Fluid structure interaction
Unbonded Flexible Risers
As the search for new gas and oil reservoirs moves to deeper waters, long slender multi-layered pipes, called unbonded flexible risers, have become the main means of conveying fluids between the well-head and the surface unit and are considered as the new-generation risers for deep water applications. However this currently poses many additional challenges to the offshore industry as these highly flexible slender structures undergo types of extreme loadings which are different to those experienced by conventional rigid risers. Furthermore, unbonded flexible risers have a very complex design, consisting of a number of different layers, some of which are made of non-metallic materials, and are free to slide with respect to each other. A typical flexible riser as shown in the figure below would include a carcass, an internal pressure sheath, an interlocked pressure armour layer, an anti-wear layer, two tensile armour layers and an outer sheath, each providing a particular function.
Brunel led three EPSRC projects, in collaboration with prestigious academic partners and supported by industries including BP, Shell and Lloyds Register. In these projects, very detailed FE models of flexible risers at the small scale were developed and for the first time the analysis of these risers was conducted by means of numerical multiscale methods.
A numerical model of a 5-layered pipe made of three polymer layers and two intermediate armour layers, each made of 40 steel tendons ( the outer layer is removed and one of the tendons is shown).
Two multiscale approaches were developed. In a first one, of sequential type, a new plasticity-like constitutive model for beams was developed, which captures the hysteretic response of risers under cyclic loading. The input parameters for this model are determined via a number of suitably designed simulations conducted on the detailed small-scale nonlinear finite-element models, in which all layers are included in the analysis and their contact and frictional slipping simulated accurately.
Bending moment vs curvature at the touch-down section of a riser subject to wave motion studied with a sequential multiscale modelling approach.
A second developed approach consists of a ‘fully nested’ multiscale analysis. This requires no assumption on the constitutive law for the beam model at the large scale and can be therefore extremely more accurate. With this method, the response of each cross section at the large scale is determined, at run time, by numerically solving the small-scale nonlinear finite-element model (which again accounts for contact and frictional slipping between layers). This is done for each ‘material point’ of the large-scale model, at each iteration of each increment of a nonlinear solution procedure. Therefore, the computational cost is high but it is manageable with the use of HPC and parallel computing.
Both methods have been developed within the rigorous framework of computational homogenisation methods, making use of periodic boundary conditions suitably implemented in python scripts to avoid spurious end effects associated with boundary conditions imposing a rigid response of the end sections.
Numerical results of a small fraction of pipe subject to prescribed bending or axial extension (shown above), show that fixed in-plane boundary conditions result in a significant spurious edge effects, whereas periodic boundary conditions lead to a much more realistic stress distribution that is uniform across the longitudinal direction.
Both types of multiscale methods for the structural analysis are unique and place Brunel at the forefront of research in this field, allowing potentially unprecedented accuracy in determination of the nonlinear dynamic response of risers and in the prediction of stresses. The latter is an essential ingredient in the evaluation of fatigue life of flexible risers and in making informed choices for life extension of existing ones.
Multi-physics and multi-scale analysis of Vortex-Induced-Vibrations (VIV) in flexible risers
The combination of the multiscale structural modelling of flexible risers with detailed fluid-dynamics simulations methods has also been studied at Brunel, where advanced fluid-structure interaction techniques have been used to predict vortex-induced-vibrations (VIV), which are a cause of significant concern in the industry for the design of risers in ultra-deep waters.
When the vortex-Shedding (vortex formation) frequency in a flow around a cylinder is sufficiently close to the natural frequency of a riser, as the flow velocity (U) increases, a condition is reached where the vortex shedding frequency (fv) will “lock in” to the natural frequency (fn) of the structure such that the unsteady pressures from the wake vortices cause the body to enter its resonance frequency range known as the ‘lock in’ region.
The elements of fluid do not necessarily coincide with the elements of the structure, therefore transferring the hydrodynamic forces and structural displacements between the fluid and structure is inevitable.
An important aspect of a FSI simulation is to solve the flow and structure equations simultaneously and apply proper boundary conditions
In view of the high computational processing requirements for full 3D simulation of long oil risers the following two strategies are followed:
- A quasi 3D approach is conducted by applying a strip theory model, in which the flow is simulated in 2D domains and certain intervals along the riser pipe.
- Each strip of flow (2D domain) is simulated within different processors. Therefore a parallel processing algorithm is used