dimensional axisymmetric inverse electromagnetic casting problem

ABSTRACTA new method based on topology optimization is proposed for solving a three-dimensional axisymmetric inverse problem regarding the configuration of electric currents used in the electromagnetic casting technique of the metallurgical industry. These electric currents must generate an electromagnetic field such that when certain mass of liquid metal is placed in the field it levitates acquiring a predefined axisymmetric shape. The method proposed is able to obtain a suitable configuration of electric currents, and is very attractive from the computational point of view, since it is based on a sparse convex quadratic programming formulation for which there are very efficient interior-point solution algorithms.

Design and simulation of the snowflake divertor control for NSTX–U

This paper presents the development of a physics-based multiple-input-multiple-output algorithm for real-time feedback control of snowflake divertor (SFD) configurations on the National Spherical Torus eXperiment Upgrade (NSTX–U). A model of the SFD configuration response to applied voltages on the divertor control coils is first derived and then used, in conjunction with multivariable control synthesis techniques, to design an optimal state feedback controller for the configuration. To demonstrate the capabilities of the controller, a nonlinear simulator for axisymmetric shape control was developed for NSTX–U which simultaneously evolves the currents in poloidal field coils based upon a set of feedback-computed voltage commands, calculates the induced currents in passive conducting structures, and updates the plasma equilibrium by solving the free-boundary Grad–Shafranov problem. Closed-loop simulations demonstrate that the algorithm enables controlled operations in a variety of SFD configurations and provides capabilities for accurate tracking of time-dependent target trajectories for the divertor geometry. In particular, simulation results suggest that a time-varying controller which can properly account for the evolving SFD dynamical response is not only desirable but necessary for achieving acceptable control performance. The algorithm presented in this paper has been implemented in the NSTX–U Plasma Control System in preparation for future control and divertor physics experiments.