The below diagrammatic framework represents the MUFFINS research programme with 7 work packages (WPs) and key deliverables for industry.
Overall, the novel aspects of the proposed project are:
- High-fidelity 3D computational fluid dynamics (CFD) to capture vital resonant effects of the coinciding slug and pipe frequencies, and the multiple resonances of slug, pipe and external vortex-shedding frequencies;
- New precise closure relationships for 3D MFIV analyses, with detailed insights into FSI phenomena and the intrinsic coupling between multiphase flow forces, excitation frequencies and structural oscillations;
- A hierarchy of novel models for predicting MFIV due to critical slug flows with experimental comparisons;
- Deeper understanding of combined MFIV-VIV interactions and effects on structural fatigue life estimation;
- Computationally-efficient tools, open-source codes and recommended guidelines, which will be utilised for the safe and reliable, real-life designs of subsea pipes and risers transporting multiphase flows in a wide range of flow-structure parameters. This is a current and immediate need for the global offshore oil and gas industry.
WP1: Flow Regime Characterisation
Multiphase flow modelling is principally unique to each flow pattern. Since the 1950s several liquid-gas flow patterns have been defined, depending on the flow rates, flow direction and fluid-pipe geometry. These maps are generally valid for steady flows in rigid pipes; insights into transient unsteady flows in long flexible pipes are relatively unknown. This poses a question: which flow patterns and correlation factors derived from different specific test data are applicable to a real slug occurrence and subsequent MFIV in a long flexible riser? An in-depth review of flow patterns (stratified, bubbly, slug, annular) and correlations for slug flow properties is being carried out by the project team. With such review, WP1 will develop a systematic approach to integrate and generalise relevant maps for identifying the liquid-gas slug flow occurrences and associated features to be recognised as initial input parameters in WP2-7.
WP2: Continuum Pipe Modelling
Previous studies usually omit the axial dynamics in deriving equations for the pipe three-dimensional motion, only focusing on transverse responses. This can lead to substantial errors in response predictions with underestimated stresses or fatigue damage. In relation to the axially-travelling internal flows and potential mean drag magnifications caused by external flow vortex-induced vibrations, it is essential to account for the pipe axial vibration and determine their potential modal contributions to overall planar and out-of-plane responses which contribute to the pipe axial/bending stress and fatigue. These will be achieved through a three-dimensional flexural-extensional nonlinear continuum beam-cable model accounting for the nonlinear stretching, large-amplitude displacement coupling, pressure change, flow-induced Coriolis and centrifugal force effects.
WP3: Computational Fluid Dynamics Simulations
This involves high-fidelity simulations of the complex interfacial dynamics using the control-volume finite-element code (Fluidity) with the interface-capturing on 3D, adaptive, unstructured meshes. Turbulence is modelled using Very Large Eddy Simulation (VLES) with implicit (Discontinuous Galerkin momentum discretisations) or explicit (Smagorinsky) LES. The mesh-to-mesh interpolation, used after mesh adaptivity, is through the conservative high-order finite element or new control volume interpolation. The liquid-solid modelling is through the Finite Element Method Discrete Element Method (FEMDEM). FEMDEM and Fluidity will be coupled to capture the gas-liquid and liquid-solid interfaces and their detailed flow features. The modelling of multiphase hydrodynamics coupled with pipe motions in WP5/WP6 will require closure expressions describing the space-time variations of interfacial frictions with phase distributions, bubble/drop entrainment, bubble-induced turbulence, phase-to-phase interactions, drag and wake effects.
WP4: Non-Intrusive Reduced-Order Models (NIROM)
Developing computationally-efficient NIROM for MFIV-FSI analyses, as well as MFIV-VIV interactions, based on Fluidity-FEMDEM is crucial for rapidly simulating realistic two-way coupling, and visualizing 3D multi-physics complicated phenomena, a recent work showing the speed increases of 5-6 orders of magnitude were achieved while the dominant details of the high fidelity models were still maintained. This novel approach will apply a technique combining the Proper Orthogonal Decomposition (POD) and the radial basis function (RBF) interpolation to reduce computational costs for simulating 3D MFIV and combined MFIV-VIV of long flexible pipes with high aspect ratio and many degrees of freedom. Novelties include the world’s first 3D multi-fluid NIROM applied to MFIV-FSI, construction of NIROM from adaptive and moving meshes by interpolating the simulation results onto a potentially optimised unstructured non-adapted mesh, the individual and combined effects of MFIV and VIV hydrodynamic forces.
WP5: Improvement of Transient Two-Fluid Models
Industry widely uses the transient 1D (i.e. averaged over pipe cross section) two-fluid models for the analysis of slug flows. Often, the temperature change has been disregarded by postulating isothermal flows. This effect will be considered through the fully coupled mass-momentum-energy conservation equations for both liquid and gas phases. Further, in practice there is little guidance as to whether and how the transient 1D models with closures derived mostly from stationary, rigid and horizontal pipes can be applied to predicting MFIV-FSI of vertical, inclined or curved oscillating pipes? With new closures derived from WP3 accounting for a wide range of flow and pipe dynamic features, the 1D two-fluid models will be improved for MFIV-FSI simulations, whereas existing closures will be used for comparisons. Novelties include improved transient two-fluid models of liquid-gas slug flows with precise closure expressions for capturing realistic MFIV-FSI phenomena and analysing coupled MFIV-VIV interactions of long flexible pipes.
WP6: Phenomenological Oscillators
The foremost concern in solving for many unknowns is still the excessive computational time and potential convergence failure when dealing with a long flexible pipe moving multi-directionally due to a 3D MFIV. Following our success in VIV studies, a novel phenomenological low-order fluid force oscillator model will be developed and validated for each slug unit comprising the elongated bubble and liquid slug. These oscillators can oscillate axially and transversely, interacting with the pipe motions. To capture the slug unsteadiness, these oscillators will have dissimilar velocity, stiffness, mass and damping properties, depending on the slug characteristics identified in WP1, WP3-5 &7. Interactions of bubbles and liquid slugs will be accounted for via empirical stiffness depending on the relative velocities, interfacial, frictional, drag and thermal forces. With practical flow and pipe boundary conditions, a series of nonlinearly coupled oscillators will be spatially connected along the pipe and fulfilling the FSI principles of internal MFIV.
WP7: Experimental Validations
In-house moderate-scale experimental tests to validate theoretical models and codes in WP1-6 will be conducted. Novelties are new test setups and measurements for capturing actual liquid-gas slug flow features in flexible pipes and MFIV phenomena, for generating a database of fluid forces and pipe vibrations, and validating MFIV models in WP3-6. The experimental model will be established with a 10-m riser pipe connected to a horizontal pipe at the bottom which allows the flow pattern development. The riser top will be allowed to rotate via a specially-designed support where a load cell is integrated for measuring forces. Internal water-air flows will be supplied with varying flow rates. Key measurement outputs will be the real-time pressure and hold up at the riser base (inlet) vs. top (outlet) locations, the slug characteristics (length, frequency), 3D pipe oscillation amplitudes, resonant frequencies and top dynamic tensions. An optical fibre sensing system will be used for tracking the pipe motions which entail curvatures, strains and stresses.