Turbulent Flow Over an Oscillating Rigid Body Assembly

In this application, AcuSolve is used to simulate the fluid-structure interaction of a fluid moving over a cylinder/plate assembly. AcuSolve results are compared with experimental results as described in Gomes and Lienhart (2009). The close agreement of AcuSolve results with the experimental results validates the ability of AcuSolve to model cases in which the fluid forces lead to structural motions.

Problem Description

The problem consists of a fluid having material properties of standard water with density of 998 kg /m3 and kinematic viscosity of 0.97e-6 m2/sec through a two dimensional channel over a cylinder and plate assembly. The diameter of the cylinder is 0.022 m and the plate length is 0.042 m, while the inlet velocity is specified to match experimental conditions with a max velocity of 1.07 m/sec, as is shown in the following image, which is not drawn to scale. The model is simulated as transient with constant inflow conditions, allowing an oscillatory motion of the assembly to develop. The Shear Stress Transport (SST) turbulence model is used to model the turbulent portion of the flow and AcuSolve's internal rigid body motion is used to capture the motion of the oscillating assembly.


Figure 1. Critical Dimensions and Parameters used for Simulating Rigid Body Motion of Flow Past a Cylinder/Plate Assembly


Figure 2. Mesh used for Simulating Rigid Body Motion of Flow Past a Cylinder/Plate Assembly

The simulation was performed as a two dimensional problem by constructing a volume mesh that contains a single layer of elements extruded in the cross stream direction, normal to the flow plane and by imposing symmetry boundary conditions on the extruded planes. The upper and lower walls are specified as no-slip and the inlet velocity is specified to match the conditions of the experiment (Gomes and Lienhart 2009).

AcuSolve Results

The AcuSolve solution reached a regularly repeating oscillatory state and the simulation was allowed to proceed for 10 seconds of physical time to obtain a sufficient number of cycles for statistical analysis. The motion of the cylinder/plate assembly is directly attributed to the vortices shedding in its wake. The fluctuating loads on the assembly that result from the vortex shedding lead to a repeating cycle of structural rotation. The dominant oscillation frequency from the simulation was found to match well with the experimental measurements, within approximately 3.5 percent. The images below show the rigid body displacement of the assembly as it oscillates within the flow. Contours of velocity magnitude demonstrate the forcing on the assembly, while the mesh motion around the structure is captured and plotted for a single time step. Two dimensional plots showing the angular displacement demonstrate the motion, showing a single red line for the AcuSolve results.


Figure 3. Velocity Contours Near the Assembly for a Single Time Step During the Simulation


Figure 4. Mesh Displacement Contours Near the Assembly for a Single Time Step During the Simulation


Figure 5. Rigid Body Displacement of the Assembly as a Function of Time, Showing the Oscillation Develop into the Pseudo-Steady Motion
The dominant frequency of the oscillation is easily identified in the Fast Fourier Transform (FFT) of the deflection angle, shown in the plot below.


Figure 6. FFT of the Rigid Body Displacement Angle, Showing Power Spectral Density as a Function of Frequency

Summary

The AcuSolve solution compares well with experimental data for flow past an oscillating cylinder/plate assembly. In this application, water moves over the cylinder/plate assembly, giving rise to unsteady loading that causes the body to rotate as a rigid body. The good agreement with the natural frequency of oscillation compared to the experimental data demonstrates that AcuSolve is capable of predicting fluid forced motion with an internal rigid body dynamic solver.

Simulation Settings for Turbulent Flow Over an Oscillating Rigid Body Assembly

AcuConsole database file: <your working directory>\cylinder_rigidbody_turbulent\cylinder_rigidbody_turbulent.acs

Global

  • Problem Description
    • Analysis type - Transient
    • Turbulence equation - SST
    • Mesh Type- Fully Specified
  • Auto Solution Strategy
    • Final Time - 10.0
    • Initial Time Increment- 0.005
    • Convergence tolerance- 0.001
    • Max stagger iterations- 3
  • Material Model
    • Water
      • Type- Constant
      • Density- 998.0 kg/m3
      • Viscosity- 0.00096806 kg/m*sec
  • Mesh Motion
    • Interpolated
      • Type- Interpolated Motion
      • Interpolated motion surfaces
        • Bottom
        • Top
    • RigidBody
      • Type- Rigid Body Dynamic
        • Z rotation- Active
        • Mass- 0.2089 kg
        • Dyadic
          • X-X - 3.7 e-5 kg-m2
          • Y-Y- 3.7 e-5 kg-m2
          • Z-Z - 3.7 e-5 kg-m2

    Model

  • Volumes
    • Volume
      • Element Set
        • Material model- Water
        • Mesh motion- Interpolated
  • Surfaces
    • Body
      • Simple Boundary Condition
        • Type- Wall
        • Mesh displacement BC type- Fixed
        • Mesh motion- RigidBody
      • Interpolated Motion Surface
    • Bottom
      • Simple Boundary Condition
        • Type- Wall
        • Mesh displacement BC type- Fixed
      • Interpolated Motion Surface
    • Inflow
      • Simple Boundary Condition
        • Type- Inflow
        • Inflow type- Velocity
        • X Velocity- 1.07 m/sec
        • Turbulence input type- Auto
        • Turbulence intensity type- High
      • Advanced Options
        • Nodal Boundary Conditions
        • X-velocity
          • Type- Linear
          • Precedence- 2
          • Curve fit variable- Y coordinate
          • Curve fit values- Provided
        • Y-velocity
          • Type- Zero
        • Z-velocity
          • Type- Zero
    • Bottom
      • Simple Boundary Condition
        • Type- Wall
        • Mesh displacement BC type- Fixed
        • Mesh motion- RigidBody
      • Interpolated Motion Surface
    • Outflow
      • Simple Boundary Condition
        • Type- Outflow
    • Top
      • Simple Boundary Condition
        • Type- Wall
        • Mesh displacement BC type- Fixed
      • Interpolated Motion Surface
    • maxZ
      • Simple Boundary Condition
        • Type- Slip
    • minZ
      • Simple Boundary Condition
        • Type- Slip

References

Gomes, J. P. and Lienhart, H. (2009) Experimental Benchmark: Self-excited Fluid-structure Interaction Test Cases, in Fluid-Structure Interaction II: Modeling, Simulation, Optimization, Bungartz, H. J., Mehl, M., Schafer, M. (eds.), 383-412, Springer-Verlag.Ryhming.