Vortex Shedding Modes Research Articles

Numerical Study of Vortex-Induced Vibration Characteristics of a Long Flexible Marine Riser

In ocean engineering, interactions between ocean currents and risers lead to regular vortex shedding on both sides of the riser, causing structural deformation. When the frequency of vortex shedding approaches the natural frequency of the structure, resonance occurs, significantly increasing deformation. This phenomenon is a critical cause of riser failure. Therefore, the dynamic response of flexible risers to vortex-induced vibrations (VIV) is crucial for their structural safety. This paper employs the finite-volume method to integrate over control volumes to solve for forces, such as pressure and shear stress, on the surface of the riser, while the finite-element method discretizes the continuous structural body into elements and nodes to solve for structural displacements and stresses. A strongly coupled method is utilized at each timestep to iteratively transfer load-displacement data between the fluid and structural fields, updating the boundary conditions of the fluid domain to achieve a bidirectional fluid–structure interaction simulation of vortex-induced vibrations in a seawater environment for flexible risers. The study finds that the three-dimensional flexible riser exhibits multi-frequency vibration phenomena and broadband vibration response characteristics under high flow velocity conditions. As the flow velocity increases, the vortex-shedding mode is observed to transition from the simple two single (2S) mode to the more complex pair + single (P + S) and two pair (2P) modes. In addition, the stiffness at the ends is enhanced by the fixed boundary conditions, and the coupling between the natural frequency of the ends and the vortex-shedding frequency triggers complex vortex-shedding phenomena in these regions. At higher flow velocities, these boundary effects result in more complex vortex-shedding modes and stronger vibration responses at both ends of the riser.

Effect of side ratio on the two-degrees-of-freedom vortex-induced vibrations of the rectangular cross section model

The effect of the mutative side ratio (D/B) on the vortex-induced vibration (VIV) characteristic, aerodynamic characteristics, and the surrounding time-averaged and transient flow field of a rectangular cross section model were simulated numerically. Based on Fluent 19.0 platform, overset grid technology and the fourth-order Runge–Kutta method were used at Re 22 000. First, a rectangular cross section model with D/B = 0.25 was selected, and the simulation method and parameter settings were validated against previous literatures. The subsequent analysis compared and evaluated the effect of side ratio on the VIV response by focusing on statistical values of aerodynamic force coefficients, self-spectra, amplitude ratio, motion trajectory, and phase transition changes for stream-wise and cross-flow directions. Moreover, the study examined the influence of different models at different reduced velocities (Ur) on wake vortex-shedding. The findings suggest that, within a fixed cross-sectional area, a smaller side ratio leads to a weaker VIV characteristic and notably lower aerodynamic performance compared to a larger side ratio. The vortex-shedding mode of the rectangular cross section, particularly with a large side ratio, is less sensitive to changes in Ur compared to the standard square cylinder. An examination of the Reynolds number (Re) effect on the minimum and maximum side ratio models reveals that it has a more pronounced impact on the aerodynamic performance and VIV of the cross-flow when compared to in-line flow. In general, it is noted that larger side ratio model exhibits a stronger sensitivity to the variation of Re.

Fluid–acoustic–structure resonance mechanism of a plane cascade via a low-speed wind tunnel test

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.

Numerical study on bifurcation characteristics of wind-induced vibration for an H-shaped section

In order to reveal the influence of initial excitation on the bifurcation phenomenon of bridge decks, a new perspective of flow characteristics is developed based on the computational fluid dynamics numerical simulation method. Then, the bifurcation mechanism of vortex-induced vibration (VIV) response and nonlinear flutter response of the H-shaped section is investigated. The results show that when the wind speed is 2 m/s, under a small torsional excitation of 0.5°, the flow field of the H-shaped section will develop into the vortex shedding mode of the vertical vibration, resulting in vertical VIV. However, while under a large excitation of 6°, the flow field will directly transform into the vortex shedding mode of the torsional vibration, resulting in torsional VIV. Therefore, the bifurcation phenomenon of the VIV response is observed. When the wind speed is 4 m/s, the H-shaped section exhibits a nonlinear flutter limit cycle oscillation under a large excitation of 8°, but its response can be ignored under a small excitation of 0.5°. This phenomenon is attributed to the significant change in the transition of the vortex shedding mode from a small amplitude to a stable large amplitude, and the flow field lacks enough energy to complete the transition of the vortex shedding mode, resulting in the bifurcation phenomenon of the nonlinear flutter response. When the wind speed is 3.0 m/s, the large excitation will change the vortex shedding frequency of the new H-shaped section, resulting in the torsional VIV.

Single degree of freedom vortex induced vibration of undulatory seal whiskers at low Reynolds number and various angles of attack: A computational fluid dynamics study

The cross-flow vortex-induced vibration (VIV) response of an elastically mounted idealized undulatory seal whisker (USW) shape is investigated in a wide range of reduced velocity at angles of attack (AOAs) from 0° to 90° and a low Reynolds number of 300. The mass ratio is set to 1.0 to represent the real seal whisker. Dynamic mode decomposition is used to investigate the vortex shedding mode in various cases. In agreement with past studies, the VIV response of the USW is highly AOA-dependent because of the change in the underlying vortex dynamics. At zero AOA, the undulatory shape leads to a hairpin vortex mode that results in extremely low lift force oscillation with a lowered frequency. The frequency remains unaffected by VIV throughout the tested range of reduced velocity. As the AOA deviates from zero, alternating shedding of spanwise vortices becomes dominant. A mixed vortex shedding mode is observed at AOA = 15° in the transition. As the AOA deviated from zero, the VIV amplitude increases rapidly by two orders, reaching the maximum of about 3 times diameter at 90°. An infinite lock-in branch is present for AOA from 60° to 90°, where the VIV amplitude remains high regardless of the increase in reduced velocity.

Dumbbell-shaped piezoelectric energy harvesting from coupled vibrations

This paper presents a novel dumbbell-shaped piezoelectric energy harvesting from vortex-induced vibration (VIV) and galloping. The designed harvester system leverages the coupled vibrations to improve the output performance. The conceptual design of the dumbbell-shaped harvester system is first developed, the theoretical model of the harvester is then established, three-dimensional simulation analyses are conducted, and the prototypes of the harvester that combines a cylinder and a cuboid are finally manufactured. The effect of the cylinder lengths and airflow velocity on the harvesting characteristics is explored. The results demonstrate the derived mathematical model is fully verified through experimental method. VIV occurs in the 0.5D and 1D dumbbell-shaped harvester systems at lower airflow velocities, while galloping takes place at higher velocities, both of which contribute to increase the output performance. In contrast, the 1D - 3D dumbbell-shaped harvesters demonstrate a VIV behavior only and suppress vibration. The maximum voltage generated by the 0.5D harvester is 12.03 V at 4.29 m s-1, which is 11.18 % higher than that of a single cuboid harvester. The vorticity fields illustrate the vortex shedding mode and intensity, as well as reveal the underlying influence mechanism.

A comprehensive investigation on flame flickering characteristics of premixed conical flame at different inclination angles

To thoroughly investigate how the inclination angle affects the flickering of premixed conical flames, a series of experiments and simulations were carried out. Propane-air conical flames were established on a Bunsen burner, and various inclination angles were tested, resulting in a wide range of flame flickering frequency data. The findings revealed that the further the inclination angle deviates from 0°, the lower the flickering frequency. Consequently, an empirical correlation that factors in the inclination angle was developed. To gain a more comprehensive understanding of the flame flickering behavior under different gas inclination angles, researchers utilized Particle Image Velocimetry (PIV) and numerical simulation to visualize the velocity fields of a typical flame. The results demonstrated that deviated inclination angles not only alter the shear strength between the burnt gas and surrounding gas but also significantly change the flame flickering mode. These factors lead to various Kelvin-Helmholtz instability patterns and vortex shedding modes, ultimately impacting flickering frequency.

Vortex-shedding modes of a pair of side-by-side thin pitching plates

We have conducted three-dimensional (3D) direct numerical simulations to analyze vortex-shedding modes past vertically arranged, side-by-side 3D pitching plates, considering cases where the plates are in the same, opposite, and different phases. The simulations are performed at a Reynolds number Re=1000, with a dimensionless pitching frequency St=1, and a maximum pitching angle θmax=15°. The vortex-shedding modes reveal horseshoe vortices transforming into distorted hairpin-like structures in the far wake for in-phase plates. Opposite phase plates exhibit helical distortion and core bifurcation, while different phase angles produce meridionally twisted, entangled hairpins. We observe a reverse von Kármán vortex street for in- and different-phase plates, while the opposite shows a reverse Kármán vortex street for the upper plate and a Kármán vortex street for the lower plate. The streakline visualizations reveal wake compression and spoke-like structures symmetrically emanating from the shear layer extremities around the plates' central region. We find leapfrog-like cross-stream vortex interaction when the plates are in phase. The line-time diagram reveals alternating patches of low-intensity cells, switching between negative and positive, alongside continuous bands of both positive and negative cells. Both plates produce similar thrust for the parameters examined in this study.

PIV And Schlieren Measurements Of A Linear Plug Nozzle Jet Interacting With External Flow

Plug nozzles represent a promising concept as part of a propulsion system for space launchers. The ability to adapt the nozzle jet to the ambient pressure level improves thrust performance in overexpanded operating conditions compared to conventional bell nozzles. In this study, the dynamics of a jet flow of a cold air plug nozzle model are investigated by means of PIV and high-speed schlieren measurements. For a fixed nozzle pressure ratio, the jet flow is studied in an externalouter flow environment with sub-, trans-, and supersonic Mach numbers. The effect of plug truncation is analyzed as well. It is found that the outer Mach number strongly influences the flow pattern, local velocity magnitudes and aerodynamic modes. The frequency and dominance of vortex shedding and jet screeching modes are found to be highly dependent on the Mach number of the surrounding flow. A truncated plug introduces local accelerations in its base wake region, causing an increased shock strength in the jet structure. In addition,it causes severe periodic fluctuations in the flow that are transmitted to the shear layer and induce acoustic wave emissions. The impact of the plug length on the flow dynamics has been seen to decrease with increasing outer Mach number.

Spatial And Temporal Modes On A Generic Tandem Configuration In Transonic Shock Buffet

Certain combinations of upstream flow conditions in transonic flight may incite a highly unsteady shock-wave/boundary-layer interaction, often referred to as transonic buffet. The coupling of periodic shock motion and intermittent separation is seen to convey a characteristic unsteadiness in the evolution of the turbulent wake. This article uses high-speed focusing Schlieren and PIV measurements at high spatial resolution to characterize the temporal and spectral modes governing the flow past a generic 2D tandem configuration. This interaction, consisting of an OAT15A supercritical airfoil as the main wing and a NACA 64A-110 profile representing the tailplane, is investigated at chord-based Reynolds numbers of 2 million and 1 million, respectively and compared against fully-established shock buffet conditions in an isolated airfoil scenario operated at identical inflow conditions. The strongest buffet is observed in both configurations for a Mach number of 0.72 and an angle of attack of 5 deg, occurring at frequencies of 112 Hz and 103 Hz. Despite an equally periodic nature of the buffet unsteadiness, both shock amplitude and frequency are seen to decrease slightly in the tandem interaction. Global spectral analysis performed on the entire field of view identifies the buffet instability as the governing mode in both flow scenarios, imposing its unsteadiness even far downstream of its origin, allowing the extraction. of relevant sensor locations for a subsequent localized assessment of the involved time scales. Except for the buffet mode, complementing DMD analyses reveal a strong influence of a vortex-shedding mode throughout the entire buffet cycle. Mode shapes and associated frequencies furthermore suggest an intermittent low-frequency/large wavelength and high-frequency/low wavelength behavior, involving leading contributions between 2000 Hz and 4000 Hz.

Coupled response of flow-induced vibration and flow-induced rotation of a circular cylinder with a triangular fairing

In this paper, a numerical simulation investigation is carried out on the coupled response of the flow-induced vibration (FIV) and flow-induced rotation (FIR) of a circular cylinder attached with a triangular fairing at a low Reynolds number of Re = 100. The primary focus is on the impact of FIR on FIV. The vibration response, hydrodynamic coefficient, vortex shedding mode, and flow field characteristics are examined for the fairings within the vibrational reduced velocity Ur range of 3–16 with shape angle of α = 45°, 60°, and 90°. The results reveal that at low Ur, all the three considered fairings have a good suppression effect on the FIV. Nevertheless, the galloping response emerges as Ur increases when α = 45° and 60°. In contrast, the vibration response of 90° fairing presents a wider lock-in region. The rotatable 2-degree of freedom (2-DoF) fairing has a better performance in the reduction of response amplitude and hydrodynamic coefficients. The 2S (two single vortices) vortex shedding mode mainly occurs in the vortex-induced vibration (VIV) region, while 2S–8S (from two to eight vortices), 2P (two pairs of vortices), 2T (two triplets of vortices), and P + T (a pair of vortices and a triple of vortices) modes emerge in the galloping branch. Moreover, four modes of wake structures are identified according to the variation of recirculation region and the migration of boundary layer separation point. Finally, the reduced regions of drag, lift, and amplitude are highlighted compared to the bare cylinder.

Wake-induced response of a flexible splitter plate detachedly placed downstream of a circular cylinder

A fluid–structure interaction numerical investigation was conducted on the flow past a circular cylinder with a detached flexible plate at a low Reynolds number Re = 160. A broad gap ratio range of 0–6.0 is examined at three plate lengths. Numerical results indicated that the vortex formation is closely related to the position of the plate with respect to the recirculation region behind the cylinder. Three wake interference regimes are identified, including the extended-body, continuous reattachment (CR), and alternate reattachment (AR). Taking into account the wake interference and vortex shedding modes and the response order, six wake flow patterns are observed. The CR regime shifts to AR at a critical gap G/D = 3, where both the vibration amplitude and frequency sharply increase. The sizes of vortex spacing and plate length determine the response mode of the flexible plate. Compared to an isolated cylinder, the optimal reduction percentages in drag and lift coefficients are around 90% and 20%, respectively.

Effects of mass and damping ratios on the flow-induced vibration of two staggered circular cylinders

The mass ratio between structure and fluid and the structural damping ratio have been shown to significantly affect the flow-induced vibration (FIV) of an isolated circular cylinder. Their influences on multiple staggered circular cylinders commonly found in offshore structures have, however, not been clearly understood. This study numerically investigates the vibration responses and flow field of two staggered circular cylinders with the shear stress transfer k–ω turbulence model and the overset mesh method. The accuracy of the numerical method adopted is validated against published experimental results, and the effects of the mass ratio and damping ratio on FIV are systematically investigated. The structural responses of the two cylinders are found more sensitive to the mass ratio than the damping ratio. The amplitude of vibration increases, in general, with a reduction in the mass ratio or damping ratio, and the vibration is much more significant when the mass ratio is less or equal to unity as compared to those from other mass ratio values. A reduction in the mass ratio is found leading to more diverse vortex shedding modes with fast transition from one into another. The self-excited dynamic forces represented by the added mass ratio ma* and added damping ratio ζa are further analyzed. It is found that the added mass ratio is positive under low inflow velocity, and it gradually becomes negative with higher inflow velocity. The added damping ratio is generally negative under low inflow velocity and it increases with the inflow velocity. Furthermore, the added damping ratio decreases with the inflow velocity only when the mass ratio is smaller than unity.

Vortex-shedding modes of a streamwise and transversely rotating sphere undergoing vortex-induced vibrations

We investigate the vortex-shedding modes of a streamwise and transversely rotating sphere undergoing vortex-induced vibration (VIV). At Reynolds number Re = 500, we have conducted direct numerical simulations for reduced velocities U∗=6,8, and 11, considering dimensionless streamwise (αx) and transverse (αz) rotation rates set at αx,z=1. At αx=1, the vortex-shedding mode exhibits twisted spiral-like structures, while at αz=1, ring-like structures form through the stretching and twisting of hairpins. For αx=1, the dimensionless circulation (Γx) decreases with increasing U∗, showing negative growth at U∗=6. Conversely, for αz=1, Γx remains negative except at U∗=8, where counterclockwise vortex rotation results in positive circulation. At αz=1, VIV is periodic for U∗=6 and 8 but intermittent at U∗=11. Phase analysis using the Hilbert transform reveals anti-phase synchronization in the phase between the sphere's displacements and the vortex force coefficient (ΔϕV) and phase slip in the phase between the sphere's displacements and the total force coefficient (ΔϕT) along the y direction for αx=1. At αz=1, phase slip with distinct phase-locking epochs is observed along the z direction for all U∗ cases. Pre-lock-in behavior with phase slip is also noted for U∗=11 along the y direction.

Splitter-plate proximity-induced transitions in flow-induced vibration of a triangular prism

The effect of a splitter-plate downstream of an elastically mounted equilateral triangular prism on flow-induced vibration is numerically investigated at Reynolds number Re = 100, mass ratio m* = 10, damping ratio ζ = 0.005, cylinder-plate gap G* = 0.3, and various angle of attacks α = 0°–60°. The α = 0° and 60° correspond to vertex and edge of the cylinder facing the free stream. Under the effect of the splitter plate, a single transition from vortex-induced vibration (VIV) to proximity-induced galloping (PIG) in the vibrational response for an axisymmetric circular cylinder is reported, whereas, for the present non-axisymmetric triangular prisms, the varying α exhibits four proximity-induced transitions: VIV to modified VIV at smaller α = 0° and 25°, VIV to PIG at α = 35°, distinct VIV-galloping to combined PIG-galloping at α = 40°, and asymmetric to symmetric-galloping at larger α = 60°. The plate results in more symmetric vibration for high α ≥ 35°, while a reduction is observed for α ≤ 25°. The gap-flow leads to onset (α = 35°) and enhancement (α = 40°) of afterbody re-attachment on the prism, which significantly enhances the galloping instability and vibrational amplitude. A reduction in galloping instability leading to a slight reduction in amplitude is found for α = 60° prism. The study shows that the presence of the splitter-plate downstream influences near-wake structure and far-wake vortex shedding modes, which lead to stabilizing and destabilizing near-wake flow and distinct vibrational characteristics—depending on the angle of attack (α).

Flow-induced vibrations of a twistable two-tandem cylinder system across varied gap ratios

This paper presents a simulation study on the flow-induced vibrations (FIVs) of a two-tandem cylinder system with three degrees of freedom, encompassing in-flow, cross-flow, and torsional motions at a Reynolds number of 150. We specifically focus on investigating the impact of gap ratios (G*) between the cylinders, considering values of 0.5, 2, and 3. The ratio of torsional natural frequency to translational natural frequency was maintained at 12.5, while the mass ratio between the cylinder system and the fluid was set to 2. Our findings reveal a notable sensitivity of the FIV responses to the gap ratio between the cylinders. It was observed that the cylinder system's vibrations can undergo locking phenomena at both the translational and torsional natural frequencies, with maximal cross-flow amplitudes occurring within the torsional locked region. Particularly, at G* = 0.5, the maximal cross-flow amplitude reached approximately 21.4 times that of the cylinder system without torsional vibration, posing potential risks of fatigue failure in offshore equipment. Conversely, at G* = 2, an unusual ultra-low frequency was detected in the in-flow vibration. This phenomenon significantly magnified the FIV of the cylinder system, despite the absence of frequency locking. Furthermore, at G* = 3, we observed an expanded range of vibrations with ultra-low frequency compared to G* = 2. Our analysis identified the differential development speed of the shear layers around the upstream and downstream cylinders as a key factor contributing to varying vortex shedding frequencies. This discrepancy led to periodic changes in the vortex shedding mode of the cylinder system over time, thereby introducing low-frequency components into the flow-induced vibration. These insights deepen our understanding of the complex dynamics governing the FIV of tandem cylinder systems, which holds implications for the design and maintenance of offshore structures.

Lattice boltzmann simulation of power-law fluids flow around a forced-oscillation circular cylinder

Direct numerical simulations of power-law non-Newtonian fluids flow around a circular cylinder are performed by lattice Boltzmann method coupled with immersed moving boundary scheme. Obvious differences in macroscopic hydrodynamics and wake vortex dynamics between shear-thinning and shear-thickening fluids are resolved. Results show that shear-thickening effect increased drag coefficient but decreased lift coefficient, and delayed separation of boundary layer leading to lower vortex shedding frequency. The position with lowest viscosity on surface of cylinder in shear-thinning fluid is closer to leading edge stagnation point than the position in shear-thickening fluid. Wake vortex appears from surface of cylinder in shear-thinning fluid, however appears after some distance away from rear end of cylinder in Newtonian and shear-thickening fluid through dynamic mode decomposition. Vortex shedding modes in shear-thinning and shear-thickening fluids are very different at high oscillation amplitudes and transited from Chaos to 2S mode (two single vortexes with opposite directions but same energy shed) or P + S mode (a pair of vortexes with opposite rotation direction shed on one side of the cylinder and a single vortex shed on the other side) when increasing power-law index.

Mechanism of periodic oscillation in low-Reynolds-number buffet around an airfoil at angle of attack 0

In this study, the low-frequency oscillations found in the compressible low-Reynolds-number regime, defined as low-Reynolds-number buffet, were investigated by numerical calculations and modal analysis. Dynamic mode decomposition (DMD) and compressive sensing methods were employed to extract periodic flow structures. Numerical simulation results showed low-Reynolds-number buffet and Kármán vortex shedding. Low- and high-frequency oscillations [St=O(0.01), O(1.0)] were extracted by DMD and named the buffet mode and vortex shedding mode, respectively. Low-Reynolds-number buffet does not necessarily exhibit supersonic regions or shock wave. Simulation results show that the thickness of the separated shear layer changes significantly under low-Reynolds-number buffet. The change in the thickness of the separated shear layer was confirmed by the buffet mode of DMD results. Two types of compression pressure waves, advecting upstream, were identified. DMD indicated that they resulted from vortex shedding. According to simulation and DMD results, the origin of the shock waves appears to be the condensation of compression pressure waves due to the vortex shedding mode and expansion in the supersonic region due to the buffet mode. The formation of the shock waves seems to be subordinated to the vortex shedding mode and the buffet mode. A feedback model for low-Reynolds-number buffet inherent in separated shear layers, which does not require supersonic regions or shock waves, was proposed. Supersonic regions highly condensed the compression pressure waves, inducing a larger separation region and amplifying the oscillation. The role of supersonic regions in determining oscillation amplitudes was evidenced, although supersonic regions are not essential to the mechanism of low-Reynolds-number buffet.

Evaluation of combustion stability of single and multi-protrusion inserted hybrid rocket motor

The present study explores the influence of protrusions on the combustion stability of a hybrid rocket motor. The primary aim is to analyze single, double, and triple-protrusion configurations taking into account variables such as their location, material, and spacing between them. Protrusions used were made of Nylon (regress during combustion) and graphite (non-regress during combustion). For the base-case (without protrusion), significant pressure oscillations were observed, arising from the interaction between vortex shedding and fundamental longitudinal acoustic modes of the chamber at the fuel grain exit. A protrusion at 0.8X/L (X-protrusion insertion point from head-end, L-fuel grain length) disrupted the interaction between acoustic modes and vortex shedding, substantially dampened its amplitude (around 96% reduction). In case of double (0.2–0.8X/L, 0.5–0.8X/L) and triple-protrusions (0.2–0.5-0.8X/L), the distance between protrusions is playing a key role in inducing the pressure oscillations. When protrusions are kept close (0.5–0.8X/L and 0.2–0.5-0.8X/L), the excitation of third mode acoustics were observed. This was attributed to the continuous increase in protrusion height. If protrusion height exceeds 6–7 mm, the flow over the front protrusion separated and impinges on the subsequent protrusion. This causes pressure oscillations in double and triple-protrusion cases. These pressure oscillations were mitigated using regressable protrusions made of nylon, as they keep the height within the range of 6–7 mm. The results of this research provide valuable perspectives on the significance of protrusions in controlling combustion instability in hybrid rockets.

Simulation of Vortex-Induced Vibration for a Cylinder with Different Rounded Corners under Re = 150

A comprehensive 2D numerical model was conscientiously developed to investigate the vortex-induced vibration phenomena in a cylindrical structure with rounded corners. The Navier-Stokes equation was adeptly solved under the specific condition of a Reynolds number (Re) of 150. The investigation reveals intricate details of the phenomena. The study aimed to systematically analyze the interaction between drag and lift force coefficients, cylinder vibration amplitude, and the patterns of vortex shedding modes under various conditions. This study systematically altered the radius of the cylinder’s rounded corners to evaluate their effects on both structural and hydrodynamic responses. This variation was crucial in comprehending how slight alterations in the cylinder’s geometry impact significant changes in the flow dynamics and correlated vibration behavior. The model’s numerical results revealed the significant impact of the curved edge ratio on both the hydrodynamic forces acting on the cylinder and its vibration response. The variation in edge curvature resulted in changes in drag and lift coefficients, leading to a significant impact on the amplitude of vibration. This elucidates the crucial role of geometric design in controlling and optimizing the structural behavior of cylindrical structures under fluid flow conditions.