Multi-scale hydro-morphodynamic modelling using mesh movement methods

Hydro-morphodynamic modelling is an important tool that can be used in the protection of coastal zones. The models can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement methods are particularly well-suited to coastal problems as they allow the mesh to move in response to evolving flow and morphology structures. This new capability is demonstrated using test cases that exhibit complex evolving bathymetries and have moving wet-dry interfaces. In order to be able to simulate sediment transport in wet-dry domains, a new conservative discretisation approach has been developed as part of this work, as well as a sediment slide mechanism. For all test cases, we demonstrate how mesh movement methods can be used to reduce discretisation error and computational cost. We also show that the optimum parameter choices in the mesh movement monitor functions are fairly predictable based upon the physical characteristics of the test case, facilitating the use of mesh movement methods on further problems.

Using Feature-Based Mesh Adaptation to Improve the Adjoint Optimisation of Transonic Compressor Blades

The benefit of mesh adaptation to improve the optimisation process of turbomachinery components is here demonstrated for the first time. Mesh movement is used to automatically cluster and align the cells with significant flow features such as shocks, shock-induced separation and wakes for every geometry tested during a transonic compressor blade optimisation. Using mesh movement means that the same size grid is used while significantly improving the accuracy of the simulation and resulting adjoint gradients. A method is demonstrated to automatically carry out feature based mesh movement during every step of an adjoint optimisation process. Optimisations are carried out using the adaptation method and also using the starting mesh as a comparison. It is shown that (when tested on a very fine grid) the adaptation-optimisation process results in a better design, due to more accurate flow and gradient prediction throughout the optimisation process. A cost breakdown of the process is given to show that using adaptation during the optimisation process only increases the overall optimisation cost by a small amount, but results in greater efficiency of the final blade design.

Dynamic characteristics of water-lubricated journal bearings

The increasing ecological awareness and stringent requirements for environmental protection have led to the development of water lubricated journal bearings. For the investigation of water-lubricated journal bearings, a new structured mesh movement algorithm for the CFD model is developed and based on this method, the nonlinear transient hydrodynamic force model is established. Then, with consideration of velocity perturbation, a method to determine dynamic coefficients and linear hydrodynamic forces is promoted. After validation of static equilibrium position and stiffness coefficients, a comparative linear and nonlinear hydrodynamic force analysis of multiple grooves water-lubricated journal bearings (MGWJBs) is conducted. The calculation results indicate that the structured mesh movement algorithm is suitable for the dynamic characteristics investigation of water-lubricated journal bearings. And the comparative study shows that there is a considerable difference between the linear and nonlinear hydrodynamic forces of MGWJBs. Further investigation should be carried to evaluate the dynamic responses of rotor supported by MGWJBs under difference force models.

Optimal Control of a Stefan Problem Fully Coupled with Incompressible Navier-Stokes Equations and Mesh Movement

The optimal control of moving boundary problems receives growing attention in science and technology. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. The Stefan problem is coupled with incompressible Navier{Stokes equations. We take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state and the control costs. With the formal Lagrange approach and an adjoint system we derive the gradient of the cost functional. The derived formulations can be used to achieve a desired interface position. Among others, we address how to handle the weak discontinuity of the temperature along the interface with mesh movement methods in a finite element framework.

Efficient Adjoint-Based Mesh Adaptation Applied to Turbo-Machinery Flows

Within an industrial setting, mesh adaptation has so far found very limited use. This is, in part, due to the complexity of the geometries and flow features that are to be dealt with. However, the successful utilisation of grid modification techniques, could help engineers achieve more accurate estimates of quantities of interest quickly and efficiently. For this reason, in this paper, adjoint error mesh adaptation technology is developed and applied to steady-3D turbo-machinery solutions. The grid modification strategy proposed comprises of a combined mesh movement and mesh refinement procedure, entirely based on errors related to the functional of interest. The node addition scheme makes use of the output to the flow adjoint solver and an interpolation to an embedded grid. The determined error is used in an edge-refinement approach developed in the in-house MeshPost software. The mesh relocation technique, instead, employs the sensitivity of the functional of interest with respect to the nodes’ coordinates to compute a Riemmannian metric. This parameter is then equi-distributed over the mesh by applying a spring-stiffness approach.