A major deepwater challenge is flow-induced vibration of long risers, or vortex induced vibration (VIV). The suspended lengths of risers can challenge physical testing and computer simulation. Without an accurate method of measuring the forces exerted on them, risers have to be designed to very high margins of safety, which increases costs and limits depth. New methods show potential in overcoming the tyranny of scales that makes modeling deepwater risers such a daunting task.

VIV is a fluid-structure interaction in which repeated vortex shedding generates forces in

Dynamic mesh model with cylinder colored by pressure and vortex structure colored by velocity magnitude at a Reynolds number of 3 x 106. (Figure courtesy of ANSYS INC.)
both in-flow and cross-flow directions. Vortex shedding causes an oscillatory multimode vibration, which can cause fatigue or even collisions with other risers. Riser designs can be tested in tow tanks or current tanks, but scaling effects and the short spans that can be practically tested limit accuracy. Scale model tests are typically limited to Reynolds numbers of 105 and short spans, while values of 106 are common in real-world applications. Riser vibrations can be modeled through a spring-mass-damper system or with computational fluid dynamics (CFD) software linked to a structural analysis code. What makes VIV prediction so challenging are the large length/diameter ratio of risers, multiple vibrational modes and variation of cross currents with depth.

Multiphysics simulation
In simulating VIV, it is necessary to model fluid flow around the riser and riser motion in response. Fluid structure interaction (FSI) problems require concurrent application of techniques from CFD and computational structural dynamics (CSD). For the CFD solver, the finite volume or finite element method is typically used. As the shape of the fluid domain changes during the calculation due to riser motion, the CFD mesh moves or deforms in response. The fluid flow solution provides the hydrodynamic loads to be used as boundary conditions for the CSD solver.

Once a CFD calculation has been performed at each time step, the computed velocities, pressures and temperatures are passed to the structural mechanics solver, where the deflection in the structure and the resulting stress are computed independently. The results from the CSD calculation are then fed back to the CFD solver where the flow field is recomputed. This so-called two-way coupling approach is needed when the computation of the flow field in the deformed domain is crucial, as when VIV occurs. Typically, two-way coupling is required when the structural displacements are of the same order of magnitude as the smallest scale of interest in the fluid flow model. In this case, solving the fluid flow in the deformed configuration requires movement and recalculation of the computational mesh, or the Computational Mesh Dynamics (CMD) solution.

Deepwater riser length makes modeling them as a full FSI problem extremely challenging. Long riser lengths quickly lead to computational problems that would require terabytes of memory and hundreds or thousands of compute nodes running in parallel.

Selection of turbulence model
The most commonly used CFD turbulence models are Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES) and Detached Eddy Simulation (DES). Most conventional simulations are done with traditional RANS methods.

For many flows RANS is not appropriate since the turbulent contribution can be large and have the same order of magnitude as the mean. For unsteady flow in general, wake flows or flows with large separated regions, it is more appropriate to use LES, in which averaging is applied to only the smallest turbulent eddies (smaller than a typical cell size). Larger eddies are computed directly or resolved in this time-dependent model. To extend LES to high Reynolds number flows, new methods have been developed. The DES model uses LES in the core turbulent region and RANS in the wall-dominated region. This makes it a practical alternative to LES simulations for high Reynolds number external hydrodynamic flows since it is able to capture the physics with the use of a smaller mesh.

In one recent example, a DES turbulence model was used to simulate a stationary riser at a Reynolds number of 2x106. The boundary conditions were a constant velocity at the inlet and periodic conditions at spanwise upper and lower edges of the domain. A constant pressure was applied to the downstream boundary. A total of 3.7 million cells and a timestep of 0.05 seconds were used. Simulation results closely matched experimental measurements of forces and shedding frequency.

Because of the strong two-way coupling between structural motion and fluid forces in VIV, validation of cylinder motion simulation is critical for gaining confidence in the methodology. Therefore, the stationary model, where the cylinder was not allowed to move, was upgraded using the dynamic mesh capability to capture the fluid-structure interaction. This methodology was first validated using available experimental data. Because the Reynolds number was low for this experimental data (around 3,800), the flow in contact with the cylinder could be assumed laminar. Therefore, a 2-D model could be employed using a RANS turbulence model to account for the wake fluctuations. Results comparing cross-stream vibrational amplitudes and frequencies agreed well with experiments. For demonstration purposes, a 3-D freely oscillating cylinder was simulated at a Reynolds number of 3 x 106, using the DES turbulence model. No experimental data are available at this Reynolds number for elastically mounted cylinders.

These and several other simulations indicate that high fidelity transient CFD models are required to simulate hydrodynamic forces accurately on bare risers. 3-D LES appears well suited for “smooth” cylinders in the transition regime (Reynolds numbers between 105 and 106) to predict the correct separation point. Above the transition regime, 3-D DES appears to be a better choice because it allows a coarser grid than LES. Preliminary results show that DES can be used at lower Reynolds numbers for risers with strakes, because the strakes interrupt the boundary layer and result in fixed separation points along the riser span.

Strip theory approach
Given the challenges of the full FSI riser simulation, the strip theory approach promises to address this problem. In a recent example by Rakshit, Atluri, and Dalton at the University of Houston, a riser was modeled by coupling independent CFD “strip” simulations at various depths to a full-length riser vibration model. Approximately 40 2-D coupled CFD runs can simulate 10 vibration modes which cover a substantial portion of the amplitude fluctuation. The Reynolds number for this case was about 104.

For higher Reynolds numbers, 3-D CFD is required in order to use LES or DES, but strip theory could be applied with a series of short 3-D strips. The authors are currently performing a grid sensitivity study to understand the impact of lower grid resolution on DES cylinder results. If the mesh size can be reduced by a factor of 1.5 or 2, it is estimated that 10 modes of vibration and 32 CFD strips could be deployed, which would take approximately 1 month to converge on a 128 compute node cluster.

Development of a validated model of a full-length riser will enable investigating the performance of alternative designs and different materials numerically in a “Virtual Current Tank.” The virtual current tank can also be used to develop novel VIV suppression devices. Also, investigating performance comparisons of these devices may not require simulation of the entire riser; comparing the behavior of short sections to show trends may provide a reasonable estimate of the relative performance of alternative designs. Behavior can then be confirmed by modeling the entire riser.