Study on Flow-Induced Vibration of a Wire-Wrapped Rod in a High-Speed Gas Environment

Ke Zhang¹, Kailun Wang², Jian Liu¹, Huanhuan Qi¹, Xiaofei Yu¹, Penglin Gao²
¹State Key Laboratory of Advanced Nuclear Energy Technology, Nuclear Power Institute of China, Chengdu, 610041
²State Key Laboratory of Mechanical Systems and Vibration, Shanghai Jiao Tong University, Shanghai, 200240

Abstract

With the ongoing development and research of high-temperature gas-cooled reactors, the issue of flow-induced vibration in wire-wrapped rod structures under high-temperature, high-speed gas conditions has garnered widespread attention. Compared to fluids such as water or liquid metal, gaseous working media exhibit higher flow velocities, lower density, and more severe turbulence, making the simulation and analysis of flow-induced vibration more challenging. Based on structural vibration equations and large eddy simulation (LES), this study employs a co-simulation technique using Star-CCM+ and Abaqus, incorporating nonlinear factors such as boundary gaps and friction, to establish a refined single wire-wrapped rod fluid-structure interaction (FSI) model. Wind tunnel experiments were conducted to validate the fluctuating pressure and structural displacement. Under an inlet wind speed of 60 m/s, both numerical simulations and experimental results for the root mean square (RMS) displacement of the single wire-wrapped rod were approximately 60 μm. This research establishes a computational method for analyzing the flow-induced vibration response of wire-wrapped rods in high-speed gas environments, validated through experiments, which can be applied to the analysis and evaluation of flow-induced vibration in wire-wrapped rod structures within high-temperature gas-cooled reactors.

Keywords: high-speed gas; wire-wrapped rod; flow-induced vibration; fluid-structure interaction; contact boundary

Introduction

High-temperature gas-cooled reactors have become a new generation of nuclear energy technology pursued by various countries due to their excellent economic performance and site applicability. However, flow-induced vibration of wire-wrapped rod bundle structures induced by high-speed gas can lead to fretting wear of fuel assemblies and even nuclear leakage, affecting the safe and stable operation of reactors. Currently, the engineering community shows considerable interest in experimental and simulation methods for flow-induced vibration of wire-wrapped rod bundles, but these efforts have primarily focused on water or liquid metal coolants, with limited research on flow-induced vibration of wire-wrapped rods caused by high-speed gas. Compared to heavy fluid coolants such as water or liquid metal, gaseous working media exhibit higher flow velocities, lower density, and more severe turbulence, making the simulation of flow-induced vibration more challenging and necessitating research on analytical methods and experimental validation.

The main body of a wire-wrapped fuel rod is a cylindrical tube, axially fixed at both ends by end plugs, with helically wound wires providing radial positioning. In lead-bismuth fast reactors and sodium-cooled fast reactors, Brockmeyer et al. \cite{1,2} established a 7-pin wire-wrapped cylinder model and a one-way coupled computational method for solving flow-induced vibration, analyzing the influence of wire wraps on system modal characteristics. Dolfen et al. \cite{3} employed a fluid force spectrum conversion method for long-duration forces, approximating the gap between wire-wrapped fuel rods as a rigid baffle. De Santis \cite{4} investigated one-way fluid-structure interaction problems for wire-wrapped cylinders in axial flow using Star-CCM+, employing the SST model for the fluid and presenting the influence of wire wraps on the flow field while calculating structural dynamic deformation; however, due to model complexity, two-way transient fluid-structure coupling calculations could not be performed. The aforementioned studies simplified the contact between wire-wrapped rods and between wire-wrapped rods and end caps using rigid baffles or degree-of-freedom constraints.

For flow-induced vibration of wire-wrapped rods in water coolant, Wu Licun \cite{5} and Liu Yu \cite{6} established simplified analysis models for wire-wrapped fuel rods and investigated flow-induced vibration mechanisms under the influence of leakage flow based on random vibration theory. Chen Deqi and Liu Haidong \cite{7} solved fluid-structure coupling problems using dynamic mesh technology based on Euler-Bernoulli beam theory. Huang Heng \cite{8} and Qi Huanhuan \cite{9} established amplitude expressions for fuel rods under turbulent excitation in axial and transverse directions based on random vibration theory.

In two-phase flow or gas media, Dae \cite{10} conducted experimental studies on flow-induced vibration of wire-wrapped rod bundles in air-water two-phase flow, investigating correlations between flow velocity, wire pitch, thickness, and flow-induced vibration. Wang et al. \cite{11} performed experimental studies on flow-induced vibration characteristics of a single wire-wrapped rod in air medium, measuring vibration responses under different constraint modes and inlet velocities of 1-3 m/s using a laser Doppler vibrometer (LDV). Results showed that the amplitude of a single rod under fixed support was 84% lower than under simply supported conditions. Wire wrap structures produced significant disturbance effects on axial flow, thereby enhancing rod vibration, with maximum amplitude reaching 189.3 μm at a flow velocity of 3 m/s.

Currently, published literature contains limited research on experimental and analytical methods for flow-induced vibration of wire-wrapped rods in high-speed gas environments, and no refined simulation methods suitable for engineering applications have been developed. This study focuses on a single wire-wrapped rod, establishes a refined fluid-structure coupling analysis model considering nonlinear factors such as boundary friction and gaps, validates fluctuating pressure and structural displacement through wind tunnel experiments, and develops a reliable vibration response calculation method.

1 Theoretical Model

Flow-induced vibration in high-speed gas environments constitutes micro-amplitude vibration. This study employs a one-way fluid-structure coupling approach for computational analysis, utilizing Star-CCM+ and Abaqus co-simulation technology. Fluid loads obtained from Star-CCM+ flow field analysis are transferred to the structural model for vibration response calculation.

Common turbulence simulation methods mainly include Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES). RANS models turbulence effects as Reynolds stress terms through time-averaging of the N-S equations, suitable for steady or quasi-steady problems. LES directly resolves large-scale eddy structures while modeling small-scale eddies, enabling high-precision capture of turbulent transient characteristics.

Therefore, this study adopts the LES method for flow field analysis. The core concept involves dividing turbulent structures into large-scale and small-scale eddies. Large-scale eddies are resolved through direct numerical simulation (DNS), while small-scale eddies are modeled using a subgrid-scale (SGS) model. The LES governing equations are obtained through spatial filtering of the N-S equations:

⋅ ∇ =− ∇p + ν∇ − ∇ ⋅ τSGS# 1 are the filtered velocity and pressure fields respectively, τSGS is the subgrid-scale stress tensor used to represent small-scale

The wire-wrapped rod structure is a slender quasi-cylinder, allowing shear deformation and rotational inertia effects to be neglected. Its motion can be represented by transverse displacement of the axis, i.e., the Euler-Bernoulli beam, with its free vibration equation given by:

The structural solid is discretized using the finite element method, loads obtained from fluid calculations are applied to element nodes in vector form \cite{12}, 2 = 0 2 = 0 The dynamic equation is as follows: + + 퐾 are the structural acceleration, velocity, and displacement respectively, M is the structural mass matrix, C is the damping matrix, K is the stiffness matrix, is the load applied by the fluid on the structure in one-way fluid-structure coupling.

2.1 Computational Domain and Mesh

The structural model includes a single wire-wrapped rod, a hexagonal flow channel, and upper and lower end caps. The single wire-wrapped rod is centrally located within the hexagonal flow channel structure, connected at the lower end to a lower end cap with 19 holes via short pins, and inserted into an upper end cap with 19 holes at the upper end. Geometric parameters of the wire-wrapped rod and flow channel are shown in Table 1 [TABLE:1], with the geometric model illustrated in Figure 1 [FIGURE:1].

The tangential structure between the wire wrap and rod creates sharp corners in flow field analysis, severely affecting mesh quality and computational results. Therefore, it is approximated as an intersecting structure, with mesh generation at the wire-rod connection shown in Figure 2 [FIGURE:2].

The fluid domain is air, with the inlet set as a velocity inlet boundary at 60 m/s and turbulence intensity of 2%. The outlet is set as a pressure outlet boundary at 0 Pa. Steady-state calculations were performed, and grid independence verification was conducted by comparing pressure drops at two measurement points located 0.1 m and 0.9 m from the inlet, as shown in Table 2 [TABLE:2]. The mean pressure drop and RMS values vary little across three mesh sizes. Considering the balance between computational accuracy and efficiency, the mesh with 10.85 million cells was selected for subsequent analysis.

2.2 Flow Field Analysis Results

Large eddy simulation was employed with a time step of 0.001 s and total duration of 3 s. Velocity contours at the 3 s moment are extracted as shown in Figures 3 [FIGURE:3] and 4 [FIGURE:4]. The results reveal significant differences in fluid velocity distribution at the inlet cross-section, with high-velocity regions distributed in the hexagonal area surrounding the central rod. This occurs because the CFD model inlet boundary includes an inlet orifice plate (Figure 5 [FIGURE:5]), causing intense mixing at the entrance. Since fluid cannot pass through the central rod position, high-velocity regions are distributed in the flow domain surrounding the central rod, with velocity decreasing from the center outward. As the flow field develops, turbulence gradually dissipates and velocity distribution becomes more uniform, eventually showing uniform flow distribution around the central rod at the outlet cross-section in Figure 4b [FIGURE:4].

Pressure time histories at two measurement points located 0.1 m (P1), 0.2 m (P2), and 0.9 m (P3) from the inlet were extracted and analyzed spectrally, as shown in Figure 7 [FIGURE:7]. Simulation measurement points are illustrated in Figure 6 [FIGURE:6].

Flow field analysis results indicate that the dominant frequencies of fluctuating pressure are concentrated in the low-frequency region, exhibiting low-frequency broadband characteristics consistent with turbulent excitation features. The P1 point near the inlet contains more frequency components, while the P3 point near the outlet is dominated by low-frequency components. This demonstrates that the orifice plate structure at the inlet creates high turbulence intensity and complex frequency components, which gradually dissipate as the flow field develops, with frequencies becoming increasingly low-frequency dominant, consistent with the velocity distribution trend. To quantify the intensity of flow field fluctuating pressure, the root mean square (RMS) values were calculated. The RMS of fluctuating pressure at the inlet (P1) is 37.3 Pa, while at the outlet (P3) it is 38.9 Pa.

3.1 Fluid-Structure Interaction Model

To accurately consider the influence of inlet and outlet boundaries on the wire-wrapped rod, solid elements were used to model the inlet pin structure, wire-wrapped rod, and outlet end cap as three components, with the geometric model shown in Figure 8 [FIGURE:8]. All materials are stainless steel with density 7860 kg/m³, elastic modulus 210 GPa, and Poisson's ratio 0.3.

Since the excitation force on the wire-wrapped rod in the flow field is relatively small and the solid's reaction force on the flow field does not constitute a significant influence, one-way fluid-structure coupling was employed for numerical calculations. Based on Star-CCM+ and Abaqus co-simulation technology, the wire-wrapped rod surface was set as the fluid-structure coupling interface, with fluid excitation loads transferred from the flow field to the structural model at each time step for vibration response calculation.

Nonlinear factors at boundaries were considered as follows:

Inlet: The rod is constrained at the inlet end by two parallel pins, allowing only translation along the pin direction. Solid pin models were established to consider pin stiffness, with friction and gap contact set between pins and rod holes. The gap was set to 0.05 mm, and the friction coefficient was set to 0.2 for steel-on-steel contact.

Outlet: At the outlet end, the wire-wrapped rod is inserted into the end cap through a clearance fit, allowing axial movement and rotation. A solid end cap model was established to consider end cap stiffness, with gap contact set between the rod and end cap center hole at 0.1 mm clearance.

3.2 Vibration Analysis Results

Vibration response calculations employed one-way coupled co-simulation technology with the flow field calculations, using a time step of 0.001 s and total duration of 1 s. Displacements at two measurement points located 0.1 m (D1) and 0.9 m (D2) from the inlet on the wire-wrapped rod were extracted, as shown in Figure 9 [FIGURE:9].

Simulation analysis results show that displacement amplitudes and trends at the inlet and outlet measurement points are similar, both exhibiting low-frequency large-amplitude oscillations superimposed with small-amplitude high-frequency vibrations. This is attributed to the absence of surrounding rod constraints for the single wire-wrapped rod, combined with gap contacts considered at both ends, resulting in overall low-frequency swinging. The small-amplitude high-frequency vibrations represent typical flow-induced vibration characteristics caused by fluid pulsation. The RMS displacement at D1 is 55 μm, while at D2 it is 46 μm.

4 Experimental Validation

A suction-type direct-current wind tunnel test rig was constructed for high-speed air environments. Fluctuating pressure in the flow field and signals such as acceleration and strain at different measurement points on the wire-wrapped rod were acquired. Acceleration signals were integrated to obtain displacement responses, enabling analysis of flow field fluctuating pressure characteristics and wire-wrapped rod vibration response characteristics to validate the accuracy and feasibility of the flow-induced vibration response calculation method for single wire-wrapped rods in high-speed gas environments.

4.1 Test Rig and Specimen

The high-speed gas environment rod bundle structure flow-induced vibration test rig consists primarily of an inlet section, contraction section, transition section, rod bundle test section, diffusion section, centrifugal fan, and data acquisition and processing system, as shown in Figure 10 [FIGURE:10]. The test section is suspended on an isolation platform using flexible membranes to achieve soft connection with the diffusion section, ensuring that vibration experienced by the test specimen originates only from flow field excitation. During testing, air enters the wind tunnel through a honeycomb and screens in the inlet section, passes through a variable cross-section contraction section into the test section, and is finally exhausted through the fan.

The wire-wrapped rod used in testing features a hollow thin-walled structure made of stainless steel, with steel wire helically wound and spot-welded onto the fuel rod. Test specimen parameters are identical to the numerical simulation model, with the structure shown in Figure 12 [FIGURE:12].

4.2 Test Results

The test section has a total length of 1000 mm. Three fluctuating pressure sensors (P1-P3) are arranged at 100 mm, 200 mm, and 900 mm from the inlet, installed via drilled holes in the flow channel wall. Two accelerometers are installed inside the wire-wrapped rod at 100 mm and 900 mm from the inlet, with perpendicular measurement directions: A1 measures vertical acceleration and A2 measures horizontal acceleration. Measurement point locations are shown in Figure 6.

At a fan shaft frequency of 66.0 Hz, the inlet velocity is 60 m/s. Signals from flow channel wall pressure measurement points and internal accelerometers were acquired to obtain time-domain curves. DC components were filtered from the time-domain curves, and power frequency was removed using a band-stop filter. After fast Fourier transform (FFT), frequency-domain curves for each sensor at different measurement points were obtained.

Time-domain and frequency-domain test curves for fluctuating pressure are shown in Figures 13 [FIGURE:13] and 14 [FIGURE:14]. Displacement time-domain and frequency-domain curves obtained by integrating acceleration signals are shown in Figure 15 [FIGURE:15].

Test results indicate:

1. Fluctuating Pressure: Pressure at the outlet is greater than at the inlet, with a maximum RMS value of 58.5 Pa due to mixing effects from the wire wrap structure. The spectrum exhibits broadband characteristics from 5 Hz to 100 Hz, consistent with turbulent excitation features.

2. Displacement and Acceleration: Spectrum curves show no fan shaft frequency or blade frequency signals, indicating good vibration isolation. The absence of high-frequency peaks demonstrates no acoustic resonance phenomena. Displacement signals are dominated by low frequencies, with RMS displacement values of 61 μm and 79 μm at the inlet and outlet, respectively.

4.3 Results Comparison and Validation

Comparisons of simulation and test results at different locations are presented in Table 3 [TABLE:3] and Figure 15. The comparison results show:

(1) The numerical simulation model demonstrates consistent trends with experimental measurements for fluctuating pressure at both inlet and outlet, showing outlet values greater than inlet values with similar magnitudes, with RMS fluctuating pressure around 50 Pa. However, the frequencies calculated in the simulation are lower than those measured experimentally, likely because the LES algorithm models small-scale eddies through subgrid-scale modeling, losing some high-frequency information.

(2) The numerical simulation model shows displacement amplitudes close to experimental values at both inlet and outlet. Under 60 m/s inlet velocity, both numerical simulation and experimental results for the RMS displacement of the single wire-wrapped rod are approximately 60 μm, both exhibiting low-frequency dominant trends. However, the displacement frequencies in the simulation are lower, likely because the simulation's excitation frequencies are lower and the consideration of friction and contact nonlinearities at boundaries dissipates high-frequency energy, resulting in lower frequency content in the simulation.

These comparison results demonstrate that the flow-induced vibration response calculation method for single wire-wrapped rods established in this study possesses reliability and accuracy, providing a new methodological reference for simulation studies of flow-induced vibration response of single wire-wrapped rods in high-speed gas environments.

5 Conclusions and Outlook

This study employs a CFD and finite element method combined approach, considering nonlinear factors such as boundary gaps and friction, to establish a refined fluid-structure coupling analysis model for single wire-wrapped rods. Fluctuating pressure at key locations and displacement responses of the wire-wrapped rod were calculated for a high-speed gas environment with 60 m/s inlet velocity. Analysis results indicate:

(1) LES simulation can effectively capture pressure characteristics of the flow field around a single wire-wrapped rod in high-speed gas environments, with RMS fluctuating pressure values near the outlet greater than those near the inlet.

(2) Flow-induced vibration of single wire-wrapped rods in high-speed gas environments is caused by turbulent excitation, with fluid excitation exhibiting low-frequency broadband characteristics.

(3) Boundary gaps and friction significantly affect structural vibration response. When gaps are considered, structural vibration response consists of macroscopic low-frequency swinging superimposed with micro-amplitude vibrations.

(4) Comparison of fluctuating pressure at flow channel inlet and outlet and vibration displacement at wire-wrapped rod inlet and outlet with high-speed gas wind tunnel tests shows consistent trends and comparable results between the numerical model and experimental data, demonstrating good agreement.

Through numerical simulation and experimental validation, this study establishes a flow-induced vibration response calculation method for wire-wrapped rods in high-speed gas environments, applicable to analysis and evaluation of flow-induced vibration in wire-wrapped rod structures in high-temperature gas-cooled reactors. Future work should consider contact and collision between wire-wrapped rods in bundles and conduct experimental and numerical studies to further reveal the flow-induced vibration mechanisms of wire-wrapped rod bundles.

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