Generalised high-order Eulerian Smoothed Particle Hydrodynamics for internal flows applied to flow-induced vibration and nuclear tube banks

Computational fluid dynamics or CFD is mature with several general-purpose commercial codes available based on the finite-volume or finite-element (mesh-based) approaches with various options for turbulence modelling. The success of CFD in industrial design has however encouraged increasing demands to be made in terms of the resolution of the flow and finer grain physics, requiring ever increasing resources to be employed, both in terms of computation and manpower. Notable successes are in nuclear reactors, turbo-machinery, combustion chambers, heat exchangers, marine turbines, vehicle aerodynamics, aeronautics, offshore engineering amongst many others. Commercial enterprise tends to focus on two key aspects for improving the efficiency and accuracy of simulations in increasingly complex and demanding practical problems: performance on massively parallel computing and optimal mesh generation. State-of-the-art in commercial CFD suggests meshes may comprise several hundred million cells, over a billion for a nuclear reactor simulation (CD-Adapco, 2016), and runs with massively parallel computing (often with thousands of processors) taking days or weeks. Implementation of High-Order (HO) methods has received comparatively less attention, but can offer flexibility and gains in efficiency and accuracy beyond what can be achieved through optimal meshing and parallelisation alone. HO methods are known to be beneficial, even necessary, in unsteady vortex-dominated and turbulent flow modelling where many problems remain beyond the reach of state-of-the-art second-order CFD even on supercomputers. Important open-source codes from academia are making headway in increasing uptake of HO methods, but optimal implementation within complex 3-D geometries (that may contain arbitrarily moving boundaries) and adaptivity remain challenging problems in a high-order framework. We propose to address these problems through an alternative numerical method that is attractive in its simplicity, amenable to high-order spatial approximations in complex domains while retaining a natural affinity for parallelisation on emerging architectures. We provide this improvement in capability by abandoning the mesh and using particles, which, in Lagrangian form, have been used widely for the modelling of highly distorted flows involving interfaces and multi-physics. The investigators have been active in the development of smoothed particle hydrodynamics (SPH) particularly in divergence-free incompressible form and in developing algorithms for energy efficient hardware. Recently an Eulerian form has been tested by the investigators with high order Gaussian interpolating kernels (up to 6th order) demonstrating spatial convergence to machine accuracy in model periodic problems. In viscous transient flow with second-order time stepping, the accuracy obtained is similar to spectral methods. This new approach opens up considerable opportunities particularly for internal flows.
One downside of this approach is that several billion particles will be required for complex systems, and the floating point operations per second (FLOPS) per particle in SPH are typically an order of magnitude greater than the finite volume/hp-element equivalent. This is compensated by the SPH formulation being ideally suited for parallel processing due to its locally interpolative (meshless) nature and ease of implementation on emerging hardware including most GPUs.

CFD is widely used by leading British and multi-national companies. New commercial projects or developments often require considerable investment in CFD simulations with many runs consuming months of CPU time. This project is to develop a relatively efficient model that can simulate the flows and also resolve the length scales associated with transient thermal effects, taking into account the highly complex geometries. The proposed developments will speed configuration set up, reduce turn round, reduce energy consumption and reduce hardware costs considerably. Importantly high performance and high throughput computing will become accessible for SMEs without previous access to massive parallel processing (e.g. 100,000 cores). While the methodology proposed is quite generic for internal flows with structural vibration and heat transfer we choose important test applications in the nuclear industry: structural vibration in tube banks relevant for PWR/EPR reactors and the hot box dome of an AGR with highly complex geometry and physics. The hot box dome has long been a source of design uncertainty due to the effect of very high temperatures (~650 degC) and hot spots on structural integrity.
The main beneficiaries from this research project will be the evolving nuclear and energy industries, the existing flow simulation industries and engineering consultancies involved in the design of nuclear reactors, and the international modelling communities working on highly transient thermal effects and response of structures.
In order to make the impact happen, we propose to carry out the following activities:
1) Involve some key stakeholders (EDF Energy R&D, NNL) and establish a User Management Group (advisory board) in order that stakeholders are directly engaged with the project achievements;
2) Organise biannual meetings with key stakeholders in addition to SPH and project workshops to widen the awareness of these achievements;
3) Organise a special session at one of the international modelling conferences, e.g. International Symposium on Turbulence Heat and Mass Transfer, to maximise the international of reach of the developments;
4) Create a section on the well-known website for SPH community and managed by Manchester to allow to open access to the information produced.