Final Report Summary - NSDSTF (Numerical simulation of deformable solids in turbulent flow) Publishable summary: The numerical simulation of deformable solids has many applications in fluid-solid interaction such as in aerospace structures and civil and marine engineering. However, the area where it can have its greatest application is in medical engineering in which it will be possible to simulate the movement of tube like structures such as the oesophagus, intestines, bile duct, fallopian tube, uterus, urethra and blood vessels etc. It will also be possible to simulate the movement and interaction of blood cells and lead to the design of better stents. Up to now, we have successfully developed a numerical scheme for the above purpose, which also involved taking into account the possible collision of the cells and their 'shielding' and imbrication by other cells. At the moment, the work performed since the beginning of the project is as the follows. (a) We have modified and developed our in-house computational fluid dynamics code CgLes so that solids within the fluid can have deformable boundaries. The immersed boundary method (IBM) was used to represent the moving and deforming boundaries inside the fluid. (b) We have coupled the CgLes code for fluid and a discrete element method (DEM) code for transport and deformation of solids. A complete fluid-structural interaction (FSI) code package has been developed to model flow with deformable discrete coarse particles and their movement and interaction with themselves and the fluid. (c) We have carried out necessary modifications, optimisation and parallelisation of the coupled code in order to achieve maximum efficiency. The original DEM code was serial, which could only run on one core of a computer. We have successfully made it fully parallelised based on spatial decomposition. The immersed boundary method was also fully parallelised. Now it can run on the United Kingdom (UK)'s high-end computing resource - HECToR with thousands of red blood cells involved. (d) We have carried out a series of step-by-step verifications for both fluid and solids including: deformation of a red blood cell was verified against a stretch test of a human red blood cell in a laboratory; adhesion of red blood cells was verified against an experiment on the separation of two red blood cells in a shear flow; fluid-solid interaction was verified against an experiment of flow induced vibration of an elastic sheet. (e) We have investigated the influence of different flow parameters on the movement, interaction and deposition of the particles based on numerical simulation results. The main result achieved so far is the large-scale deformation and aggregation of human red blood cells. The large scale of the simulation presented in this paper has enabled us to have a macroscale verification and investigation into the overall characteristics of RBCs aggregations, rather than just focusing on several individual cells. The comparisons of RBC aggregation for the experimental and the simulated cases show apparent similarities of blood micro-structure between the experiment and the simulation. Under the high shear rate (shear rate=100/s), both the experiment and the simulation show no aggregation of RBCs. The similarity between the two is more obvious for the 10 / s case when severe aggregation occurs. Qualitatively, both results show large aggregation structures of the RBCs and gaps of similar size. For human blood with haematocrit of 45 %, aggregation characteristics such those simulated in the present study have been widely reported in clinical experiments. Based on the achieved results, we will further investigate the relationship between the RBC aggregation and the macroscale behaviour of human blood flow, such as blood viscosity variation and red blood cell orientation distribution in the blood vessels with various sizes. The potential benefits of our simulation with the fluid-structural interaction code package are enormous as it possible to investigate the exact cell movement mechanism - something that is very difficult, if not impossible, to adequately measure experimentally. The results from the high confidence numerical simulations could also help researchers and doctors to understand the fundamental linking between the blood flow properties and many blood-related diseases by investigating the motion and behaviour of individual red blood cells.
