Axisymmetric Body Research Articles

Exponentially convergent numerical scheme for the stream function of potential flow over axisymmetric bodies

A boundary element scheme for the problem of potential flow over an axisymmetric toroidal body is considered. An integral equation for the velocity distribution on the body is derived. It is shown that the numerical scheme for solving the considered equation converges exponentially.

Non-equilibrium turbulent boundary layers in high reynolds number flow at incompressible conditions: effects of streamline curvature and three dimensionality

The physics and computational prediction of turbulent boundary layer flow over axisymmetric and three-dimensional bodies are examined. Three cases were considered for which extensive experimental results and companion Reynolds-averaged Navier Stokes (RANS) solutions were obtained and/or available in the open literature. These cases all have Reynolds numbers based upon the freestream velocity and body geometric scale on the order of 10 5 to 10 6 , which is large for laboratory scales but small compared to the maximum scales observed for full-scale vehicles. Despite significant differences in approach flow fields and geometries for these three cases, some common themes emerged in the findings. All cases involved complications due to pressure gradients combined with streamwise curvature, and all exhibited regions of turbulence reduction due to accelerated flow. These complications led to discrepancies in computed results even in attached flow regions where it is often assumed that RANS models provide reliable predictions. The authors recommend further work on modelling approaches that can capture rapid distortion effects on turbulence transport that can be incorporated into industry-useful frameworks. Two cases involving laterally symmetric, three-dimensional wall-mounted hills with aft-body separation revealed that asymmetric mean flow fields are likely to result. This finding has been observed in experiments conducted in multiple facilities and in computations using multiple solvers and turbulence models. It is concluded that non-unique and asymmetric global flow solutions are fundamental to flow cases with lateral geometric symmetry involving turbulent boundary layer separation. Further work is also needed to accurately predict low-frequency unsteadiness due to geometries that produce non-unique mean flow fields. For such flows, it remains to be definitively determined whether experimentally observed modes of the mean flow are equivalent, or nearly equivalent, to asymmetric mean flow solutions obtained using RANS approaches.

Numerical investigation on effect of non-parallelism on natural transition in boundary layers around underwater axisymmetric bodies

For both fluid mechanics and practical engineering problems, it is important to study the effect of non-parallelism on the natural transition in boundary layers around underwater axisymmetric bodies. This paper develops the method of harmonic linearized Navier–Stokes (HLNS) equations for such boundary layers. The method can be used to study the evolution of small disturbances considering the non-parallelism of the basic flow. Based on the results of the HLNS equations, the transition positions of the boundary layers are predicted by the eN method. Because traditional linear stability theory (LST) neglects non-parallelism, the difference between the results using the HLNS method and those given by LST represents the effects of non-parallelism. Numerical calculations are performed for five classical forebody shapes, and the effect of non-parallelism is identified. (i) At each streamwise location, non-parallelism suppresses low-frequency disturbances while promoting high-frequency ones. The influence on high-frequency disturbances is more obvious. (ii) The effect of non-parallelism on the neutral curve focuses on the region near the critical instability position. Non-parallelism slightly delays the critical instability position for most forebody shapes and pushes the unstable zone toward the high-frequency direction while broadening its frequency bandwidth. (iii) The streamwise range at each growth-rate level is widened, implying that non-parallelism destabilizes the boundary layers. (iv) The transition occurs earlier, indicating that non-parallelism promotes the transition. (v) Non-parallelism shifts the dangerous frequency band toward the high-frequency direction. (vi) Non-parallelism enhances the wall pressure fluctuations (WPF) in the unstable laminar zone.

Steady secondary flow in a turbulent boundary layer past a slender axisymmetric body

The turbulent boundary layer in a viscous incompressible fluid developing longitudinally past the surface of a thin cone or cylinder at a finite distance from the laminar–turbulent transition zone is studied. The characteristic Reynolds number, determined from the external flow velocity and the length of the body, is assumed to be large, and the thickness of the boundary layer is small and comparable to the radius of the body. The asymptotic method of multiple scales is used to find solutions to the Navier–Stokes equations. Instead of the traditional decomposition of the solution into time-averaged values and their fluctuations, the velocities and pressure are expressed as an asymptotic series consisting of steady and perturbed terms. As a result, the viscous steady flow (‘secondary’) that arises in the boundary layer as a mandatory component of fast turbulent fluctuations was described. Analytical and numerical solutions for the radial steady velocity are presented, describing the self-induced suction of fluid from the external flow into the boundary layer. Further analytical solutions are obtained for the longitudinal and circumferential velocities, which differ markedly from the laminar regime. The solutions found are somewhat similar to the degenerate (one-dimensional) case of self-sustaining longitudinal thin structures in turbulent shear flows. A qualitative comparison with direct numerical simulations is presented.

The Blockage Effect on Resistance Coefficients Estimation for AUVs with Different Configurations in the Towing Tank

When a resistance test of an underwater vehicle model is conducted in a towing tank, the blockage effect will inevitably occur, particularly since the experimental model is relatively large. This paper investigates the estimation of resistance coefficients for an Axisymmetrical Rotary Body Underwater Vehicle (ARBUV) and a Blended Wing Body Underwater Vehicle (BWBUV). The Computational Fluid Dynamics (CFD) method is employed to predict the resistance of Autonomous Underwater Vehicles (AUVs). In order to quantify the blockage effect on the resistance coefficients of AUVs with different configurations, the resistance coefficients of AUVs are calculated in the infinite domain and finite domain under various blockage ratios. Through analysis of the resistance results, velocity distribution, and pressure distribution, the action law of the blockage effect is provided. It indicates that blockage effects have a greater influence on the pressure resistance for ARBUV. Surprisingly, the resistance coefficients of BWBUV are less affected, though it is closer to the sidewalls. It suggests that the blockage ratio of ARBUV and BWBUV should be separately smaller than 0.375% and 2.5% in the towing tank test. The towing tank experiments satisfy the blocking ratio with a Reynolds number greater than 107, which saturates the blocking effect and further reduces the effect on the drag coefficient.

Chirotactic response of microswimmers in fluids with odd viscosity

Odd viscosity is a property of chiral active fluids with broken time-reversal and parity symmetries. We show that the flow of such a fluid around a rotating axisymmetric body is exactly solvable and use this solution to determine the orientational dynamics of surface-driven microswimmers. Swimmers with a force-dipole moment exhibit precession around the axis of the odd viscosity. In addition, pushers show bimodal chirotaxis, i.e., alignment parallel or antiparallel to the axis, while pullers orbit in a plane perpendicular to it. A chiral swimmer that itself has a broken parity symmetry can exhibit unimodal chirotaxis and always align in the same direction. Published by the American Physical Society 2024

Multi-scale characteristics and inter-scale interaction in a transitional boundary layer over an axisymmetric body of revolution

Multi-scale characteristics and inter-scale interaction in a transitional boundary layer over an axisymmetric body of revolution

Validating Volumetric Measurements Using Helium-Filled Soap Bubbles in a Turbulent Boundary Layer And Wake Of An Axisymmetric Body Of Revolution

This study focuses on the validation of a volumetric measurement technique to characterize the turbulent boundary layers (TBL) and wake of a slender axisymmetric body. Specifically, Lagrangian Particle Tracking (LPT) was employed to analyse a TBL subjected to an adverse pressure gradient (APG) and transverse curvature at the tail of an axisymmetric body, with a Reynolds number based on model length of 3.95×10 6 . For the LPT method, a seeding rake with 100 nozzles was used to disperse helium-filled soap bubbles (HFSB), which served as tracers. These tracers were illuminated by high-powered LED arrays, allowing their motion to be captured by three high-speed cameras at acquisition rates up to 20 kHz. A key aspect of this research was using shadowgraphy to measure the diameter of the bubbles exiting the nozzles and obtaining their statistical variations across the various nozzles in the seeding rake. The study identified that the diameter of bubbles averaged 0.45 mm, indicating a state of near-neutral buoyancy. The LPT results were then obtained using the shake-the-box (STB) tracking alogirthm, while ensemble bin-averaging of the scattered particle tracks was used to obtain turbulence statistics on a regular grid. To validate the LPT results, comparisons were made with time-resolved 2D Particle Image Velocimetry (TR-PIV) and highly resolved hot-wire anemometry. This comparative analysis revealed good agreement of the mean profiles across the methodologies, highlighting the robustness and accuracy of the LPT technique. While the turbulence levels in the outer layer were well captured by the LPT, some discrepancies were observed near the wall in both PIV and LPT data, indicating limitations in capturing small-scale phenomena. The implications of these findings, particularly in understanding the complex 3D flow effects of such TBLs and the resulting wake flow field are discussed.

High-fidelity simulations of boundary layer transition on an underwater axisymmetric body with stability theory

During the cruise status of an underwater high-speed vehicle, the flow around the vehicle's head typically transitions from a laminar to a turbulent state, triggering flow noise that can interfere with the normal operation of sonar. In order to accurately investigate this flow noise through numerical simulation, a high-fidelity turbulent flow field solution is essential. Common traditional turbulence numerical simulation methods, such as unsteady Reynolds-averaged simulation and large eddy simulation (LES), struggle to capture high-frequency turbulent fluctuations accurately due to their inability to directly resolve small-scale eddy structures, which results in compromising the simulation accuracy of high-frequency flow noise. To address this issue, this paper employs direct numerical simulation (DNS) to achieve high-fidelity resolution of the turbulent flow field, thereby enabling a more accurate assessment of flow noise distribution on the vehicle's surface. Meanwhile, considering significant computational resources required to solve the entire flow field in an underwater high Reynolds number environment, this study also incorporates the fixed transition modeling method and stability theory to confine the DNS computational domain to the vicinity of the transitional zone to improve simulation efficiency. Comparative analysis of flow noise monitoring results in the laminar, transitional, and turbulent zones revealed that the flow noise source in the laminar zone exhibits the lowest amplitude across all frequencies, while the flow noise source in the transitional zone features the highest amplitude, approximately 10 dB higher than that in the turbulent zone. Moreover, significant amplitudes in high-frequency components (above 30 kHz) are detected in both the transition and turbulent zones. Additionally, this study employs LES with the Smagorinsky model to simulate the flow field within the same computational domain as DNS, demonstrating the limitations of the Smagorinsky model-based LES in capturing high-frequency flow noise.

Influence of bow shape and model scale on the natural transition in boundary layers on underwater axisymmetric bodies with a superhydrophobic surface

This study uses numerical methods to investigate the influence of bow shape and model scale on the natural transition in bow boundary layers on underwater axisymmetric bodies with a superhydrophobic surface. The transition locations for eight bow shapes and four model scales are predicted by using the eN method, which is based on a linear stability theory. The results show that the superhydrophobic surface always stabilizes the boundary layer and delays the transition for different bow shapes and model scales. However, differences are observed in the basic laminar flow, boundary-layer stability, and transition location when different bow shapes are used. These differences are not prominent at the small model scale, but become significant at the medium and large model scales. As the model scale increases, the transition location in the boundary layer on the superhydrophobic surface moves upstream and then downstream, leading to a “dangerous” scale, at which the transition location is closest to the leading edge. Furthermore, this study provides the optimal bow shape with the latest transition location at each model scale, and the optimal bow shape with the longest transition delay distance.

Detached Eddy Simulations of a Reaction Control Jet from an Axi-Symmetric Body in a Supersonic Crossflow

The introduction of a control jet into a supersonic cross flow yields a substantial region of separated flow, manifesting in the vicinity of the injection site. This, in turn, alters the distribution of pressure on the primary body, thereby influencing the effectiveness of the injected jet’s capacity to produce the desired control forces and moments. In the context of an axi-symmetric parent body, this disruption typically leads to a reduction in effectiveness, owing to the overflow of the shock structures encompassing the parent body. The present study investigates the injection of a reaction control jet into a supersonic crossflow using different Detached Eddy Simulation (DES) techniques. The side jet is injected from an orifice on an axi-symmetric parent body, which is aligned with the crossflow direction. The effects of the side jet on the flow field are analysed in terms of general flow features and spectral behaviour of pressure and turbulent kinetic energy. The DES results are compared with those obtained from RANS using various turbulence models. The overall effect of a transient interaction pulse is characterized using URANS and two different DES models.

Optimal sensor placement for ensemble-based data assimilation using gradient-weighted class activation mapping

We introduce an optimal sensor placement method using convolutional neural networks for ensemble-based data assimilation. The proposed method utilizes the gradient-weighted class activation mapping of the convolutional neural networks to identify important regions for assimilation processes. It is achieved by using the initial ensemble of samples for data assimilation as training data to construct a convolutional neural network-based surrogate model. In doing so, the method can estimate optimal sensor locations in an a priori manner, allowing for sensor placement before conducting data assimilation processing. Moreover, the gradient-weighted class activation mapping is used to alleviate the effect of error accumulation during the backpropagation process through global averaging. Further, these observation sensors are incorporated to reconstruct mean turbulent flow fields based on the ensemble Kalman method. The proposed optimal sensor placement method is applied to two flow applications with complex geometries, i.e., flows around periodic hills and an axisymmetric body of revolution. Both cases demonstrate that the proposed method can significantly reduce the number of sensors without sacrificing the accuracy of the reconstructed flow field.

Fluidic control of a precessing axisymmetric body by near-wake coupling

Fluidic control of a precessing axisymmetric body by near-wake coupling

Fidelity of Finite Element–Based Virtual Tire Assembly Models Used for Vehicle Noise, Vibration, and Harshness Structural-Borne Noise Performance Considering Vibrational Modal and Steady-State Dynamic Simulation

ABSTRACT The increasing presence of battery electric vehicles brings about new challenges to the noise, vibration, and harshness performance of tires. One of the new challenges involves the expansion of frequency range for structural-borne noise virtual predictions. Current standard virtual tire simplifies the tire geometry as an axisymmetric body, neglecting the effect of complex tread pattern. It is perceived that this simplification can lead to prediction error for a tire’s structural-borne noise performance at mid-frequency range (250∼500 Hz). This study investigates how different tread pattern representation affects the structural-borne noise prediction. This study uses linear, steady-state dynamics finite element simulations of a modified SAE J2710 test and traveling sinusoid test. The resulting frequency responses of the virtual tires and the computational time to obtain each frequency response are compared. The comparison shows that while including the 3D tread pattern does show some differences under certain conditions, it is not necessary to use this technique for every case, especially during the early evaluation stage.

Analyzing the dynamics of a charged rotating rigid body under constant torques

This study explores the dynamical rotary motion of a charged axisymmetric spinning rigid body (RB) under the effect of a gyrostatic moment (GM). The influence of transverse and invariable body fixed torques (IBFTs), and an electromagnetic force field, is also considered. Euler’s equations of motion (EOM) are utilized to derive the regulating system of motion for the problem in a suitable formulation. Due to the lack of torque exerted along the spin axis and the nearly symmetrical nature of the RB, the spin rate is nearly unchanged. Assuming slight angular deviations of the spin axis relative to a fixed direction in space, it is possible to derive approximate analytical solutions (AS) in closed form for the attitude, translational, and rotational movements. These concise solutions that are expressed in complex form are highly effective in analyzing the maneuvers performed by spinning RBs. The study focuses on deriving the AS for various variables including angular velocities, Euler’s angles, angular momentum, transverse displacements, transverse velocities, axial displacement, and axial velocity. The graphical simulation of the subsequently obtained solutions is presented to show their precision. Furthermore, the positive impacts that alterations in the body’s parameters have on the motion’s behavior are presented graphically. The corresponding phase plane curves, highlighting the influence of different values in relation to the electromagnetic force field, the GM, and the IBFTs are drawn to analyze the stability of the body’s motion. This study has a significant role in various scientific and engineering disciplines. Its importance lies in its ability to optimize mechanical systems, explain celestial motion, and enhance spacecraft performance.

Optimization design of forebody shape of an underwater axisymmetric body for transition delay using a genetic algorithm

The forebody shape of an underwater vehicle significantly influences the transition position of the boundary layer, which, in turn, impacts the flow-induced noise that can interfere with the sonar in the head. Typically, underwater vehicle forebodies are axisymmetric. Optimizing the forebody shape of an axisymmetric body can effectively delay the boundary layer transition and reduce the interference caused by flow noise on the sonar. This study applies an artificial intelligence algorithm for the optimization of the forebody shape. Specifically, a genetic algorithm is adopted to establish the optimization design method. The non-uniform rational B-spline (NURBS) method is used to parameterize the forebody shape, and the eN method based on linear stability theory is employed to predict the transition position. The optimization is conducted at the scale of a real vehicle and at a fixed velocity. After 45 generations, the genetic algorithm converges to an optimized shape. The transition position of the optimized shape is significantly delayed in comparison to that of the optimal original shape, with the relative delay amounting to an impressive 20.8%. Furthermore, the optimized shape effectively suppresses wall pressure fluctuation (WPF) in the unstable laminar region, also contributing to a reduction in flow-induced noise.

Large eddy simulation of the cavity shedding characteristics of ventilated cavitation around the underwater vehicle

Ventilated cavitation is utilized for reducing drag and improving the headway of underwater vehicles. The ventilated cavitating flow around the axisymmetric body is simulated using the Large Eddy Simulation (LES) method in this study. Three cavity morphologies with different ventilation rates (Cq) are observed: Foamy Cavity (FC), Continuous Transparent and Foamy Cavity (CTFC) and Super Cavity (SC). The cavity shedding characteristic of the three different cavity morphologies is revealed. For partial cavity, the periodic cavity shedding is dominated by the local high pressure, re-entrant jet and vortex. The distributions of the turbulent kinetic energy and the pulsation enstrophy exhibit different migration mechanisms during the cavity shedding. The energy characteristic is reflected by three terms of the entropy generation. And the entropy production rate by direct dissipation occupies a dominant position, accounting for about 80% of the total entropy production, while the entropy production rate by viscous dissipation only accounts for 4%. For super cavity, gas leakage is dominated by a re-entrant jet induced by the intense adverse pressure gradient. And the results also demonstrated the velocity and vorticity pulsations around the test body wrapped in a super cavity are not intense.

Time delay in the gravitational field of an axisymmetric body with full mass and spin multipole structure

Time delay in the gravitational field of an axisymmetric body with full mass and spin multipole structure

Exponentially Convergent Numerical Scheme for the Stream Function of Potential Flow over Axisymmetric Bodies

Exponentially Convergent Numerical Scheme for the Stream Function of Potential Flow over Axisymmetric Bodies

An improved laminar–turbulent transition cavitation model using the IDDES method

Prediction of the detachment positions of sheet cavitation remains an unsolved problem, being not only dependent on local pressure but also closely related to the boundary layer transition. For hydrofoils, traditional cavitation models tend to predict premature cavity detachment positions. In the study reported here, to obtain cavity detachment positions that match experimental results, improvements are made to both turbulence models and cavitation models. A scale-resolving transition turbulence model is established by incorporating transport equations to represent boundary layer transition that are based on the improved delayed detached eddy simulation (IDDES) method. The intermittency γ, representing the probability of turbulence at a specific point in space, is introduced into the homogeneous cavitation model to account for the influence of the laminar–turbulent transition on the sheet cavitation detachment position. Numerical results show that the IDDES-based transition turbulence model combines transition and scale-resolving capabilities. The improved turbulence transition cavitation model proposed here is shown to be able to accurately predict the detachment position of sheet cavitation around two-dimensional hydrofoils and a typical axisymmetric ITTC body.