Axisymmetric Body Research Articles

Smith–Watson–Topper Parameter in Partial Slip Bimodal Oscillations of Axisymmetric Elastic Contacts of Similar Materials: Influence of Load Protocol and Profile Geometry

Based on a very fast numerical procedure for the determination of the subsurface stress field beneath frictional contacts of axisymmetric elastic bodies under arbitrary 2D oblique loading, the contact mechanical influences of loading parameters and contact profile geometry on the Smith–Watson–Topper (SWT) fatigue crack initiation parameter in elastic fretting contacts with superimposed normal and tangential oscillations are studied in detail. The efficiency of the stress calculation allows for a comprehensive physical analysis of the multi-dimensional parameter space of influencing variables. It is found that a superimposed normal oscillation of the contact can significantly increase or decrease the SWT parameter, depending on the initial phase difference and frequency ratio between the normal and tangential oscillation. Written in proper non-dimensional variables, the rounded flat punch always exhibits smaller values of the SWT parameter, compared to a full paraboloid with the same curvature, while the truncated paraboloid exhibits larger values. A small superimposed profile waviness also significantly increased or decreased the SWT parameter, depending on the amplitude and wave length of the waviness. While both the load protocol and the profile geometry can significantly alter the SWT parameter, the coupling between both influencing factors is weak.

Post-Newtonian Orbital Effects Induced by the Mass Quadrupole and Spin Octupole Moments of an Axisymmetric Body

The post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an isolated, oblate spheroid of constant density that is rigidly and uniformly rotating on the motion of a test particle are analytically worked out for an arbitrary orbital configuration and without any preferred orientation of the body’s spin axis. The resulting expressions are specialized to the cases of (a) equatorial and (b) polar orbits. The opportunity offered by a hypothetical new spacecraft moving around Jupiter along a Juno-like highly elliptical, polar orbit to measure them is preliminarily studied. Although more difficult to be practically implemented, also the case of a less elliptical orbit is considered since it yields much larger figures for the relativistic effects of interest. The possibility of using the S-stars orbiting the supermassive black hole in Sgr A* at the Galactic Center as probes to potentially constrain some parameters of the predicted extended mass distribution surrounding the hole by means of the aforementioned orbital effects is briefly examined.

Wake dynamics in buoyancy-driven flows: Steady-state-Hopf-mode interaction with O(2) symmetry revisited.

We present a detailed mathematical study of a truncated normal form relevant to the bifurcations observed in wake flow past axisymmetric bodies, with and without thermal stratification. We employ abstract normal form analysis to identify possible bifurcations and the corresponding bifurcation diagrams in parameter space. The bifurcations and the bifurcation diagrams are interpreted in terms of symmetry considerations. Particular emphasis is placed on the presence of attracting robust heteroclinic cycles in certain parameter regimes. The normal form coefficients are computed for several examples of wake flows behind buoyant disks and spheres, and the resulting predictions compared with the results of direct numerical flow simulations. In general, satisfactory agreement is obtained.

Mathematical Model of Impact Projectile Flight Dynamics as an Element of its Digital Twin

This paper gives the analysis of the structure and characteristics of the mathematical model of the impact projectile’s flight dynamics. The model is designed for being used as an element of the projectile’s digital twin. The model is based on differential motion equations of a gyro-stabilized solid with an axisymmetric mass distribution. Different types of angle variables were chosen for describing aerodynamics and formulating equations of motion. Non-linear (considering the nutation angle) dependences for aerodynamic coefficients are proposed. They are created by applying proven scientific concepts and research methods in aerodynamics of axisymmetric body and by comparing with known numerical and experimental results obtained in exterior ballistics of gyro-stabilized aviation and artillery projectiles. Special aspects of initial conditions for angles and angular velocity were also studied. Since the impact projectile is considered as an axially symmetric body, its self-rotation angle is not of practical inte rest. Using algebraic manipulations, the differential equation for this angle was eliminated from the set of equations. This has made it possible to significantly reduce stiff of the remaining system of differential equations. The Dormand-Prince method is recommended as a method of numerical integration. The method of the eight-order (with seventh-order uncertainty estimate) allows getting the high accurate solution of the differential equations set under relatively small computing costs. The model allows computing the projectile trajectory under various initial conditions, including the flight with high nutation angles up to 87°—89°. As a result, there is a possibility to determine the nature of the interaction between impact projectiles and typical targets (ricochet, surface effect, after-penetration effect) within a wide range of approach angles to the target’s surface (skin) unattainable during the full-scale tests. The possibility of solving similar problems allows to recommend the designed model as an element of the impact projectile’s digital twin intended for testing its exterior ballistics on the digital (virtual) test range. All testing calculations and final modeling were made by using the "GNU Octave" computational software package.

Numerical investigation of the natural transition in boundary layers on underwater axisymmetric bodies with superhydrophobic surfaces

The natural transition in boundary layers on axisymmetric bodies with superhydrophobic surfaces is studied using numerical methods. By boundary layer, we mean the boundary layer around the forebody and around the parallel body of an underwater vehicle. A method of calculating basic laminar flows on axisymmetric bodies with superhydrophobic curved surfaces is proposed, and a method of linear stability analysis for the boundary layers that considers the slip-velocity boundary condition for small disturbances is established. The eN method is used to predict the transition locations of the boundary layers. On a superhydrophobic surface, the slip velocity on the wall increases and then decreases along the streamwise direction, resulting in a maximum value at the forebody. The boundary layer thickness on a superhydrophobic surface becomes smaller than that on an ordinary surface. The superhydrophobic surface stabilizes the boundary layer and thus delays the natural transition. As the slip length on the superhydrophobic surface increases, the unstable zone shrinks, and the transition location moves further downstream, indicating that the delay effect of the superhydrophobic surfaces becomes stronger. As the oncoming flow velocity increases, the transition location on the superhydrophobic surface moves upstream and then downstream, leading to a “dangerous” velocity, at which the transition location is closest to the leading edge. The underlying mechanism of the dangerous velocity phenomenon is discussed: An increasing velocity has both stabilizing effect and destabilizing effect on the boundary layer.

Measurements of steady manoeuvring forces and moments over an axisymmetric body with appendages in a wind tunnel

ABSTRACT Steady manoeuvring forces and moments over a generic submarine hull form (SUBOFF) at various angles of incidence were investigated through scaled model tests in the Wind Tunnel Facility at the Naval Science and Technological Laboratory, India. Measurements were performed for a range of angles of incidence in angle of attack (±18°) and drift (±18°) including control surface deflections (±15°) on a 1.372 m model at Reynolds number 1.7 × 106. The present study at angles of incidence is to gather steady-state force, and moment data and validate such load measurements performed in a Wind Tunnel. The particulars of the SUBOFF model, experimental facility and measurement technique, test results for load measurements and estimated hydrodynamic coefficients are highlighted in the paper. The measurement data generated from the above studies will complement the current research on hydrodynamic characteristics for submerged bodies both computationally and experimentally.

Flow pattern regime and unsteady characteristics of ventilated cavitating flow around the axisymmetric bodies with different headforms

This paper presents an experimental investigation of the flow pattern regime and unsteady characteristics of ventilated cavities with different headform shapes. The test model consists of a removable headform with three different forebodies (the conical, the blunt, and the hemispherical) and a common cylinder rear body. Experiments are conducted in a closed-loop cavitation tunnel. First, the flow pattern regimes on the ventilated cavity for different headforms are discussed in detail, and the dimensions of several flow patterns are measured. The results show that the cavity dimension and the regime are strongly dependent on the headform shape, and all typical flow patterns are introduced by schematic illustrations. Second, the ventilation hysteresis that happened during the flow pattern transition is pointed out. A quantitative gas leakage model is employed to explain the cause of hysteresis and flow pattern transition, and the results show the Strouhal number for different headforms is approximately ∼0.21. However, the blunt presented stronger gas leakage with a large constant parameter, K = 0.80. Finally, the unsteady characteristics of the ventilated cavity around different tested headforms are involved through descriptions of developments of the recirculating vortex and transparent cavity. In addition, an estimated cavitation number is applied to investigate the unsteady characteristics, and the maximum cavitation number and the strongest characteristic are obtained by the blunt headform due to the large drag coefficient and strong flow separation.

Numerical analysis of turbulent fluctuations around an axisymmetric body of revolution based on wall-modeled large eddy simulations

Numerical analysis of turbulent fluctuations around an axisymmetric body of revolution based on wall-modeled large eddy simulations

Global optimization of underwater vehicle hull shape on flow resistance

For underwater vehicle with axisymmetric revolution body, the hull shape in the rotation axis section is the key issue on flow resistance. In this paper, we propose to use the elliptic Fourier descriptors for arbitrary hull shape modeling. By doing so, we can achieve global optimization of underwater vehicle hull shape on flow resistance. Experimental results using the computational fluid dynamics show superior improvement compared to the extensive used Myring shape with only first order elliptic Fourier descriptors under the same displacement constraint. In addition, the proposed method can be easily extend to the global optimization on flow noise.

Universal law of skin-friction coefficient in a fully developed zero pressure gradient axisymmetric turbulent boundary layer flow

Understanding the skin friction in an axisymmetric turbulent boundary layer (ATBL) flow is a key to designing and optimising the flow past axisymmetric bodies, for example, a rocket engine nozzle and a submarine hull. In this study, we propose a universal law of the skin-friction coefficient in an ATBL flow. The flow is steady and fully developed with a zero pressure gradient. The governing equation for the ATBL flow is derived by methodically applying the boundary layer approximation. Subsequently, the scaling law of the Reynolds shear stress, caused by turbulent eddies, at the surface tangential to the wall roughness summits is derived by incorporating the role of transverse curvature. The skin-friction coefficient in a smooth ATBL flow is found to depend on two parameters, namely, the Reynolds number based on the cylinder radius, Rea, and the ratio of boundary layer thickness to cylinder radius, δ/a. The analysis predicts a simple form of the skin-friction coefficient as ${C_f} = 4.56 \times {10^{ - 2}}{[R{e_a}\ln (1 + \delta /a)]^{ - 1/4}}$ , which agrees satisfactorily with the available experimental data and the numerical simulations in all the axisymmetric flow regimes. The proposed law, in the limit of infinite radius, is consistent with the classical law of the skin-friction coefficient in a plane turbulent boundary layer flow as ${C_{f0}}\sim Re_\delta ^{ - 1/4}$ , where Reδ is the Reynolds number based on the boundary layer thickness. This study reveals that, for δ/a < 1, the relative skin-friction coefficient, $({C_f} - {C_{f0}})/{C_{f0}}$ , follows a linear law with δ $/$ a.

Locomotion performance of an axisymmetric ‘flapping fin’

Inspired by the jet-propulsion mechanism of aquatic creatures such as sea salps, a novel locomotion system based on an axisymmetric body design is proposed. This system consists of an empty tube with two ends open. When the diameters of the front and back openings are changed periodically, the forward-backward symmetry is broken so that the system starts swimming. Viewed within a cross section, this system resembles a two-dimensional flapping fin with its leading edge located at the front opening and the trailing edge at the back opening. The feasibility of this system has been proven via numerical simulations using a fluid-structure interaction model based on the immersed-boundary framework. According to the results, at relatively low Reynolds number (O(102)), this simple locomotion method can easily achieve a mean swimming speed of 2 to 3 body lengths per deformation period. Further simulations illustrate the following characteristics: (1) within the chamber, the hydrodynamic interactions among different parts of the body leads to a performance-enhancing mechanism similar to the ground effect; (2) reducing the diameter of the body can strengthen this effect so that both the swimming speed and the energy efficiency are improved; (3) for better performance the amplitude of diameter oscillation at the trailing edge should be larger or at least equal to the one at the leading edge.

Analytical closed-form solution of the Navier–Stokes equations for the aerodynamic near-field and sonic boom from axisymmetric bodies

An analytical closed-form solution is presented for the aerodynamic near-field and ground signature from an axisymmetric body with a low thickness ratio. The Navier–Stokes equations are formulated as a boundary value problem that incorporates the incoming ambient flow-field and the aerodynamic properties on the body surface. The shape of the aerodynamic body is defined as a product of generalized functions. A direct solution for the density of the aerodynamic near-field, represented as a function of both space and time, is proposed through the integration of the Navier–Stokes equations in a generalized functional form. Pressure, temperature, velocity, and Mach number are then derived in the near-field. The methodology, being fully nonlinear, surpasses the traditional F-function, impulse, and hypersonic similarity theories originally developed for near-field prediction. The presentation outlines the major steps in deriving the analytical solution and provides predictions from an aerodynamic body in the near-field, along with the associated ground signature. The methodology is focused on aerodynamic bodies operating at high-speeds, ranging from the supersonic to the hypersonic regime. [Work supported by the Defense Advanced Research Project Agency, under Grant No. W911NF-21-1-0342.]

Efficient post-processing of electromagnetic plane wave simulations to model arbitrary structured beams incident on axisymmetric structures

The study of an optical beam interacting with material structures is a fundamental of nanophotonics. Computational electromagnetic solvers facilitate the rapid calculation of the scattering from material structures with arbitrary geometry and complexity, but have limited efficiency when employing structured excitation fields. We have developed a post-processing method and package that can efficiently calculate the full three-dimensional electric and magnetic fields for any optical beam incident on a particle or structure with at least one axis of continuous rotational symmetry, called an axisymmetric body (such as a sphere, cylinder, cone, torus or surface). Provided an initial batch of plane wave simulations is computed, this open-source package combines data from computational electromagnetic solvers in a post-processing fashion using the angular spectrum representation to create arbitrarily structured beams, including vector vortex beams. Any and all possible incident beams can be generated from the initial batch of PWSs, without the need for further simulations. This allows for efficiently performing parameter sweeps such as changing the angle of illumination or translating the particle position relative to the beam, all in post-processing, with no need for additional time-consuming simulations. We demonstrate some applications by numerically calculating optical force and torque maps for a spherical plasmonic nanoparticle in a tightly focused Gaussian beam, a plasmonic nanocone in an azimuthally polarised beam and compute the fields of a non-paraxial Laguerre–Gaussian vortex beam reflecting on a multilayered surface. We believe this package, called BEAMS, is a valuable tool for rapidly quantifying electromagnetic systems that are beyond traditional analytical methods.

Theoretical analysis of convective transport over a slender body of revolution

The study of thermal transport in the laminar boundary layer had been a great area of research since long ago because of its practical necessity in different fields of engineering such as aerodynamics, electronics cooling, designing of turbine blades, etc. The primary goal of the research has always been to look into geometries or shapes that have higher heat transfer rates but a less viscous drag. This is also a topic of fundamental interest to the aerospace industry. For this purpose, a cone-shaped body of revolution has been considered. Such geometries are chosen due to their wider acceptance in modern aerodynamics, with their enhanced heat transfer rates and lower aerodynamic drag. In this connection, axisymmetric bodies of revolution having different body contours and involving surface transverse curvature are usually considered. The selection of such a curved body and the imposed particular type of momentum and thermal boundary conditions make the problem of non-similar nature. Such kinds of problems are normally dealt with by an implicit finite difference scheme due to the accuracy of the solution. The current problem has also been solved with the same numerical scheme. It is concluded that a more streamlined body of revolution has a less spread of velocity and temperature within the boundary layer with a large heat transfer rate and wall skin-friction. On the other hand, the parabolic body of revolution has a large distribution of velocity and temperature but less heat transfer rate and wall skin-friction. Moreover, the assisting role of surface transverse curvature on temperature distribution and wall skin-friction has also been observed in this study.

Intermittent behavior of a bypass transition of boundary layers over an axisymmetric body of revolution

A transitional boundary layer developing over the forebody of a SUBOFF model subject to high free-stream turbulence (FST) was experimentally measured using both laser induced fluorescence and time-resolved two-dimensional particle image velocimetry. Typical coherent structures in the bypass transition, including low-speed streaks, hairpin-like vortices and vortex packets, are clearly visualized. Continue wavelet transform analysis on the time-frequency characteristics of instantaneous Reynolds shear stress (RSS) indicates that the intermittent behavior is mainly confined in mild-to-high-frequency domain, whereas low-frequency component is attributed to the Klebanoff mode. A wavelet-based approach was proposed to detect multi-scale turbulent events from wavelet coefficients of RSS, and the spatial evolution of the multi-scale intermittency factor was then calculated. Furthermore, the conditional sampling of laminar and turbulence events provides a new perspective on the route of the disturbance growth in the bypass transition. It is clearly shown that FST-introduced disturbances with moderate-to-high frequency are unable to penetrate the near-wall region; meanwhile, multi-scale characteristics inside the boundary layer evolve spontaneously from the Klebanoff mode.

The dynamic analysis of axisymmetric bodies with damping effects using the modified radial integration boundary elements method (MRIBEM)

This paper investigates the elastodynamic analysis of axisymmetric bodies under axisymmetric dynamic loads using the modified radial integration boundary elements method (MRIBEM). Purposely, the governing integral equations have been developed in cylindrical coordinates by employing the three-dimensional (3D) static fundamental solution. The axisymmetric bodies can be modeled as a two-dimensional (2D) problem, which is much simpler than 3D analysis and only requires a one-dimensional boundary mesh. In the proposed formulation, the effects of inertial and damping forces appear as 2D domain integrals. The domain variables are approximated using global radial basis functions (RBFs), and the modified radial integration method (MRIM) is employed to deal with the domain integral as the main idea of the present research. Various sample problems are provided in order to illustrate the capability of the presented method for analyzing axisymmetric bodies with concave geometry and damping effect under different types of transient loads. The Newmark and Houbolt methods were applied for time marching, and their efficiency was examined. The results of the present study were also validated by the axisymmetric FEM formulation and other available references.

Extensions to the theorems of Pappus to determine the centroids of solids and surfaces of revolution

Extensions to the first and second theorems of Pappus are presented, whereby the centroid of a surface or solid of revolution can be determined using only the geometric properties of the generating plane curve or figure and the arc of revolution. The derivations are well suited to first-year-level courses in mathematics and engineering. From a didactic perspective, the resulting formulas are simple to apply, especially since the required geometric properties are typically available in standard tables of plane sections or relatively routine to derive. Furthermore, the formulas provide a general scaffold for students to attempt problems involving axisymmetric bodies while also reinforcing and embedding their knowledge of the properties of the generating plane shapes. A selection of illustrative problems is discussed that are generally regarded to be challenging for introductory mechanics courses but for which the formulas derived in this article provide straightforward solutions.

Experimental Determination of Drag Constant for Slow Moving Axisymmetric Bodies

A body moving through a fluid experiences drag, which primarily consists of two components: form drag and viscous drag. At high velocities, the form drag predominates whereas at low velocities, the viscous drag predominates. The form drag is characterized by the drag coefficient which is determined experimentally for various configurations. Similarly, the viscous drag is characterized by the drag constant which in turn is known only for specific cases and its generic governing model is not well established yet. The current study puts forward a generalized mathematical model for determination of the drag constant for frontally streamlined small axisymmetric bodies moving slowly through a fully-enclosing fluid at zero angle of attack. It has been accomplished by establishing a governing mathematical model for viscous drag, validating it via wind tunnel experiments and then comparing it with the standard linear drag equation. Conclusively, the drag constant has been determined in terms of the fluid properties and dimensions of the moving body. This paper describes the above-mentioned mathematical model followed by the process of its experimental validation and determination of drag constant.

The use of FFT algorithm for circumferential coordinate in axisymmetric analysis of solids by generalized finite difference method

A formulation is presented for GFDM analysis of axisymmetric viscoelastic bodies under general loading conditions. The proposed formulation reduces the dimension of analysis by one by using complex Fourier series for circumferential coordinate ((θ) dependency) of field variables. For θ (Fourier) transform computations, the discrete Fourier transform formulas with FFT algorithm are employed. Radiational effects are accounted for through the use of perfectly matched layer (PML) with the equation being modified in accordance with the proposed formulation. For the assessment of the formulation, several sample problems are presented. The results indicate its capability in estimating the response even for that requiring sensitive analysis, such as, those in wave propagation analysis.

Forebody Articulation at High Angles of Incidence

An experimental investigation was carried out to understand the effect of forebody articulation on the aerodynamic characteristics and the flowfield development over a slender body at high angles of incidence. The experiments were carried out at the Florida A&M University and Florida State University low-speed wind tunnel over a range of forebody deflection (, , and ) and flow conditions. The results show that a positive forebody deflection increases the normal-force coefficient, whereas a negative forebody deflection decreases the normal-force coefficient at high angles of incidence. Pitching moment characteristics showed that all forebody deflections tested produce a pitching moment despite minimal normal force at low angles of incidence. Lateral aerodynamic characteristics showed that the side-force onset angle does not solely depend on the semi-apex angle of the forebody (as predicted for axisymmetric slender bodies), and the role of the forebody-to-aftbody transition geometry in initiating vortex asymmetry is equally important. The particle image velocimetry results show that a positive forebody deflection increases the size, strength, and circulation of the vortices developing on the body, leading to an increase in aerodynamic forces and moments. The flowfield development for a negative forebody deflection is dominated by secondary shear-layer vortices originating from the forebody to aftbody junction.