Andreas Mark

Derivation and validation of a novel implicit second-order accurate immersed boundary method

A novel implicit second-order accurate immersed boundary method (IBM) for simulating the flow around arbitrary stationary bodies is developed, implemented and validated in this paper. The IBM is used to efficiently take into account the existence of bodies within the fluid domain. The flow domain consist of simple Cartesian cells whereas the body can be arbitrary. At the triangulated interface of the body and the fluid, the immersed boundary, the coefficients obtained from discretizing the Navier-Stokes equations are closed with a second-order accurate interpolation arising from the immersed boundary condition employed at the interface. Two different conditions are developed in this paper and it is shown that for the mirroring method the resulting coefficients lead to a well-posed and diagonally dominant system which can be efficiently solved with a preconditioned Krylov sub-space solver. The immersed boundary condition generates a fictitious reversed velocity field inside the immersed boundary, which is excluded from the continuity equation to account for the presence of the IB in the pressure correction equation, resulting in no mass flux over the IB. The force acting on the object from the fluid is determined by integrating the pressure and the viscous forces over the object. The method is validated by simulating the flow around a sphere for a range of Re numbers. It is shown that the drag is very well in agreement with experimental data. Accuracy and convergence studies are employed, proving the second-order accuracy of the method and showing the superiority in convergence rate compared to other IBM. Finally the drag force of a cluster of non-spherical particles is employed to show the generality and potential of the method.

Optimisation of robotised sealing stations in paint shops by process simulation and automatic path planning

Application of sealing materials is done in order to prevent water leakage into cavities of the car body, and to reduce noise. The complexity of the sealing spray process is characterised by multi-phase and free surface flows, multi-scale phenomena, and large moving geometries, which poses great challenges for mathematical modelling and simulation. The aim of this paper is to present a novel framework that includes detailed process simulation and automatic generation of collision free robot paths. To verify the simulations, the resulting width, thickness and shape of applied material on test plates as a function of time and spraying distance have been compared to experiments. The agreement is in general very good. The efficient implementation makes it possible to simulate application of one meter of sealing material in less than an hour on a standard computer, and it is therefore feasible to include such detailed simulations in the production preparation process and off-line programming of the sealing robots.

Improved Spray Paint Thickness Calculation From Simulated Droplets Using Density Estimation

Advancements in the simulation of electrostatic spray painting make it possible to evaluate the quality and efficiency of programs for industrial paint robots during Off-Line Programming (OLP). Simulation of the spray paint deposition process is very complex and requires physical simulation of the airflow, electric fields, breakup of paint into droplets, and tracking of these droplets until they evaporate or impact on a surface. The information from the simulated droplet impacts is then used to estimate the paint film thickness. The current common way of measuring paint thickness on complex geometrical shapes is to use histogram based methods. These methods are easy to implement but are dependent on good quality meshes. In this paper, we show that using kernel density estimation not only gives better estimates but it also is not dependent on mesh quality. We also extend the method using a multivariate bandwidth adapted using estimated gradients of the thickness. To show the advantages of the proposed method, all three methods are compared on a test case and with real thickness measurements from an industrial case study using a complex automotive part.

Simulations of 3D bioprinting: predicting bioprintability of nanofibrillar inks

3D bioprinting with cell containing bioinks show great promise in the biofabrication of patient specific tissue constructs. To fulfil the multiple requirements of a bioink, a wide range of materials and bioink composition are being developed and evaluated with regard to cell viability, mechanical performance and printability. It is essential that the printability and printing fidelity is not neglected since failure in printing the targeted architecture may be catastrophic for the survival of the cells and consequently the function of the printed tissue. However, experimental evaluation of bioinks printability is time-consuming and must be kept at a minimum, especially when 3D bioprinting with cells that are valuable and costly. This paper demonstrates how experimental evaluation could be complemented with computer based simulations to evaluate newly developed bioinks. Here, a computational fluid dynamics simulation tool was used to study the influence of different printing parameters and evaluate the predictability of the printing process. Based on data from oscillation frequency measurements of the evaluated bioinks, a full stress rheology model was used, where the viscoelastic behaviour of the material was captured. Simulation of the 3D bioprinting process is a powerful tool and will help in reducing the time and cost in the development and evaluation of bioinks. Moreover, it gives the opportunity to isolate parameters such as printing speed, nozzle height, flow rate and printing path to study their influence on the printing fidelity and the viscoelastic stresses within the bioink. The ability to study these features more extensively by simulating the printing process will result in a better understanding of what influences the viability of cells in 3D bioprinted tissue constructs.

Simulation of Spray Painting in Automotive Industry

Paint and surface treatment processes in the car paint shop are to a large extent automated and performed by robots. Having access to tools that incorporate the flexibility of robotic path planning with fast and efficient simulation of the processes is important to reduce the time required for introduction of new car models, reduce the environmental impact and increase the quality. The combination of high physical complexity, large moving geometries, and demands on near real time results constitutes a big challenge. We have developed an immersed boundary octree flow solver, IBOFlow, based on algorithms for coupled simulations of multiphase and free surface flows, electromagnetic fields, and particle tracing. The solver is included in an in-house package for automatic path planning, IPS. The major improvement of computational speed compared to other approaches is partly due to the use of grid-free methods which in addition simplifies preprocessing.

Robust intersection of structured hexahedral meshes and degenerate triangle meshes with volume fraction applications

Two methods for calculating the volume and surface area of the intersection between a triangle mesh and a rectangular hexahedron are presented. The main result is an exact method that calculates the polyhedron of intersection and thereafter the volume and surface area of the fraction of the hexahedral cell inside the mesh. The second method is approximate, and estimates the intersection by a least squares plane. While most previous publications focus on non-degenerate triangle meshes, we here extend the methods to handle geometric degeneracies. In particular, we focus on large-scale triangle overlaps, or double surfaces. It is a geometric degeneracy that can be hard to solve with existing mesh repair algorithms. There could also be situations in which it is desirable to keep the original triangle mesh unmodified. Alternative methods that solve the problem without altering the mesh are therefore presented. This is a step towards a method that calculates the solid area and volume fractions of a degenerate triangle mesh including overlapping triangles, overlapping meshes, hanging nodes, and gaps. Such triangle meshes are common in industrial applications. The methods are validated against three industrial test cases. The validation shows that the exact method handles all addressed geometric degeneracies, including double surfaces, small self-intersections, and split hexahedra.

Simulation of a highly elastic structure interacting with a two-phase flow

PurposeThe aim of this paper is to present and validate a modeling framework that can be used for simulation of industrial applications involving fluid structure interaction with large deformations.BackgroundFluid structure interaction phenomena involving elastic structures frequently occur in industrial applications such as rubber bushings filled with oil, the filling of liquid in a paperboard package or a fiber suspension flowing through a paper machine. Simulations of such phenomena are challenging due to the strong coupling between the fluid and the elastic structure. In the literature, this coupling is often achieved with an arbitrary Lagrangian Eulerian framework or with smooth particle hydrodynamics methods. In the present work, an immersed boundary method is used to couple a finite volume based Navier-Stokes solver with a finite element based structural mechanics solver for large deformations.ResultsThe benchmark of an elastic rubber beam in a rolling tank partially filled with oil is simulated. The simulations are compared to experimental data as well as numerical simulations published in the literature. 2D simulations performed in the present work agree well with previously published data. Our 3D simulations capture effects neglected in the 2D case, showing excellent agreement with previously published experiments.ConclusionsThe good agreement with experimental data shows that the developed framework is suitable for simulation of industrial applications involving fluid structure interaction. If the structure is made of a highly elastic material, e.g. rubber, the simulation framework must be able to handle the large deformations that may occur. Immersed boundary methods are well suited for such applications, since they can efficiently handle moving objects without the need of a body-fitted mesh. Combining them with a structural mechanics solver for large deformations allows complex fluid structure interaction problems to be studied.

Multiobjective Optimization of a Heat-Sink Design Using the Sandwiching Algorithm and an Immersed Boundary Conjugate Heat Transfer Solver

The thermal management is an ever increasing challenge in advanced electronic devices. In this paper, simulation-based optimization is applied to improve the design of a plate-fin heat-sink in terms of operational cost and thermal performance. The proposed framework combines a conjugate heat transfer solver, a CAD engine and an adapted Sandwiching algorithm. A key feature is the use of novel immersed boundary (IB) techniques that allows for automated meshing which is perfectly suited for parametric design optimization.

Math-Based Algorithms and Software for Virtual Product Realization Implemented in Automotive Paint Shops

We present a simulation framework that makes it possible to accurately simulate spray painting of e.g. a truck cab in only a few hours on a standard computer. This is an extreme improvement compared to earlier approaches that require weeks of simulation time. Unique algorithms for coupled simulations of air flows, electrostatic fields and charged paint particles make this possible. In addition, we demonstrate that the same framework can be used to efficiently simulate the laydown of sealing or adhesive material. In the virtual paint factory the production preparation process can be performed in the computer, which allows the engineers to replace physical prototypes with virtual ones to shorten the lead time in product development, and avoid future unforeseen technological and environmental problems that can be extremely costly if they are discovered at the end of the production line, or even worse by the costumer.

A Multi-Scale Simulation Method for the Prediction of Edge Wicking in Multi-Ply Paperboard

When liquid packaging board is made aseptic in the filling machine the unsealed edges of the board are exposed to a mixture of water and hydrogen peroxide. A high level of liquid penetration may lead to aesthetic as well as functional defects. To be able to make a priori predictions of the edge wicking properties of a certain paperboard material is therefore of great interest to the paper industry as well as to packaging manufacturers. In this paper an extended multi-scale model of edge wicking in multi-ply paperboard is presented. The geometric and physical properties of the paperboard are modeled on the micro-scale, and include fillers and fines. The absolute air permeabilities and pore size distributions are validated with experimental and tomographic values. On the macro-scale random porosity and sizing distributions, time and sizing dependent contact angles, and inter-ply dependence are modeled. Arbitrary shapes of the paperboard are handled through an unstructured 3D surface mesh. Stationary and transient edge wicking simulations are validated against experiments with excellent agreement. The simulations show that the diffusive menisci between the liquid and air phases together with the two-ply model is necessary to achieve good agreement with the transient edge wicking experiments.