In-house Fluid Structure Interaction Research Articles

Abstract 17617: Toward Improving Diagnosis and Interventional Predictability in Aortic Valve Stenosis Using Computational Modeling

Introduction: Watchful waiting for symptoms or critical hemodynamics to intervene on aortic stenosis (AS) may delay too long. While stress tests can detect symptoms in allegedly asymptomatic AS patients, image-based computations based on advanced modeling techniques can provide critical biomechanical insights. Hypothesis: Advanced computational modeling techniques utilizing patient data backed by high-performance computing can inform a personalized understanding of disease progression, diagnosis, and anticipated post-op hemodynamics to predict interventional efficacy. Methods: A validated in-house Fluid-structure Interaction (FSI) algorithm that allows easy translation of patient-specific anatomies was utilized to perform "virtual stress test" on a moderate AS with increasing LV contraction to predict systolic ejection dynamics under stress. TAVR was virtually implanted and post-op aortic hemodynamics were quantitatively compared with pre-op (diseased) data. Results: Predictions demonstrated that that aortic flow turbulence in moderate AS (Re = 11,700) during exercise (115 bpm) can be similar to severe AS (Re=10,000) at rest (70 bpm) resulting in a greater dissipation losses rising linearly with heart rates. As LV contraction rose, each valve cusp underwent a distinct non-linear rise (>100%) in mechanical stresses that can accelerate calcification. Interestingly, our evaluation revealed that the heterogenous ΔP vs. Q relationship in AS observed clinically can be attributed to a non-linear rise in aortic valve area occurring during mid-systole. Aortic hemodynamics improved post-TAVR by reducing dissipation losses by ~11 fold and restoring near-normal peak-systolic velocity (1.7 m/s) in the ascending aorta. Conclusions: High-performance based multi-physics algorithms incorporating patient data might offer comprehensive biomechanical insights into diagnosis and interventional suitability for aortic valve stenosis.

Propulsive performance of a two-dimensional elliptic foil undergoing interlinked pitching and heaving

We computationally study the propulsive performance of a two-dimensional elliptic foil undergoing interlinked pitching-heaving motion. This motion is realized by pitching the foil about an axis on its centerline outside the foil and by varying the distance between the pitching point and the leading edge. A distance of 0 and −∞ corresponds to leading edge pitching and pure heaving. An in-house fluid-structure interaction solver based on the sharp interface immersed boundary method is employed to resolve the flow field around the foil. We conducted simulations for different cases of the location of the pitching axis and pitching frequency at a Reynolds number of 100. The thrust generation is explained by the dynamics of leading-edge and trailing-edge vortices. The wake corresponding to thrust is either reverse von Kármán or a deflected reverse von Kármán vortex street. Analysis revealed the existence of an optimal pitching point for maximum thrust or propulsive efficiency at a given reduced pitching frequency. The optimal regions of the thrust and propulsive efficiency are quantified as a function of reduced pitching frequency and the location of the pitching axis. The pitching point for the maximum thrust and efficiency is found to be different. We discuss the fluid-mechanical reasons for the variation of propulsive performance with the location of the pitching point and the pitching frequency and corroborate our reasoning with the wake signatures.

Chordwise flexible aft-tail suppresses jet-switching by reinstating wake periodicity in a flapping foil

The effect of a chordwise flexible aft-tail of a rigid heaving aerofoil on the dynamical transitions of the trailing-wake is studied here. The two-way coupled fluid–solid dynamics is simulated using an in-house fluid–structure interaction (FSI) platform, comprising a discrete forcing immersed boundary method based incompressible Navier–Stokes solver, weakly coupled with a finite difference method based structural solver. The FSI dynamics is studied in comparison to the corresponding rigid tail configuration. For the latter, mild jet-switching due to quasi-periodic movement of the wake vortices gives way to vigorous jet-switching as the dynamics transitions to a state of intermittency, where the quasi-periodic behaviour gets interspersed with chaotic windows. Introduction of a moderately flexible tail regularises this intermittent dynamics, eliminating jet-switching. The wake exhibits a deflected reverse Kármán pattern with fluctuating angles, governed by quasi-periodicity. With a highly flexible tail (very low rigidity), the wake shows almost a symmetric reverse Kármán street as periodicity is restored. Flexibility of the aft-tail is next controlled by changing its length, and flow is regularised and periodicity retained for moderate rigidity for increased length. Different dynamical states are established through robust nonlinear dynamical tools. The underlying flow-field behaviour, instrumental in suppressing the jet-switching phenomenon, is identified through a detailed investigation of the near-field vortex interactions dictated by the dynamics. A suite of measures has also been derived from the unsteady flow field to quantify the interactions of the key near-field vortices with a view to understanding the mechanism of switching and its subsequent suppression through flexibility.

High Order Accurate Numerical Simulation of Vortex-Induced Vibrations of a Cooled Circular Cylinder Case using Solution Dependent Weighted Least Square Gradient Calculations

In this paper, the fluid-structure interaction problem: vortex-induced vibration of a cooled circular cylinder involving thermal buoyancy is numerically investigated. The elastically mounted cylinder having a temperature lower than the flowing fluid is modelled using mass-spring-damper hence allowed to vibrate in the transverse direction to the flow direction. The gravity is acting opposite to the flow direction. In-house fluid-structure interaction solver is developed based on Harten Lax and van Leer with contact for artificial compressibility Riemann solver. The arbitrarily Lagrangian-Eulerian formulation is employed here, and the mesh is dynamically moved using radial basis function-based interpolation. The solution-dependent weighted least squares based gradient calculations are developed to achieve higher-order accuracy over unstructured meshes. The laminar incompressible flow at Reynolds number, Re = 200, and Prandtl number, Pr = 0.71, is simulated for the mass ratio of 1 and reduced damping coefficient of 0.001. The flow is investigated for Richardson number (-1, 0) and over a wide range of natural frequencies of the cylinder. The heat transfer characteristics from a cylinder are captured and compared with the existing literature results. From the study, it can be observed that in the presence of the thermal boundary layer, the oscillation of the cylinder increases to its maximum amplitude, particularly for values of natural frequencies (0.063 – 0.3).

Harnessing flow-induced vibration of a D-section cylinder for convective heat transfer augmentation in laminar channel flow

Flow-induced vibration (FIV) of a D-section cylinder is computationally studied and utilized to augment convective heat transfer in a heated laminar channel flow. An in-house fluid–structure interaction (FSI) solver, based on a sharp-interface immersed boundary method, is employed to solve the flow and thermal fields. In conjunction, a spring–mass system is utilized to solve for the rigid structural dynamics. Using numerical simulations, we highlight that the oscillations of a D-section cylinder are driven by vortex-induced vibration and galloping. It is observed that as the cylinder vibrates, vortices are shed from the apex of the cylinder due to the separating shear layers. These vortices, categorized using shedding patterns, interact with the heated channel walls. This interaction results in disruption of the thermal boundary layer (TBL), thus leading to heat transfer augmentation. The enhancement in thermal performance has been quantified using time and space-averaged Nusselt numbers at the channel walls. It is observed that the oscillation amplitude of the D-section cylinder and the extent of vortex–TBL interaction are crucial for determining heat transfer augmentation. Both symmetric and asymmetric thermal augmentation at the top and bottom channel walls have been reported. Finally, to assess the effectiveness of heat transfer augmentation, the D-section cylinder FIV is compared to other FSI systems operating under similar conditions.

Thrust generation by pitching and heaving of an elastic plate at low Reynolds number

We computationally study thrust generation and propulsive characteristics of an elastic plate pitching and/or heaving in free stream laminar flow. The pitching is considered about the leading edge, and the Reynolds number based on the plate length and free stream velocity is 150. An in-house fluid–structure interaction (FSI) solver is employed to simulate the large-scale flow-induced deformation of the structure along with active pitching and heaving in two-dimensional coordinates. The FSI solver utilizes a partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structural dynamics solver. We elucidate the mechanism of the thrust generation in the rigid and elastic plate by comparing the time-variation of thrust and work done by the plate, together with the wake signatures in the downstream. The time variation of the thrust is explained using first-order scaling arguments. The computed thrust as a function of pitching frequency for the rigid pitching plate shows a similar trend as compared to the published data of rigid foils, while the elastic plate exhibits a strong influence of the flow-induced deformation of the plate. They both exhibit reverse von Kármán-like vortex shedding in the downstream. We quantify the differences in propulsive characteristics of these two plate types as a function of pitching frequency. We found that there lies an optimum pitching frequency for the elastic plate for efficient propulsion, while the rigid one outperforms the elastic plate at larger pitching frequency. This is due to the fact that the elastic plate locks in to a higher mode of vibration at a larger pitching frequency. Furthermore, the influence of mass ratio, flexural rigidity, pitching amplitude, and Reynolds number on the performance of the elastic plate is also investigated. Finally, we study the combined effect of pitching and heaving on the propulsive performance. The pitching frequency for the maximum efficiency is lesser for the combined heaving and pitching plate as compared to only heaving or only pitching. Our results provide fundamental insights into the propulsive characteristics of the elastic pitching and/or heaving plates, which could help design autonomous underwater vehicles.

Computational modeling and analysis of flow-induced vibration of an elastic splitter plate using a sharp-interface immersed boundary method

We present the development and benchmarking of an in-house fluid–structure interaction (FSI) solver. An implicit partitioned approach is utilized to couple a sharp-interface immersed boundary method-based flow solver and a finite-element method-based structural solver. In the present work, the coupling is accelerated using a dynamic under-relaxation scheme. The revised coupling is around two to three times faster and numerically stable, as compared to the one that uses a constant under-relaxation parameter. The solver is validated against two FSI benchmarks in which a thin, finite thickness, elastic splitter plate is attached to the lee side of a circular or square rigid cylinder, subjected to laminar flow. In these two-dimensional benchmarks, the flow induces a wave-like deformation in the plate, and it attains a periodic self-sustained oscillation. We employ the FSI solver to analyze the flow-induced vibration (FIV) of the plate in a uniform laminar free-stream flow for a wide range of mass ratio and bending stiffness at Reynolds number (Re) of 100, based on the diameter of the cylinder. At the given Re, two-dimensional numerical simulations show that the FIV of the plate effectively depends only on the mass ratio and bending stiffness. The largest displacement of the plate vibration is found to occur in the lock-in region, where the vortex shedding frequency of the coupled fluid–structure system is close to the natural frequency of the splitter plate. We briefly discuss wake structures and phase plots for different cases of mass ratio and bending stiffness.

Aeroelastic vibration analysis of a 1.5 stage compressor

Aeroelastic vibration problems are commonly found in modern compressors operating in off-design conditions. Large amplitude vibration could lead to high cycle fatigue (HCF) of blade and usually occurs in front stages of axial compressors. In this study, the influence of tip gap size on aeroelastic stability is analyzed in a 1.5 stage compressor with an in-house fluid-structure interaction code. A three-dimensional unstructured finite-volume compressible flow solver is applied in the fluid domain and a structure dynamic solver with the modal superimposition method for blade motion is used in the structure domain. Rotor tip clearances of 1%, 2% and 3% of tip axial chord at maximum rotor loading conditions at off-design speeds are analyzed for aeroelastic stability. The tip leakage flow and vortex structure can be seen near the blade tip region at a larger tip gap size. The aeroelastic stability of rotor blade at different tip gap sizes is mainly influenced by the 1st torsion mode, and the variation of aerodynamic damping is not monotonous. The intensity of the tip vortex and shock wave are the key factors affecting the aeroelastic stability of rotor when tip gap size increases.

Vortex-induced vibration of a cooled circular cylinder

We numerically investigate vortex-induced vibration of a cooled circular cylinder in the presence of thermal buoyancy. We employ an in-house fluid-structure interaction solver based on a sharp-interface immersed boundary method. The cylinder is elastically mounted and is free to vibrate transversely to the flow direction. The surface of the cylinder is prescribed at a temperature lower than that of the fluid, and the gravity is aligned opposite to the flow direction. Numerical simulations are carried out for the following parameters: Reynolds number, Re = 150, Prandtl number, Pr = 7.1, Richardson number, Ri = [−1, 0], mass ratio, m = 2, and reduced velocity, UR = [3, 20]. The oscillation amplitude of the cylinder is larger in the presence of the thermal buoyancy for 4 < UR < 15. The amplitude is maximum at UR = 11 and is around ≈1D* in the presence of the thermal buoyancy, where D* is the diameter of the cylinder. However, this amplitude is ≈0.6D* at UR = 4 in the absence of the thermal buoyancy. The lock-in (synchronization) region is obtained for a wider range of UR in the presence of the thermal buoyancy. In the presence of the thermal buoyancy, along with a dominating vortex shedding frequency, we obtain multiple weak as well as strong even and odd harmonics along with subharmonics of the fundamental frequency in the lift signal. However, the secondary frequencies are limited to only a weak third harmonic of the fundamental frequency in the absence of the thermal buoyancy. We observe elongated as well as wider vortices and isotherms in the presence of the thermal buoyancy although the vortex shedding mode remains “2S.” Our results show that there exists a critical minimum absolute value of Ri in order to achieve the lock-in and this value increases with UR.

Response of a linear viscoelastic splitter plate attached to a cylinder in laminar flow

The flow-induced deformation of a viscoelastic thin plate attached to the lee side of a circular cylinder subjected to laminar flow is numerically investigated. An in-house fluid–structure interaction solver couples the sharp-interface immersed boundary method for fluid dynamics with a finite-element method for structural dynamics. Extending published results on elastic materials, the Standard Linear Solid (SLS) model is used to represent viscoelasticity of the plate, governed by the following two parameters: (a) the ratio of the non-equilibrium to equilibrium Young’s modulus (R), and (b) the ratio of dimensionless material damping to the dimensionless non-equilibrium Young’s modulus (τ). The focus of the present study is to examine the dynamic response of the viscoelastic plate at Reynolds number of Re=100. The amplitude and the time to achieve a dynamic steady state of a plate with 0.1<R<5 and 0.1<τ<10 have been investigated. The plate attains a self-sustained time-periodic oscillation with a plateau amplitude for the range of R=[0.1–5] for all values of τ. The dimensionless tip displacement amplitude (AY,tip) is found to be a non-monotonic function of τ. When the forcing frequency (vortex shedding frequency) is lesser (greater) than the natural frequency (considering the equilibrium Young modulus) of the plate, AY,tip decreases (increases) asymptotically. The theoretical analysis of a simple spring–mass–dashpot model of SLS is undertaken to understand the effect of sinusoidal forcing on the plate dynamics. Analytical predictions show general agreement with the non-monotonic behaviour of the numerically computed AY,tip. The results suggest that careful tuning of the damping may be effectively employed to enhance power output for energy extraction applications or to suppress flow-induced vibration when it is detrimental to the structure.

A sharp interface immersed boundary method for vortex-induced vibration in the presence of thermal buoyancy

We report the development of an in-house fluid-structure interaction solver and its application to vortex-induced vibration (VIV) of an elastically mounted cylinder in the presence of thermal buoyancy. The flow solver utilizes a sharp interface immersed boundary method, and in the present work, we extend it to account for the thermal buoyancy using Boussinesq approximation and couple it with a spring-mass system of the VIV. The one-way coupling utilizes an explicit time integration scheme and is computationally efficient. We present benchmark code verifications of the solver for natural convection, mixed convection, and VIV. In addition, we verify a coupled VIV-thermal buoyancy problem at a Reynolds number, Re = 150. We numerically demonstrate the onset of the VIV in the presence of the thermal buoyancy for an insulated cylinder at low Re. The buoyancy is induced by two parallel plates, kept in the direction of flow and symmetrically placed around the cylinder. The plates are maintained at the hot and cold temperature to the same degree relative to the ambient. In the absence of the thermal buoyancy (i.e., the plates are at ambient temperature), the VIV does not occur for Re ≤ 20 due to stable shear layers. By contrast, the thermal buoyancy induces flow instability and the vortex shedding helps us to achieve the VIV at Re ≤ 20, lower than the critical value of Re (≈21.7), reported in the literature, for a self-sustained VIV in the absence of the thermal buoyancy. The present simulations show that the lowest Re to achieve VIV in the presence of the thermal buoyancy is around Re ≈ 3, at Richardson number, Ri = 1. We examine the effect of the reduced velocity (UR), mass ratio (m), Prandtl number (Pr), Richardson number (Ri) on the displacement of the cylinder, lift coefficient, oscillation frequency, the phase difference between displacement and lift force, and wake structures. We obtain a significantly larger vibration amplitude of the cylinder over a wide range of UR as compared to that in the absence of the thermal buoyancy.

The response of an elastic splitter plate attached to a cylinder to laminar pulsatile flow

The flow-induced deformation of a thin, elastic splitter plate attached to the rear of a circular cylinder and subjected to laminar pulsatile inflow is investigated. The cylinder and elastic splitter plate are contained within a narrow channel and the Reynolds number is mostly restricted to Re=100, primarily covering the two-dimensional flow regime. An in-house Fluid-Structure Interaction code is employed for simulations, which couples a sharp-interface immersed boundary method for the fluid dynamics with a finite-element method to treat the structural dynamics. The structural solver is implicitly (two-way) coupled with the flow solver using a partitioned approach. This implicit coupling ensures numerical stability at low structure-fluid density ratios. A power spectrum analysis of the time-varying plate displacement shows that the plate oscillates at more than a single frequency for pulsatile inflow, compared to a single frequency observed for steady inflow. The multiple frequencies obtained for the former case can be explained by beating between the applied and plate oscillatory signals. The plate attains a self-sustained time-periodic oscillation with a plateau amplitude in the case of steady flow, while the superimposition of pulsatile inflow with induced plate oscillation affects the plateau amplitude. Lock-in of the plate oscillation with the pulsatile inflow occurs at a forcing frequency that is twice of the plate natural frequency in a particular mode and this mode depends on the plate length. The plate displacement as well as pressure drag increases at the lock-in condition. The percentage change in the maximum plate displacement, and skin-friction and pressure drag coefficients on the plate, due to pulsatile inflow is quantified. The non-linear dynamics of the plate and its coupling with the pulsatile flow are briefly discussed.