Fluid-solid Interaction Problem Research Articles

A flow-reconstruction based approach for the computation of hydrodynamic stresses on immersed body surface

This study focuses on obtaining reliable hydrodynamic stresses on the surface of rigid bodies in the simulation of fluid-solid interactions using the diffuse-interface immersed boundary method (IBM). In order to obtain the pressure and velocity gradient information on the immersed boundary, we employ a model to reconstruct the near-boundary fluid flow along the surface normal direction. Different from most existing flow reconstruction models in diffuse-interface IBMs based on the boundary layer approximation, we propose a new reconstruction model relying only on the non-slip velocity and local flow information. With this improvement, the present reconstruction model is theoretically applicable to fluid flows with intermediate Reynolds numbers (with the existence of a laminar boundary layer) and low Reynolds numbers (in the absence of a boundary layer). To examine the validity of the present reconstruction model, we conduct a series of simulations, including the uniform flow past a fixed body and the settling of a rigid body in a quiescent fluid. It is demonstrated that the present reconstruction model has a better performance than existing models in predicting hydrodynamic stresses on the immersed boundary within a wide range of Reynolds numbers from O(1) to O(100). The capability and robustness of the proposed model demonstrate its potential to address fluid-solid interaction problems with a-priori unknown or time-varying Reynolds numbers, such as fully resolved simulations of particle laden flows.

The random feature method for solving interface problems

Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization schemes or unfitted meshes with tailored schemes to achieve controllable accuracy and convergence rate. Along another line, mesh-free methods bypass mesh generation but lack robustness in terms of convergence and accuracy due to the low regularity of solutions. In this study, we propose a novel method for solving interface problems within the framework of the random feature method (RFM). This approach utilizes random feature functions in conjunction with a partition of unity as approximation functions, and solves a linear least-squares system to obtain the approximate solution. In the context of interface problems, two innovative and crucial components are incorporated into the RFM. Firstly, we utilize two sets of random feature functions on each side of the interface, allowing for the inclusion of low regularity or even discontinuous behaviors in the solution. Secondly, the construction of the loss function is based on the assessment of the partial differential equation, initial/boundary conditions, and the interface condition on collocation points. This approach ensures that these conditions are equally satisfied. Consequently, the challenges arising from geometric complexity primarily manifest in the generation of collocation points, a task amenable to standard methods. Importantly, the proposed method retains its meshfree characteristics and robustness when addressing problems featuring intricate geometries. We validate our method through a series of linear interface problems with increasingly complex geometries, including two-dimensional elliptic and three-dimensional Stokes interface problems, a three-dimensional elasticity interface problem, a moving interface problem with topological change, a dynamic interface problem with large deformation, and a linear fluid–solid interaction problem with complex geometry. Our findings show that despite the solution often being only continuous or even discontinuous, our method not only eliminates the need for mesh generation but also maintains high accuracy, akin to the spectral collocation method for smooth solutions. Remarkably, for the same accuracy requirement, our method requires two to three orders of magnitude fewer degrees of freedom than traditional methods, demonstrating its significant potential for solving interface problems with complex geometries and predetermined intricate evolution.

Numerical Study of Fluid–Solid Interaction in Elastic Sluice Based on SPH Method

In this paper, the fluid–solid interaction problem involving structural movement and deformation is considered, and an SPH (smoothed particle hydrodynamics) interaction method is proposed to establish a numerical fluid–solid model and to correct the particle velocities in the momentum conservation equations. It is found that, when the smoothing coefficient is equal to 0.93, the similarity of the free surface curves reaches up to 91.9%, and calculations are more accurate. Under the same working conditions, the classical model of elastic sluice discharge is established based on the SPH method and the finite element method, and the validity and accuracy of the model based on the SPH method are verified by analyzing the flow pattern of the sluice discharge, the opening of the elastic gate, and the change trend in the free liquid surface curve. On this basis, a number of characteristic points on the sluice gate are selected based on the SPH model to investigate the change rule of pressure at the fluid–solid interface, and the results are as follows: (1) based on the numerical model established by the SPH method, the flow pattern of the water, the opening of the elastic gate, and the change in the free liquid level curve are all in better agreement with the experimental results in the literature than those of the finite element method, and the computational results are also better; (2) the pressure of the solid on the fluid at each characteristic point is equal to the pressure of the fluid on the solid, which satisfies the principle of action–reaction and laterally verifies the nature of the dynamic boundary between the fluid and the solid, further verifying the validity of the program; and (3) in the process of sluice discharge, the elastic sluice presents a large force at both ends and a small force in the middle, meaning that the related research in this paper can act as a reference for flow–solid interaction problems related to sluice discharge.

A multigrid partition coupled Eulerian–Lagrangian method for fluid–solid interaction problems

In this paper, a multigrid partition coupled Eulerian–Lagrangian method (PCELM) is proposed to model fluid–solid interactions between fluids and moving or fixed rigid bodies. In this method, Lagrangian particles are arranged in Eulerian grids to track the interface, and the partition weighted bidirectional mapping method is used to improve the mapping accuracy between particles and grids. The multigrid domain is established to realize independent and contact calculations of the fluid and solid, which can solve for the cross-interference of multiple velocity fields in a single grid domain. Moreover, based on the contact in the particle volume domain, a more accurate fluid–solid interaction method, in which the contact properties of real grid nodes are identified by judgment and search criteria and then corrected, is proposed to overcome false contact and nonphysical penetration problems. Then, the accuracy and stability of the PCELM are verified using representative fluid–solid interactions. Finally, experiments and simulations of dam-break floods impacting the dam board are carried out. These experiments prove that the PCELM can accurately capture the free surface of dam-break floods and can provide suggestions for the installation of dam boards in hydraulic engineering.

A novel method for studying fluid-solid interaction problems of the rotor system in air bearings with manufacturing errors

A novel method for studying fluid–solid interaction problems of the rotor system in air bearings is proposed. The overall transfer equation of the rotor system is established based on the new version of transfer matrix method for multibody systems (NV-MSTMM), coupling with the extended transient Reynold equation, which achieves the two-way fluid–solid interaction analysis of the rotor system. The transfer matrix of the spatial flexible Timoshenko beam is first derived based on NV-MSTMM. The accuracy of the proposed approach is verified by an experiment and published literature. The influence of manufacturing errors including roundness, convexity, concavity and tapers on the dynamic performance of the rotor system is investigated comprehensively. The results show that the types and amplitude of manufacturing errors have complex effects on dynamic performance. Roundness with spatial numbers of 3 to 6, concavity and taper1 errors decrease the error motion amplitude, while convexity and taper2 errors increase it. Especially, roundness errors with spatial numbers of 1 and 2 notably increase the error motion amplitude, which should be avoided strictly.

A flexible forcing immersed boundary scheme-based one-step simplified lattice Boltzmann method for two-dimensional fluid-solid interaction problems

In this study, we coupled the one-step simplified lattice Boltzmann method (OSLBM) [1] with flexible forcing immersed boundary (FFIB) scheme [2] and proposed a computationally efficient FFIB-OSLBM solver for complex two-dimensional fluid-solid interaction problems. The adopted OSLBM algorithm has the benefits of lower virtual memory requirement and easy implementation of physical boundary conditions over the traditional lattice Boltzmann (LBM) solver and is also computationally more efficient than the simplified lattice Boltzmann method (SLBM) [3]. Unlike in SLBM, the macroscopic variable is updated in one-step in OSLBM, thus avoiding the predictor and corrector steps and reducing the computational time. Furthermore, the adopted FFIB algorithm uses an implicit approach to calculate the body force density, which accurately satisfies the no-slip velocity condition at the boundary of the immersed solid. Moreover, this method requires less computational effort since it discards the time-consuming, complex matrix inversion process associated with the conventional immersed boundary (IB) method. We have conducted the numerical accuracy test and noticed that the proposed FFIB-OSLBM solver is nearly second-order accurate in space, which is higher than the typical coupled IB-LBM solvers. In addition, the applicability of the present solver is tested through a set of benchmark problems, and the results obtained from the present solver show an excellent agreement with the data available in the references. Compared to the FFIB-LBM [2], the present solver consumes at least 20% less computational memory and CPU time for all the validation problems investigated in this study.

The finite element method for modified transmission eigenvalues for inverse scattering in a fluid–solid interaction problem

Based on the work of Monk and Selgas (2022), we explore the finite element method for the modified transmission eigenvalues for inverse scattering in a fluid–solid interaction problem. Under minimal regularity on the solution, we give a complete error analysis including the a priori and the a posteriori error estimates. We also present adaptive computations.

Mathematical problems of dynamical interaction of fluids and multiferroic solids

In the paper, we consider a three-dimensional mathematical problem of fluid-solid dynamical interaction, when an anisotropic elastic body occupying a bounded region is immersed in an inviscid fluid occupying an unbounded domain . In the solid region, we consider the generalized Green–Lindsay's model of the thermo-electro-magneto-elasticity theory. In this case, in the domain we have a six-dimensional thermo-electro-magneto-elastic field (the displacement vector with three components, electric potential, magnetic potential, and temperature distribution function), while we have a scalar acoustic pressure field in the unbounded domain . The physical kinematic and dynamical relations are described mathematically by the appropriate initial and boundary-transmission conditions. Using the Laplace transform, the dynamical interaction problem is reduced to the corresponding boundary-transmission problem for elliptic pseudo-oscillation equations containing a complex parameter τ. We derive the appropriate norm estimates with respect to the complex parameter τ and construct the solution of the original dynamical problem by the inverse Laplace transform. As a result, we prove the uniqueness, existence, and regularity theorems for the dynamical interaction problem. Actually, the present investigation is a continuation of the paper [Chkadua G, Natroshvili D. Mathematical aspects of fluid-multiferroic solid interaction problems. Math Meth Appl Sci. 2021;44(12):9727–9745], where the fluid-solid interaction problems for elliptic pseudo-oscillation equations associated with the above mentioned generalized thermo-electro-magneto-elasticity theory are studied by the potential method and the theory of pseudodifferential equations.

Simulations of interaction between flow and a thin elastic beam using CIP-based model with adaptive mesh

The simulation of interaction between flow and the elastic structure is a complicated fluid-solid interaction problem, involving the structure's large deformation and fluid interface variation. In this paper, an adaptive CIP (constrained interpolation profile)-based numerical model has been presented to simulate this problem. In this CIP-based model, the constrained interpolation profile method, a high-order finite difference method, is employed as the base flow solver and THINC/SW (Tangent of Hyperbola for Interface Capturing with Slope Weighting) method, a volume of fluid method, is applied to capture the flow interface. IBM (immersed boundary method) method is used to treat the fluid-solid interface. The body deformation is calculated by coupled FDM-FEM (finite difference method and finite element method) method. Adaptive mesh is generated by Afivo (Adaptive Finite Volume quadtree/Octree mesh) framework. The cases of flow past a square and water entry of a symmetric solid wedge are carried out to validate the reliability of the flow solver in this present model. Cantilever beam deformation case is used to validate the accuracy of the solid solver in the present model. Then cases of a thin elastic beam in sloshing tank and dam-break flow are carried out by using this model. After that, the case of regular wave past a membrane breakwater is studied. Our numerical results are compared with previous experimental and numerical studies, and good agreements are obtained. It is demonstrated that this present numerical model has good applicability to simulate the interaction between flow and a thin elastic beam.

Finite strain poro-hyperelasticity: an asymptotic multi-scale ALE-FSI approach supported by ANNs

This contribution introduces and discusses a formulation of poro-hyperelasticity at finite strains. The prediction of the time-dependent response of such media requires consideration of their characteristic multi-scale and multi-physics parameters. In the present work this is achieved by formulating a non-dimensionalised fluid–solid interaction problem (FSI) at the pore level using an arbitrary Lagrange–Euler description (ALE). The resulting coupled systems of PDEs on the reference configuration are expanded and analysed using the asymptotic homogenisation technique. This approach yields three partially novel systems of PDEs: the macroscopic/effective problem and two supplementary microscale problems (fluid and solid). The latter two provide the microscopic response fields whose average value is required in real-time/online form to determine the macroscale response (a concurrent multi-scale approach). In order to overcome the computational challenges related to the above multi-scale closure, this work introduces a surrogate approach for replacing the direct numerical simulation with an artificial neural network. This methodology allows for solving finite strain (multi-scale) porohyperelastic problems accurately using direct automated differentiation through the strain energy. Optimal and reliable training data sets are produced from direct numerical simulations of the fully-resolved problem by including a simple real-time output density check for adaptive sampling step refinement. The data-driven approach is complemented by a sensitivity analysis of the RVE response. The significance of the presented approach for finite strain poro-elasticity/poro-hyperelasticity is shown in the numerical benchmark of a multi-scale confined consolidation problem. Finally, to show the robustness of the method, the system response is dimensionalised using characteristic values of soil and brain mechanics scenarios.

A boundary integral equation method for the fluid-solid interaction problem

<abstract><p>In this paper, a boundary integral equation method is proposed for the fluid-solid interaction scattering problem, and a high-precision numerical method is developed. More specifically, by introducing the Helmholtz decomposition, the corresponding problem is transformed into a coupled boundary value problem for the Helmholtz equation. Based on the integral equation method, the coupled value problem is reduced to a system of three coupled hypersingular integral equations. Semi-discrete and fully-discrete collocation methods are proposed for the singular integral equations. The presented method is based on trigonometric interpolation and discretized singular operators applied to differentiated interpolation. The convergence of the method is verified by a numerical experiment.</p></abstract>

Time‐domain PML analysis of a fluid–solid interaction problem above a rough surface

This paper is concerned with the time‐dependent acoustic–elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well‐posedness and stability of the problem are first established by using the Laplace transform and the energy method. A perfectly matched layer (PML) is then introduced to truncate the interaction problem above a finite layer containing the elastic body, leading to a PML problem in a finite strip domain. We further establish the existence, uniqueness, and stability estimate of solutions to the PML problem. Finally, we prove the exponential convergence of the PML problem in terms of the thickness and parameter of the PML, based on establishing an error estimate between the DtN operators of the original problem and the PML problem.

Coupling of an SPH-based solver with a multiphysics library

A two-way coupling between the Smoothed Particle Hydrodynamics-based (SPH) code with a multiphysics library to solve complex fluid-solid interaction problems is proposed. This work provides full access to the package for the use of this coupling by releasing the source code, completed with guidelines for its compilation and utilization, and self-contained template setups for practical uses of the novel implemented features, is provided here. The presented coupling expands the applicability of two different solvers allowing to simulate fluids, multibody systems, collisions with frictional contacts using either non-smooth contact (NSC) or smooth contact (SMC) methods, all integrated under the same framework. The fluid solver is the open-source code DualSPHysics, highly optimised for simulating free-surface phenomena and structure interactions, uniquely positioned as a general-purpose Computational Fluid Dynamics (CFD) software with a GPU-accelerated solver. Mechanical systems that comprise collision detection and/or multibody dynamics are solved by the multiphysics library Project Chrono, which uses a Discrete Element Method (DEM). Therefore, this SPH-DEM coupling approach can manage interactions between fluid and complex multibody systems with relative constraints, springs, or mechanical joints. Program summaryProgram title: DualSPHysics-ChronoCPC Library link to program files:https://doi.org/10.17632/g2cc37dw4f.1Licensing provisions: DualSPHysics and DSPHChronoLib under GNU Lesser General Public License (LGPL); Project Chrono under BSD-3-Clause License.Programming language: C++ and CUDANature of problem: The simulation of turbulent free-surface flows in interaction with complex fixed or floating structures is essential to address typical marine and coastal engineering problems. The Smoothed Particle Hydrodynamics (SPH) method is particularly suitable for solving this type of nonlinear problems. However, this type of application usually requires mechanical restrictions between the different structural elements (spherical joints, hinges, or springs), as well as the correct simulation of collisions between solid objects. In these cases, it is necessary to combine the SPH method with other numerical methods that allow performing these multiphysics simulations.Solution method: DualSPHysics-Chrono is a two-way coupling between an SPH solver and a multiphysics library that combines fluid simulation using a Lagrangian approximation and interactions between solids using Discrete Element Method (DEM). DualSPHysics solver is a GPU-optimized implementation of the SPH method that allows efficient simulation of fluid-structure interaction problems. Whereas Project Chrono is a DEM implementation for simulating multibody dynamics that includes collision detection and numerous mechanical constraints to solve complex mechanisms. The coupling of DualSPHysics and Project Chrono combines the capabilities of both models under a free software framework.Additional comments including restrictions and unusual features: The SPH solver includes a version implemented with CUDA (Compute Unified Device Architecture) to exploit the parallelism of NVIDIA graphics processing units (GPUs).

A multigrid preconditioner for spatially adaptive high-order meshless method on fluid–solid interaction problems

We present a monolithic geometric multigrid preconditioner for solving fluid–solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-order meshless method, the generalized moving least squares (GMLS) with adaptive h-refinement. For solving fluid–solid interaction problems, we need to deal with a tightly coupled system consisting of the flow field and solid bodies, resulting in a linear system of equations with a block structure. In Stokes limit, solid kinematics can be dominated by the singularities governing the lubrication effects. Resolving those singularities with adaptive h-refinement can lead to an ill-conditioned linear system of equations. The key ingredients of the multigrid preconditioner include the interpolation and restriction operators and the smoothers. For constructing the interpolation and restriction operators, we utilize the geometric information of hierarchical sets of GMLS nodes generated in adaptive h-refinement. We build decoupled smoothers through physics-based splitting and then combine them via a multiplicative overlapping Schwarz approach. Through numerical examples with the inclusion of different numbers and shapes of solid bodies, we demonstrate the performance and assess the scalability of the designed preconditioner. As the total degrees of freedom and the number of solid bodies increase, the proposed monolithic geometric multigrid preconditioner can ensure convergence and good scalability when using the Krylov iterative method for solving the linear systems of equations generated from the spatially adaptive GMLS discretization. More specifically, for a fixed number of solid bodies, as the discretization resolution is incrementally refined, the number of iterations of the linear solver can be maintained at the same level, indicating nearly linear scalability of our preconditioner with respect to the total degrees of freedom. When the number of solid bodies Ns increases, the number of iterations is nearly proportional to Ns, implying the sublinear optimality with respect to the number of solid bodies.

Numerical studys on passive paramerters of a fluid-solid interaction problem derived by natural convection in a circular enclosure

The natural convection through a partitioned circular enclosure by a deformable middle wall was analyzed. To solve the FSI problem, a forceful connection between the fluid and flexible wall was established. In order to solve the problem under consideration, the Arbitrary Lagrangian-Eulerian (ALE) perspective was utilized. The finite element method (FEM), was also unilized in solving a set of model equations. Effect of wall Angle (30 ≤ η ≤ 90), flexibility (0.71 ≤ Eτ ≤ 200), Position of heat source and sink (-60 ≤ α ≤ +60) has been studied within a circular enclosure. The results indicate that a reduction in flexibility reduces the force (stress) applied to the wall as well as the average Nusselt number to some extent. Also, Increased angle of the wall leads to an enhancement in the Nu. The maximum applied stress and also wall distortion occur at specific positions of hot and cold sector, the buoyancy force and, therefore, the strength of the fluid flow are also higher, causing the heat transfer rate to increase. For The average Nusselt number, A decrease of 8.5 % for η = 90° has been reported compared to η = 30°. Also, the average Nusselt number for α = −60° is up to 124.5 % higher than for α = 60°.

Modal measurement and identification of hexagonal air cushions

Air cushions have been widely utilised as roofs and facades for large-span buildings owing to their advantages such as ultra-light weight and aesthetic appearance. The dynamic performance of air cushions, which is a typical fluid-solid interaction problem, is complex, because the top layer, bottom layer, and inner air are highly coupled. However, there is a paucity of effective dynamic experimental studies to test the modal characteristics of entire air cushions. Therefore, in this study, a modal measurement and identification method was developed to simultaneously calculate the dynamic properties of both the top and bottom layers of air cushions. A laser displacement sensor array was employed to record the time-history displacement data at the observation points, and the combined application of the fast Fourier transform (FFT) and stochastic subspace identification (SSI) methods was used for modal identification. A hexagonal air cushion was adopted for testing, and the first eight frequencies and modes were successfully identified. The test results indicated that the first mode shape was significantly different from that of a single-layer foil. The one-wave vibration mode shape appeared after the multi-wave mode shapes, which was a unique phenomenon for air cushions. The frequencies and mode shapes of the top and bottom layers were almost identical. The mode deformation of the two layers can be in the same direction or opposite directions, and the frequencies corresponding to the mode shapes of layers vibrating in the same direction were higher than those of layers vibrating in opposite directions.

A Unified Arbitrary Lagrangian\u2013Eulerian Model for Fluid\u2013Structure Interaction Problems Involving Flows in Flexible Channels

In this work a finite element-based model for analyzing incompressible flows in flexible channels is presented. The model treats the fluid–solid interaction problem in a monolithic way, where the governing equations for both sub-domains are solved on a single moving grid taking advantage of an arbitrary Lagrangian/Eulerian framework (ALE). The unified implementation of the governing equations for both sub-domains is developed, where these are distinguished only in terms of the mesh-moving strategy and the constitutive equation coefficients. The unified formulation is derived considering a Newtonian incompressible fluid and a hypoelastic solid. Hypoelastic constitutive law is based on the strain rate and thus naturally facilitates employing velocity as a kinematic variable in the solid. Unifying the form of the governing equations and defining a semi-Lagrangian interface mesh-motion algorithm, one obtains the coupled problem formulated in terms of a unique kinematic variable. Resulting monolithic system is characterized by reduced variable heterogeneity resembling that of a single-media problem. The model used in conjunction with algebraic multigrid linear solver exhibits attractive convergence rates. The model is tested using a 2D and a 3D example.

A coupled LBM-DEM method for simulating the multiphase fluid-solid interaction problem

In this paper, we develop a numerical model for simulating the solid-liquid-gas three-phase flow in unconsolidated particle layers. Based on the discrete element method (DEM) and the multiphase fluid model in the framework of the lattice Boltzmann method (LBM), a multiphase fluid-solid two-way coupling algorithm is proposed. In this model, the fluid-fluid interface is tracked using a phase-field method, and the multiphase fluid-particle interaction is tackled by a combination of the momentum exchange method for the flow field and the immersed boundary method for the phase field. We applied the method to simulate the upward migration of the leaked gas bubbles through a brine-filled sediment column at the seafloor, and investigated the influences of the leak flow rate and the interfacial tension on the bubble rising behavior. The results indicate three different flow regimes: connected finger flow, transition flow, and dispersed bubbly flow. These flow regimes can be distinguished by the dimensionless Eötvös and Weber numbers. The proposed numerical method can accurately characterize various multiphase interaction mechanisms at the mesoscopic scale and has powerful advantages in simulating complex fluid-particle coupling problems.

Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems

As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.

Dynamics of axially functionally graded pipes conveying fluid using a higher order shear deformation theory

This study presents a novel approach for addressing dynamical characteristics of fluid conveying axially functionally graded pipes. The variation of material properties of the pipe along axial direction is taken into account according to a power-law function. Owing to a unified expression for displacement field, the developed model can be recast into classical Euler – Bernoulli and Timoshenko tube models as well as a newly developed higher order shear deformable tube model; the latter satisfies zero-shear conditions on free surfaces, and hence yields more realistic results. The system of partial differential equations governing dynamics of fluid conveying axially functionally graded pipes is derived through utilization of Hamilton’s principle. Differential quadrature scheme is used to discretize the system of differential equations and generate numerical results. Detailed numerical investigations of the current fluid-solid interaction problem elucidate the effects of material gradation pattern, transverse shear deformation distribution profile along radial direction and fluid velocity on the natural frequencies of fluid conveying functionally graded pipes. The critical fluid velocity, which is a significant design parameter, can also be determined by means of developed procedures in this study.