Frequency Ratio Fr Research Articles

Numerical analysis of an oscillating square and circular bluff body submerged in the wake of an identical static bluff body: A GPU Accelerated Immersed Boundary-Lattice Boltzmann Approach

Hydrodynamic forces acting on marine structures, tubes, and objects can trigger disruptive vibrations. This study is an effort to encapsulate the results of wake induced vibration among tandem bodies. Specifically, impact of a static upstream body on a downstream oscillating body at Reynolds number 100 and constant frequency ratio Fr=1.0. The effects of streamwise displacement are investigated in a tandem arrangement of 1.05≤Lx/D≤12.0. In this study an in-house developed code employed that combines an immersed boundary lattice Boltzmann method with a structural equation and is accelerated using a graphical processing unit. When comparing scenario 1 (both bodies oscillate) to scenario 2 (only the downstream body oscillates), the study finds that the upstream square body motion has little effect on the downstream square body oscillation. However, the upstream circular body motion significantly impacts the downstream body oscillation. In addition, the study observes that the maximum amplitude occurs after reaching the critical spacing in scenario 2, whereas it occurs at and after the critical spacing in scenario 1. The critical spacing ratio is similar in both scenarios but varies for square and circular bodies. Lastly, the study examines the flow physics and hydrodynamic force coefficients of the downstream oscillating body.

Advancements in mapping landslide susceptibility in Bafoussam and its surroundings area using multi-criteria decision analysis, statistical methods, and machine learning models

Landslides pose a significant threat to lives and socio-economic stability globally. In this study, we conducted a comprehensive landslide susceptibility mapping (LSM) in the western region of Cameroon, focusing on Bafoussam and its surroundings. The integration of multi-criteria decision analysis models (AHP), statistical methods (Information Value IV, Shannon Entropy SE, Frequency Ratio FR), and machine learning algorithms (Naïve Bayes and Logistic Regression) provided a robust assessment of landslide risk. Our analysis, based on 54 recorded landslides, carefully selected Landslide Conditioning Factors (LCF), and influential parameters such as lithology, slope, altitude, and precipitation, resulted in susceptibility maps categorizing the area into five risk zones. The Spatial distribution shows the centre and northwestern regions as high-risk areas. Model sensitivity differences underscore the need for tailored LSM selection. Validation using the Area Under Curve/Receiver Operating Characteristics (AUC/ROC) method indicates the LR and NB methods have the highest accuracy (82.7% and 84.1%, respectively). Comparative analysis of landslide events in Gouaché, Sichuan, Souk Ahras, and Kekem reveals correlations between heavy rainfall and geological conditions. The study supplies valuable insights for decision-makers in landslide-prone areas, emphasizing the importance of integrating multiple methodologies for comprehensive risk assessment and management.

Numerical simulation of flow past an 8:1 oscillating rectangular cylinder at Re = 22 000

To investigate the influence of structure’s oscillatory motion on flow, the present study employs the arbitrary Lagrangian–Eulerian method in k–ω shear stress transport (SST) turbulence model to simulate the flow past an oscillating rectangular cylinder at Re= 22 000. The cylinder undergoes reciprocating sinusoidal motion at a specified frequency f e, and the frequency ratio fr (defined as the ratio of cylinder oscillation frequency f e to the stationary cylinder vortex shedding frequency f 0), ranges from 0 to 4. The results demonstrate that, in the synchronization region (0.8 ⩽ fr⩽ 1.2), the drag coefficient shows the most notable variation and reaches its maxima at fr= 1.1 and the root mean square (r.m.s.) of the lift coefficient is proportional to the square of fr (, R 2 = 0.99). Moreover, the present study compares the similarities and differences of vortex shedding morphology between stationary and oscillating cylinders. With the increase of fr, the wake vortex gradually transforms from a single-row arrangement on the wake centerline to a parallel double-row arrangement, with the main vortex modes in the wake region observed as ‘2S’, ‘P + S’, ‘2P’ and ‘C’. Furthermore, spectral analysis, including amplitude spectrum analysis and wavelet analysis, in addition to probability density function statistical methods, are employed to comprehensively understand the velocity characteristics of the wake region. The results indicate that the oscillation of the cylinder reduces the correlation of the wake velocity. Those are beneficial in understanding the interaction between turbulence and structural fluid-induced motion.

Laminar Flow over a Square Cylinder Undergoing Combined Rotational and Transverse Oscillations

This work numerically investigates the effects of combined rotational and transverse oscillations of a square cylinder on the flow field and force coefficients. The primary non-dimensional parameters that were varied are frequency ratio fR (0.5, 0.8), Re (50-200), phase difference (ϕ) between the motions and rotational amplitude (θ0) with the influence of the last three parameters being discussed in detail. The amplitude of transverse oscillations is fixed at 0.2D, where D is the cylinder width. The study has been validated using the mean drag coefficient for stationary and transversely oscillating square cylinders from literature. Output data was obtained in the form of force coefficient (Cd), vorticity and pressure contours. The governing equations for the 2dimensional model were solved from an inertial frame of reference (overset meshing) using finite volume method. The interplay between the convective field and prescribed motion has been used to explain many of the results obtained. The relative dominance of cylinder motion over the flow stream was determined using Discrete Fast Fourier Transform. The influence of Re on Cd disappears when the motions are completely out of phase (ϕ = π). In general, the Cd for low Re flows exhibited low sensitivity to change in other parameters. Direct correlation has been observed between frontal area, vortex patterns and drag coefficient

Flow behavior behind a clockwise-and-counterclockwise rotational oscillating cylinder

Flow characteristics downstream of a rotational oscillating cylinder at Reynolds number Re = 300 was investigated. The experiments were conducted using a model cylinder in a recirculating open water channel and the flow field was captured by using the Particle Image Velocimetry (PIV) technique. The model cylinder was set to undergo clockwise-and-counterclockwise rotation at selected angular amplitude (angular amplitude α varying from 0° to 360°) and at the lock-on frequency ratio Fr = 1.0 (where Fr = fn/fv, the ratio of the forcing frequency fn to the natural vortex shedding frequency fv). The effects of rotational movement of the cylinder on the near wake downstream of the cylinder were interpreted in terms of the instantaneous vorticity patterns, as well as the time-averaged streamline topology, mean velocity distributions and Reynolds shear stress contours. Based on the observation of the flow patterns and vortex contours, it was deduced that the clockwise-and-counterclockwise rotation produced significant effect on the wake and modified the wake flow structures and vortex shedding patterns. The time-averaged streamline structures appeared to be non-symmetrical about the longitudinal axis of the flow.

Effect of spacing on a pair of naturally oscillating circular cylinders in tandem arrangements employing IB-LB methods: Crossflow-induced vibrations

An efficient velocity-correction based immersed boundary-lattice Boltzmann method (IB-LBM) is employed and coupled with structural equations to investigate the vortex-induced vibration characteristics of two identical circular cylinders in various tandem arrangements at a low Reynolds number of 100 with 1.0 < Sx/D ≤ 12.0 and frequency ratio Fr=1.0; here, Sx is the streamwise displacement between the cylinder centers, D is the cylinder diameter, and Fr is the ratio of the vortex shedding frequency to the natural frequency of the oscillator. The cylinders are set to oscillate naturally in the transverse direction only, and a mass-spring system characterizes their motion. Considering a similar flow and structural parameters, a single cylinder is also studied for reference and comparison. Furthermore, a fixed cylinder and two stationary cylinders in tandem arrangements with same spacing ratios are also examined. Four distinct regimes of cylinder arrangements have been identified based on the cylinder maximum, gradual decrease to a minimum, persistence, and single cylinder response. At Sx/D=1.5, the cylinders vibrate violently with overall maximum amplitude. A critical spacing at (Sx/D)c=3.5 is observed both in the stationary and oscillated cylinders, where the forces and amplitude have the minimum values. The response amplitude and force coefficients remain constant over a range of spacing, i.e., Sx/D=4.0−8.0. The cylinders behave as single cylinders when placed more than eight-diameters apart as the interaction between the fluid and structure are decoupled. The interference and wake effects are diminished in this regime. The hydrodynamic force coefficients and flow physics of the oscillating tandem cylinders are also discussed. The results reveal that the flow in the gap between the cylinders and in the wake significantly affects the forces and hence, the dynamic response of the tandem structure.

Orthogonal test and regression analysis of the strain on silty soil in Shanghai under metro loading

Cyclic triaxial test by means of the geotechnical digital system is conducted for the soil near the Guoquan Road Station of Metro Line 10 in Shanghai to analyze the strain characteristics and the variation law of saturated silty soil under subway loading. Orthogonal design method is used to arrange the experiment, considering the following factors: frequency ratio f R, cyclic stress ratio σ R, vibration time ratio N R, and the interaction function among them. Results show that the cyclic stress ratio σ R, the frequency ratio f R, the vibration time ratio N R, and the interaction between the cyclic stress ratio σ R and the vibration time ratio N R have a significant effect on the axial strain of the subway tunnel. The effect of the interaction between the cyclic stress ratio σ R and the vibration time ratio N R is also significant. From the analysis of variance and regression theory, the nonlinear regression equation of the cumulative plastic strain of silty soil under subway loading is established. Residual analysis proves that the equation is ideal and credible. The results have important value for the design of subway tunnels.

Unsteady Flow Mixing Effect in Bionic Micro-Flow Channel

Micro-mixers are studied extensively due to their high mixing efficiency. A periodic flow variation at the channel entrance will be used to drive fluids in this study to achieve a mixing effect. Numerical analysis is used and verified by experiment in the study to identify the group of operating factors, such as Reynolds number Re, the driving phase difference ? and the driving frequency ratio Fr, needed for the fluid to achieve the best mixing result for a bionic micro-mixer. It is found in this study that the mixing efficiency is related to the velocity period distribution; the more even the velocity period distribution becomes, the better the mixing efficiency and the best group of operating factors is found (Re2 = 1, Rer = 0.85, Fr = 1, F2 = 50 Hz, I/Am = 1, ? = 3/4 ?). Furthermore, a larger aspect ratio results in a better mixing efficiency. The influence of wall-effect on the flow mixing decreases with AR. It is found that there exists an optimal mixing efficiency at aspect ratio AR = 10. These research results could be used to improve the design of a bionic micro-mixer.

Unsteady Flow Mixing Effect in Bionic Micro-Flow Channel

Micro-mixers are studied extensively due to their high mixing efficiency. A periodic flow variation at the channel entrance will be used to drive fluids in this study to achieve a mixing effect. Numerical analysis is used and verified by experiment in the study to identify the group of operating factors, such as Reynolds number Re, the driving phase difference ? and the driving frequency ratio Fr, needed for the fluid to achieve the best mixing result for a bionic micro-mixer. It is found in this study that the mixing efficiency is related to the velocity period distribution; the more even the velocity period distribution becomes, the better the mixing efficiency and the best group of operating factors is found (Re2 = 1, Rer = 0.85, Fr = 1, F2 = 50 Hz, I/Am = 1, ? = 3/4 ?). Furthermore, a larger aspect ratio results in a better mixing efficiency. The influence of wall-effect on the flow mixing decreases with AR. It is found that there exists an optimal mixing efficiency at aspect ratio AR = 10. These research results could be used to improve the design of a bionic micro-mixer.

Temporal evolution of wake behind a rotationally oscillating circular cylinder

The temporal evolution of the near-wake behind a circular cylinder undergoing rotational oscillatory motion with a relatively high forcing frequency has been investigated experimentally using a dynamic particle image velocimetry velocity field measurement technique. Experiments were carried out varying the frequency ratio FR (=ff∕fn), the ratio of the forcing frequency ff to the natural vortex shedding frequency fn, in the range of 0.0 (stationary) to 1.0 at an oscillation amplitude of θA=30° and Reynolds number of Re=4.14×103. Depending on the forcing condition (FR), the near-wake flow showed markedly different flow regimes: stationary (FR=0.0), non-lock-on (FR=0.4) and lock-on (FR=1.0) regimes. However, at all the frequency ratios tested, the power spectral density distributions showed a single dominant peak at the same vortex shedding frequency. As the forcing frequency was increased, the rotational oscillatory motion of the cylinder decreased the length of the vortex formation region and enhanced the mutual interaction between large-scale vortices across the wake centerline. In particular, the entrainment of ambient fluid seemed to play an important role in controlling the near-wake flow and shear-layer instability. The shear-layer instability showed different mechanisms compared with the case of small oscillation amplitude. A strong vortex motion appeared in the near-wake region. In addition, the rotational oscillatory motion of the cylinder changed the local mean flow structure significantly; thereby mean velocity profiles for each frequency ratio varied markedly in the vortex formation region. The configuration of vorticity contours shrunk toward the cylinder as the frequency ratio was increased. The temporally resolved flow information extracted in the present work is useful for understanding the evolution of vortex structure and analyzing the effects of open-loop active flow control technique on the near-wake flow structure.

Flow Structure in the Wake of a Rotationally Oscillating Cylinder

The characteristics of the flow in the wake of a circular cylinder performing rotational oscillation about its own axis and placed horizontally in a cross-stream is investigated. The governing equations based on stream function-vorticity formulation are solved numerically to determine the flow field structure. The parameters dominating flow structure are Reynolds number, Re, amplitude of oscillation, ΘA and frequency ratio FR=S/S0 where S is the forcing frequency and S0 is the natural frequency of vortex shedding. The ranges considered for these parameters are 40⩽Re⩽200, 0⩽ΘA⩽π and 0⩽FR⩽2. The lock-on phenomenon has been predicted and its effect on the flow hydrodynamics has been determined. The lock-on phenomenon is found to occur within a band of frequency encompassing the natural frequency. This band, however, becomes wider as the amplitude of oscillation increases. The obtained results show that the flow pattern in the near wake has a strong dependence on the oscillation parameters but not the far wake. [S0098-2202(00)01102-0]