Fluid-structure Interaction Model Research Articles

Simulating cardiac fluid dynamics in the human heart.

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions (FSIs). However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the valves are limited in their abilities to predict valve performance, capture fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac FSI in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart's microstructure. Further, it is the first FSI model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and that its responses to changes in loading conditions are consistent with the Frank-Starling mechanism. These complex relationships emerge intrinsically from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical interventions. They also can provide platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients.

Computational haemodynamics for pulmonary valve replacement by means of a reduced fluid-structure interaction model.

Pulmonary valve replacement (PVR) consists of substituting a patient's original valve with a prosthetic one, primarily addressing pulmonary valve insufficiency, which is crucially relevant in Tetralogy of Fallot repairment. While extensive clinical and computational literature on aortic and mitral valve replacements is available, PVR's post-procedural haemodynamics in the pulmonary artery and the impact of prosthetic valve dynamics remain significantly understudied. Addressing this gap, we introduce a reduced Fluid-Structure Interaction (rFSI) model, applied for the first time to the pulmonary valve. This model couples a three-dimensional computational representation of pulmonary artery haemodynamics with a one-degree-of-freedom model to account for valve structural mechanics. Through this approach, we analyse patient-specific haemodynamics pre and post PVR. Patient-specific geometries, reconstructed from CT scans, are virtually equipped with a template valve geometry. Boundary conditions for the model are established using a lumped-parameter model, fine-tuned based on clinical patient data. Our model accurately reproduces patient-specific haemodynamic changes across different scenarios: pre-PVR, six months post-PVR, and a follow-up condition after a decade. It effectively demonstrates the impact of valve implantation on sustaining the diastolic pressure gradient across the valve. The numerical results indicate that our valve model is able to reproduce overall physiological and/or pathological conditions, as preliminary assessed on two different patients. This promising approach provides insights into post-PVR haemodynamics and prosthetic valve effects, shedding light on potential implications for patient-specific outcomes.

Verification Study of in Silico Computed Intracardiac Blood Flow With 4D Flow MRI.

Major challenges for clinical applications of in silico medicine are limitations in time and computational resources. Computational approaches should therefore be tailored to specific applications with relatively low complexity and must be verified and validated against clinical gold standards. This study performed computational fluid dynamics simulations of left ventricular hemodynamics of different complexity based on shape reconstruction from steady state gradient echo magnetic resonance imaging (MRI) data. Computed flow results of a rigid wall model (RWM) and a prescribed motion fluid-structure interaction (PM-FSI) model were compared against phase-contrast MRI measurements for three healthy subjects. Extracted boundary conditions from the steady state MRI sequences as well as computed metrics, such as flow rate, valve velocities, and kinetic energy show good agreement with in vivo flow measurements. Regional flow analysis reveals larger differences. Basic flow structures are well captured with RWM and PM-FSI. For the computation of further biomarkers like washout or flow efficiency, usage of PM-FSI is required. Regarding boundary-near flow, more accurate anatomical models are inevitable. These results delineate areas of application of both methods and lay a foundation for larger validation studies and sensitivity analysis for healthy and diseased cases, being an essential step upon clinical translations.

Modelling and analysis of two-dimensional static and dynamic aeroelasticity of Fish Bone Active Camber morphing aerofoils

As a continuous and smooth morphing concept for aerofoils, the Fish Bone Active Camber (FishBAC) concept has demonstrated significant aerodynamic efficiency improvements over traditional hinged flaps. In this paper, to investigate the static and dynamic aeroelasticity of FishBAC aerofoils, an unsteady two dimensional coupled fluid-structure interaction model is developed, which includes the structural response of the FishBAC spine, skin, stringers, tendons and actuator, coupled to an unsteady aerodynamics model. The structural dynamic model is Timoshenko beam-theory-based, while the aerodynamic model is based on Peters’ unsteady model. The static and dynamic aeroelasticity is studied after the model is validated. Results show that the increase in pulley rotational angle reduces the zero-lift angle of attack, while keeping the slope between the lift coefficient and angle of attack the same. A shorter morphing region closer to the trailing edge is beneficial for generating larger lift coefficient with the same tendon moment and angle of attack. Flutter occurs with the increase of the air speed. When the morphing end position is fixed at 0.9 chord, increasing the morphing length reduces the critical flutter speed significantly, with the second bending mode tending to drive instability. With the same morphing length, moving the morphing region closer to the leading edge increases the critical flutter speed, and the unstable mode changes from the second mode into the first mode.

Fluid-structure interaction analysis of a healthy aortic valve and its surrounding haemodynamics.

The opening and closing dynamics of the aortic valve (AV) has a strong influence on haemodynamics in the aortic root, and both play a pivotal role in maintaining normal physiological functions of the valve. The aim of this study was to establish a subject-specific fluid-structure interaction (FSI) workflow capable of simulating the motion of a tricuspid healthy valve and the surrounding haemodynamics under physiologically realistic conditions. A subject-specific aortic root was reconstructed from magnetic resonance (MR) images acquired from a healthy volunteer, whilst the valve leaflets were built using a parametric model fitted to the subject-specific aortic root geometry. The material behaviour of the leaflets was described using the isotropic hyperelastic Ogden model, and subject-specific boundary conditions were derived from 4D-flow MR imaging (4D-MRI). Strongly coupled FSI simulations were performed using a finite volume-based boundary conforming method implemented in FlowVision. Our FSI model was able to simulate the opening and closing of the AV throughout the entire cardiac cycle. Comparisons of simulation results with 4D-MRI showed a good agreement in key haemodynamic parameters, with stroke volume differing by 7.5% and the maximum jet velocity differing by less than 1%. Detailed analysis of wall shear stress (WSS) on the leaflets revealed much higher WSS on the ventricular side than the aortic side and different spatial patterns amongst the three leaflets.

Dynamic Characteristics of Pressure-Balanced Metal Bellows in Fluid–Structure Interaction

As a flexible component in high-pressure vessels and pipeline systems, bellows experience significant fluid–structure interaction effects under high-speed internal fluids and external vibrations. Nevertheless, their dynamic response mechanisms coupled with fluid–structure interaction mentioned below have not yet been clarified so far. In this work, a novel pressure-balanced metal bellow (PBMB) for low-stiffness and high-pressure resistance is firstly proposed. Several fluid–structure interaction models were considered to study the dynamic response characteristics of the PBMB. An experimental platform associated with fluid–structure interaction was established to validate the effectiveness of its vibration attenuation performance. The results indicate that the PBMB has an obvious vibration attenuation effect in the range of 5–90[Formula: see text]Hz, and super-harmonic and sub-harmonic resonance phenomena occur in the range of 90–200[Formula: see text]Hz. Under constant fluid conditions, fluid density, viscosity, flow velocity, and pressure are positively correlated with the response amplitude of the PBMB. The response of the PBMB oscillates at the fluid entry point due to both pulsating flow velocity and pulsating pressure. After several cycles, the response caused by pulsating flow velocity gradually decays and stabilizes. Thus, the impact of pulsating frequency on the stability of the response of bellows is insignificant during the initial cycles.

Experimental investigation and fluid-structure interaction modelling of the casting of self-compacting concrete for CRTS III slab track in the curved segments

Ensuring the casting quality of self-compacting concrete (SCC) is crucial for the operational safety and durability of China railway track system (CRTS) III slab track. However, the mechanisms of key factors influencing flow behaviors of SCC and structural responses remain insufficiently understood, nor is the relationship between flow behaviors and structural responses during casting. In this study, fluid-structure interaction (FSI) models of SCC casting were developed and verified by full-scale physical tests, comprising slump flow, L-box flow and casting of SCC in an actual track at the field of Laixi-Rongcheng high-speed railway. Through in-depth analysis on the casting process of SCC in curved segments with a super elevation of 80 mm, the relationship between flow behaviors and structural responses was established. Furthermore, the influence mechanisms of key factors on flow behaviors and structural responses were investigated systematically. Results show that during gravity-fed SCC casting, its flow velocity diminishes, thus increasing the static pressure and the forces exerted on the slab by SCC. These vertical and lateral forces increase to 147.16 and 7.83 kN through three stages of development, acceleration and stabilization, resulting in commensurate structural responses. At the end of casting process, the central region of the slab exhibits maximum vertical deformation of 0.95 mm and tensile stress of 1.07 MPa. The tension rods at the side with lower elevation bear greater vertical and lateral forces than the ones at the side with higher elevation. The rise of funnel height from 1.05 to 1.35 m accelerates the casting process but increases the forces exerted by SCC by up to 26 % and augments the associated response of entire structures, whereas the funnel diameter shows little effect. Increasing yield stress of SCC from 9.3 to 49.3 Pa produces a more uniform flow morphology and thus higher static pressure and force by SCC in the middle region of the slab, impacting the structural responses by up to 15 %. The growth of plastic viscosity from 59 to 99 Pa⋅s significantly affects the volume rate and casting time by up to 66 % but has little effect on the flow morphology, fluid pressure and structural responses. In order to ensure high quality casting of SCC, five clamping beams are suggested with two beams positioned at either side of the slab and the other three evenly placed along the middle region of the slab.

Dissecting contributions of pulmonary arterial remodeling to right ventricular afterload in pulmonary hypertension.

Pulmonary hypertension (PH) is defined as an elevation in the right ventricle (RV) afterload, characterized by increased hemodynamic pressure in the main pulmonary artery (PA). Elevations in RV afterload increase RV wall stress, resulting in RV remodeling and potentially RV failure. From a biomechanical standpoint, the primary drivers for RV afterload elevations include increases in pulmonary vascular resistance (PVR) in the distal vasculature and decreases in vessel compliance in the proximal PA. However, the individual contributions of the various vascular remodeling events toward the progression of PA pressure elevations and altered vascular hemodynamics remain elusive. In this study, we used a subject-specific one-dimensional (1D) fluid-structure interaction (FSI) model to investigate the alteration of pulmonary hemodynamics in PH and to quantify the contributions of vascular stiffening and increased resistance towards increased main pulmonary artery (MPA) pressure. We used a combination of subject-specific hemodynamic measurements, ex-vivo mechanical testing of arterial tissue specimens, and ex-vivo X-ray micro-tomography imaging to develop the 1D-FSI model and dissect the contribution of PA remodeling events towards alterations in the MPA pressure waveform. Both the amplitude and pulsatility of the MPA pressure waveform were analyzed. Our results indicated that increased distal resistance has the greatest effect on the increase in maximum MPA pressure, while increased stiffness caused significant elevations in the characteristic impedance. The method presented in this study will serve as an essential step toward understanding the complex interplay between PA remodeling events that leads to the most severe adverse effect on RV dysfunction.

Water-tank metabarrier for seismic Rayleigh wave attenuation.

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Computational Study on the Effects of Valve Orientation on the Hemodynamics and Leaflet Dynamics of Bioprosthetic Pulmonary Valves.

Pulmonary valves do not display a fibrous annulus as do other valves in the heart; thus, pulmonary valves can be implanted at multiple orientations and locations within the right ventricular outflow tract (RVOT). This gives surgeons more freedom when implanting the valve but it also results in uncertainties regarding placement, particularly with respect to valve orientation. We investigate the pulmonary artery hemodynamics and valve leaflet dynamics of pulmonary valve replacements (PVRs) with various orientations via fluid-structure interaction (FSI) models. A canonical model of the branching pulmonary artery is coupled with a dynamic model of a pulmonary valve, and from this we quantify the effect of valve implant orientation on the postvalvular hemodynamics and leaflet dynamics. Metrics such as turbulent kinetic energy (TKE), branch pulmonary artery flow distributions, projected valve opening area (PVOA), and pressure differentials across the valve leaflets are analyzed. Our results indicate that off-axis orientation results in higher pressure forces and flow and energy asymmetry, which potentially have implications for long-term durability of implanted bioprosthetic valves.

Experimental and numerical study on dynamic response of a photovoltaic support structural platform with a U-shaped tuned liquid column damper

A tuned liquid column damper (TLCD) is widely used in offshore structures as a passive energy dissipation device to reduce the harm of wind, wave, and current loads to the safety of offshore platforms. This investigation explores the dynamic response and interaction mechanism of a photovoltaic support structural platform (SSP) equipped with a TLCD by experimental and numerical analysis. The vibration mitigation performance of the TLCD under varying liquid depth ratios, external excitation frequencies, and amplitudes is systematically evaluated. The experiments focus on assessing the structural dynamic response and wall pressure to determine the vibration reduction efficiency of the TLCD for structures with fundamental frequencies more than 2 Hz. The experimental results indicate that the TLCD can reduce the structural response maximally near the natural frequency (2.52 Hz) of the structure, with vibration reduction effectiveness ranging from 42.0% to 85.1%. Additionally, one develops a two-way fluid-structure interaction (FSI) model to investigate further the impact of hydrodynamic pressure caused by sloshing inside the TLCD on the SSP motion response, which providing a more detailed explanation for the different phenomena observed in the experimental results.

Fluid-structure interaction modeling of dry wire drawing by coupling OpenFOAM models of lubricant film and metal wire

Fluid-structure interaction modeling of dry wire drawing by coupling OpenFOAM models of lubricant film and metal wire

Simulation study on the effect of eccentricity on the performance of a reciprocating seal

This article establishes a three-dimensional fluid-structure interaction (FSI) model for reciprocating rod seals. Based on this model, a novel method using a two-dimensional FSI model to solve the average sealing performance across multiple sections is proposed for the first time. This method allows for the dimensional reduction of solid mechanics, contact mechanics, and fluid mechanics analysis. The performance of the sealing system was calculated and analyzed under static eccentricity (which does not change with piston rod motion) and dynamic eccentricity (which changes with piston rod motion) using the aforementioned models. The results indicate that the sealing performance calculated by both models is highly consistent, demonstrating that, within the permissible engineering limits, the two-dimensional FSI model can replace the three-dimensional model, thereby reducing computational costs and improving convergence. Additionally, the results show that eccentricity increases the friction and leakage rates of the sealing system, with dynamic eccentricity having a greater impact on sealing performance than static eccentricity due to the viscoelasticity of the rubber.

Simulation and verification of cylinder head’s temperature field for marine low-speed engine

Abstract The high load capacity of marine low-speed engines poses a challenge to the thermal load of the cylinder head and temperature field simulation can guide its structural design and optimization. The 3-dimensional models of the fluid domain for the cooling water and the solid domain for the cylinder head are established and meshed, the fluid domain model is simulated to research the heat transfer pattern by Fluent software, and the surface temperature and heat transfer coefficient of the cooling water is calculated. The thermal boundary conditions of the gas in the cylinder are simulated through the analysis of the engine working process. The temperature of the cylinder head is calculated based on the fluid-structure interaction model with the thermal boundary conditions by Workbench software. The validation of the model is carried out by comparing the simulated and measured temperature data in the heated inner wall of the cylinder head. The research results show that compared with the measured value, the error of simulation results is small, which shows that the model and method are reasonable. The temperature in the inner wall of the combustion chamber is low, which can provide possibilities to appropriately improve the power density of the low-speed engine and reduce the risk of low-temperature corrosion.

Elucidating the mechanism of overcuring in microchannels fabricated via vat photopolymerization (VPP) for precise microfluidic chip printing

Vat Photopolymerization (VPP) technology is highly regarded for precision micromachining applications like microfluidic chip fabrication, owing to its fine resolution, adaptability, and rapid prototyping capabilities. However, the challenge of resin over-curing resulting from UV energy penetration poses a significant obstacle in microchannel printing. This study addresses this challenge by investigating the intricate relationship between resin properties and over-curing. Diverse microfluidic chips were printed utilizing VPP technology, and the overall cross-sectional over-curing characteristics of the channels were systematically examined. A novel combination of the classical UV light curing model and computational Fluid-Structure Interaction (FSI) model with the VPP printing process was proposed to examine the complex hydrodynamics and exfoliation dynamics within VPP-printed microchannels. The simulation results suggest that resins with higher viscosities and surface roughness are better suited for microchannel printing. Subsequent experiments using five different resins verified these findings and showed that the microchannels obtained with resins of lower viscosity and surface roughness resins have an irregular trapezoidal cross-section, which is uncontrollable and unpredictable and seriously affects the microchannel printing accuracy. Conversely, resins with higher viscosity and surface roughness have an ideal rectangular cross-section, which can be compensated by the model further refined printing to print microchannel. Finally, microfluidic chips were printed using "high precision 8 K resin" and "8 K-clay resin" with higher viscosity and surface roughness. The results proved that the microchannels printed by these resins had the desired rectangular cross-section, which was consistent with the "DLP light-curing" model. This study elucidates, for the first time, the intricate interplay between resin properties, printing structure, and microchannel over-curing, and this provides a solid groundwork for advancing high-precision microfluidic chip fabrication via DLP printing.

AnXplore: a comprehensive fluid-structure interaction study of 101 intracranial aneurysms.

Advances in computational fluid dynamics continuously extend the comprehension of aneurysm growth and rupture, intending to assist physicians in devising effective treatment strategies. While most studies have first modelled intracranial aneurysm walls as fully rigid with a focus on understanding blood flow characteristics, some researchers further introduced Fluid-Structure Interaction (FSI) and reported notable haemodynamic alterations for a few aneurysm cases when considering wall compliance. In this work, we explore further this research direction by studying 101 intracranial sidewall aneurysms, emphasizing the differences between rigid and deformable-wall simulations. The proposed dataset along with simulation parameters are shared for the sake of reproducibility. A wide range of haemodynamic patterns has been statistically analyzed with a particular focus on the impact of the wall modelling choice. Notable deviations in flow characteristics and commonly employed risk indicators are reported, particularly with near-dome blood recirculations being significantly impacted by the pulsating dynamics of the walls. This leads to substantial fluctuations in the sac-averaged oscillatory shear index, ranging from -36% to +674% of the standard rigid-wall value. Going a step further, haemodynamics obtained when simulating a flow-diverter stent modelled in conjunction with FSI are showcased for the first time, revealing a 73% increase in systolic sac-average velocity for the compliant-wall setting compared to its rigid counterpart. This last finding demonstrates the decisive impact that FSI modelling can have in predicting treatment outcomes.

Flexibility evaluation of psammophytes using Young’s modulus based on 3D numerical simulation

Flexible psammophytes play an important role in controlling soil wind erosion and desertification, owing to their characteristics. Although flexibility of psammophytes has been considered in previous studies, the interaction between flexible psammophytes and the surrounding airflow field still remained unclear. In this study, we used the Young’s modulus to describe plant flexibility and conducted a 3D computational fluid dynamics simulation using a standard k-ε model and a fluid–structure interaction model. Taking Caragana korshinskii (Caragana), a typical psammophyte, as the research object, we constructed 3D geometric models with different diameters to simulate the airflow field around the flexible psammophytes. By comparing with the simulation results of rigid plants and simulation results of flexible plants at different wind speeds, we could verify the rationality of the simulation method. Based on the simulation results, the maximum swing amplitude of the model and the Young’s modulus were found to have a negative correlation, presenting an exponential functional relationship with good fitting. The relationship between the actual Young’s modulus of the plant branches and that of different diameter models in the numerical simulation was also established. This study is expected to improve our basic understanding of the interaction between flexible psammophytes and the surrounding airflow field, and provide some qualitative reference for the numerical simulation of the airflow field around flexible psammophytes.

Enhancing heat transfer in L-shaped enclosures with combined natural convection-fluid structure interaction: Incorporating flexible fin and elastic wall

In the present investigation, a numerical investigation of the flow and heat transfer characteristics inside an L-shaped enclosure with a flexible fin and an elastic wall has been carried out using the finite element method. The Fluid-Structure Interaction model is used to capture the interaction between the fluid and the solid structure. The free end of the flexible fin is exposed to sinusoidal vertical force and the upper wall of the enclosure is considered to be elastic and a sinusoidal force is applied on this elastic wall. The obtained results showed that the fluid flow through the enclosure is entirely influenced by the periodic oscillation of the flexible fin and elastic wall. Besides, the Nusselt number over the horizontal and vertical hot walls of the L-shaped enclosure is strongly affected by the amplitude and frequency of the applied sinusoidal forces on the flexible fin and elastic wall. The heat transfer over the vertical hot wall is enhanced considerably with an increase in the amplitude and frequency of the applied sinusoidal forces. Moreover, the Nusselt number over the hot vertical wall is increased with the decrease of the elastic modulus value of the elastic wall. The results also show that the combination of the flexible fin and elastic wall has contributed to the extra enhancement of the Nusselt number over the hot vertical wall of the L-shaped enclosure.

FSI Modeling and simulation analysis of superimposed valves in flow state of hydraulic shock absorbers*

Abstract This study, through rigorous bench testing, has identified the pivotal parameters influencing the oil flow state within the shock absorber. Based on the Reynolds number parameter model, a reduced parameter model was established, incorporating the number of holes in the throttle valve, their diameters, and the diameters of the piston and piston rod as fundamental parameters. To ensure the model’s precision, this study developed high-accuracy solid and fluid finite element models, defined specific time steps for both laminar and turbulent flows along with their respective numerical methods, and executed a detailed Fluid-Structure Interaction (FSI) finite element simulation analysis. The findings indicate that fluid-structure interaction simulation accurately captures the shock absorber oil’s flow states across laminar, transitional, and turbulent phases, identifying the maximum Reynolds number position, with the simulation’s velocity-specific results aligning closely with the parameter model, showing a maximum deviation of 22%, a minimum of 2%, and an overall average error of 9.1%.

Experimental and numerical investigations to the aeroelastic response of flexible thin airfoil

The paper investigates the phenomenon of the aeroelastic response of flexible thin airfoils under various angles of attack (AOAs) and flow velocities through wind tunnel experiments and numerical simulations. The vibration modal characteristics are explored, including vibration frequencies, amplitudes, modal transition, and instantaneous characteristics. Vibration is directly measured using non-contact laser sensors, and the numerical model is appropriately configured to simulate the fluid–structure interaction (FSI) problem under large deformation. Experiments cover a range of AOAs (1°–20°) and incoming velocities (from 10 to 73 m/s), with dynamic responses measured using four laser sensors. Both average and instantaneous modal response features are analyzed, revealing multi-modal characteristics as velocity and AOA increase. The vibration mode transitions from pure bending to higher-order modes as incoming velocity increases. Specifically, at higher velocities and increased AOA, the high-order vibration component shifts from bending-torsional coupled mode to pure-torsional mode. Comparison of vibration frequencies between experimental measurements and finite element method simulations highlights significant shifts, particularly in the pure-torsional mode. Furthermore, employing commercial software ANSYS CFX and ANSYS Mechanical, a two-way three-dimensional FSI model successfully replicates flutter boundaries observed experimentally at 1° AOA and approximately incoming velocity 73 m/s. This FSI model is extended to simulate the multi-modal vibrations at 15° AOA, yielding insights into flow phenomena contributing to multi-modal vibration at this AOA. An explanation is provided for the multi-modal vibration phenomenon observed in the experiments based on the above insight. Finally, the differences between the experimental and numerical simulations are speculated upon.