Abstract
The present paper is addressed to the numerical analysis of fluid-structure instabilities in a flexible tubes bundle subjected to the loads induced by a water turbulent crossflow, using the arrangement presented in Weaver and Abd-Rabbo (J Fluids Eng, 1985 [1]) as benchmark. The physical phenomena involved by the water turbulent crossflow raise strong interest from the scientific community. The nuclear industry is particularly concerned as the design of reliable large-scale exchangers is of primary importance to ensure good performance of nuclear plants. As a matter of fact, their detailed simulation is characterised by challenging traits such as the large amplitude of the tubes vibrations, the strong coupling between water and tubes, the need for an accurate evaluation of the fluid damping and critical flow velocity which vibration instabilities arise at, as well as the complex transition of the fluid-structure behaviour. To tackle these challenges in an effective way, unsteady Fluid-Structure Interaction (FSI) studies were performed applying the mode-superposition approach by means of a mesh morphing technique founded on the mathematical framework of Radial Basis Functions (RBF). In particular, the computational outputs were gained by employing a combined use of ANSYS® Fluent®, ANSYS® Mechanical™ and RBF Morph™ software. The two-equation realizable κ-ε turbulence model was adopted to run the U-RANS simulations on high-fidelity structured hexahedral meshes. The achieved numerical results were compared with well-documented experimental data, and a satisfying agreement was finally attained. Furthermore, the operative crossflow velocity guaranteeing the stable functioning of the tubes array was also identified. We demonstrated that the proposed modal approach, in combination with mesh morphing, allows designers to set-up an effective workflow to predict unsteady FSI problems that can be widely adopted for industrial applications under the hypothesis of linear structural behaviour.
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Abbreviations
- β :
-
Coefficients of the polynomial correction
- γ :
-
Vector of coefficient of the RBF
- φ:
-
Radial basis function
- ω :
-
Circular natural frequency (rad/s)
- C :
-
Damping matrix
- d, D:
-
Diameter of tubes
- \( d_{s} \) :
-
Diameter of the steel rods
- \( F(t) \) :
-
Vector of externally applied forces
- g :
-
Vector of displacement at source points
- h:
-
Multi-variate polynomial
- K :
-
Stiffness matrix of the system
- M :
-
Mass matrix of the system
- \( M_{int} \) :
-
Interpolation matrix
- Q :
-
Vector of modal forces
- \( n_{s} \) :
-
Total number of source points (RBF centres)
- P :
-
Constraint matrix
- q :
-
Vector of modal coordinates
- s:
-
Interpolant function
- \( V_{u} \) :
-
Upstream inlet flow velocity (m/s)
- \( V_{c} \) :
-
Critical or threshold flow velocity based on \( V_{u} \) (m/s)
- \( x_{k} \) :
-
Position of RBF source points
- \( x_{p} \) :
-
Position of a generic node
- \( \{ x\} \) :
-
Displacement vector
- \( \{ \dot{x}\} \) :
-
Velocity vector
- \( \{ \ddot{x}\} \) :
-
Acceleration vector
- \( y^{ + } \) :
-
Dimensionless wall distance
- CAE:
-
Computer-Aided Engineering
- CAD:
-
Computer-Aided Design
- CFD:
-
Computational Fluid Dynamics
- FEA:
-
Finite Element Analysis
- FEM:
-
Finite Element Method
- FSI:
-
Fluid-Structure Interaction
- GS:
-
Gaussian
- IMQ:
-
Inverse multiquadric
- IQ:
-
Inverse quadratic
- LSCB:
-
Least Squares Cell Based
- MQ:
-
Multi-Quadric
- RBF:
-
Radial Basis Functions
- RMS:
-
Root Mean Square
- Rn:
-
Spline type
- SC:
-
System Coupling
- SST:
-
Shear-Stress Transport
- SAS:
-
Scale-Adaptive Simulation
- TPSn:
-
Thin plate spline
- U-RANS:
-
Unsteady Reynolds Averaged Navier Stokes
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Costa, E., Groth, C., Lavedrine, J., Caridi, D., Dupain, G., Biancolini, M.E. (2020). Unsteady FSI Analysis of a Square Array of Tubes in Water Crossflow. In: Biancolini, M., Cella, U. (eds) Flexible Engineering Toward Green Aircraft. Lecture Notes in Applied and Computational Mechanics, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-030-36514-1_8
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