Search

We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration. Furthermore, since the surface energy is an interfacial property depending on the types of materials on either side of an interface, spatial variation is required for modeling the contact angle at the triple junction between a liquid, solid and surrounding air. Our discretization is based on the surface energy itself, rather than on the associated traction condition most commonly used for discretization with particle methods. Our energy based approach automatically captures surface gradients without the explicit need to resolve them as in traction condition based approaches. We include an implicit discretization of thermomechanical material coupling with a novel particle-based enforcement of Robin boundary conditions associated with convective heating. Lastly, we design a particle resampling approach needed to achieve perfect conservation of linear and angular momentum with Affine-Particle-In-Cell (APIC) [Jiang et al. 2015]. We show that our approach enables implicit time stepping for complex behaviors like the Marangoni effect and hydrophobicity/hydrophilicity. We demonstrate the robustness and utility of our method by simulating materials that exhibit highly diverse degrees of surface tension and thermomechanical effects, such as water, wine and wax.

We present an updated Lagrangian discretization of surface tension forces for the simulation of liquids with moderate to extreme surface tension effects. The potential energy associated with surface tension is proportional to the surface area of the liquid. We design discrete forces as gradients of this energy with respect to the motion of the fluid over a time step. We show that this naturally allows for inversion of the Hessian of the potential energy required with the use of Newton's method to solve the systems of nonlinear equations associated with implicit time stepping. The rotational invariance of the surface tension energy makes it non-convex and we define a definiteness fix procedure as in [Teran et al. 2005]. We design a novel level-set-based boundary quadrature technique to discretize the surface area calculation in our energy based formulation. Our approach works most naturally with Particle-In-Cell [Harlow 1964] techniques and we demonstrate our approach with a weakly incompressible model for liquid discretized with the Material Point Method [Sulsky et al. 1994]. We show that our approach is essential for allowing efficient implicit numerical integration in the limit of high surface tension materials like liquid metals.

Dynamic aeroelastic behavior of structurally nonlinear Joined Wings is presented. Three configurations, two characterized by a different location of the joint and one presenting a direct connection between the two wings (SensorCraft-like layout) are investigated. The snap-divergence is studied from a dynamic perspective in order to assess the real response of the configuration. The investigations also focus on the flutter occurrence (critical state) and postcritical phenomena. Limit Cycle Oscillations (LCOs) are observed, possibly followed by a loss of periodicity of the solution as speed is further increased. In some cases, it is also possible to ascertain the presence of period doubling (flip-) bifurcations. Differences between flutter (Hopf

The postbuckling behavior of joined-wing configurations has not been fully addressed in the past. This topic is extensively discussed in this work. Starting from a baseline configuration, geometrical parameters as well as wings’ load repartition are varied to assess their influence on buckling occurrence. The snap-buckling phenomenon and postcritical pattern are investigated with the adoption of the arc-length technique. The complex load transferring through the joint induces a deformation shape that can no longer carry additional load after a critical point is reached. An abrupt snap to a configuration that is not continuously adjacent to the previous one is then observed. Comparison with the instability state obtained via eigenvalue analysis demonstrates that buckling prediction through linear-buckling analysis is inadequate, and often, the actual critical load is overestimated. This study shows that, for PrandtlPlane joined-wing configurations, increasing the height-to-wingspan ratio is beneficial as f...

Dynamic aeroelastic behaviour of structurally nonlinear Joined Wings is presented. Three configurations, two characterized by a different location of the joint and one presenting a direct connection between the two wings (Sensorcraft-like layout) are investigated. As a first step, the snap-divergence is studied from a dynamic perspective in order to assess the real response of the configuration. Later on, the investigations focus on the flutter occurrence (critical state) and go further in analyzing postcritical phenomena: Limit Cycle Oscillations (LCOs) are observed followed by a lost of periodicity of the solution as speed is further increased. In some cases, it is also possible to ascertain the presence of period doubling (flip-) bifurcation. Differences between flutter (Hopf ’s bifurcation) speed evaluated with linear and nonlinear analyses are discussed in depth, in order to understand if a less computationally intense approach may be used with confidence. Both frequency and time-domain approaches are compared. Moreover, aerodynamic solvers based on the potential flow are critically examined and discussed. In particular, it is assessed in what measure the use of more sophisticated (and computationally more intensive) aerodynamic and interface models impacts the aeroelastic predictions. These differences range from the methods adopted for load transferring to the models employed to describe the wake. When the use of the tools gives different results, a physical interpretation of the leading mechanism generating the mismatch is provided. In particular, for PrandtlPlane-like configurations the aeroelastic response is very sensitive to the wake’s shape. As a consequence, it is suggested that a more sophisticated modelling of the wake positively impacts the reliability of aerodynamic and aeroelastic analysis. For Sensorcraft-like configurations some LCOs are characterized by a non-synchronous motion of the inner and outer portion of the lower wing: the wings’ tip exhibits a small oscillation during the descending or ascending phase, whereas the mid-span station describes a sinusoidal-like trajectory in the time domain.