In this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which regularization and the principle of least action are applied. We obtain two different equations, whose discrete counterparts coincide with the scheme used traditionally in the Smoothed Particle Hydrodynamics (SPH) numerical method [27], and with the equation treated by Di Lisio et al. in [9], respectively. Additionally, we prove the convergence in the Wasserstein distance of the corresponding measure-valued evolutions, moreover providing the order of convergence of the SPH method. The convergence holds for a general class of force fields, including external and internal conservative forces, friction and non-local interactions. The proof of convergence is illustrated numerically by means of one and two-dimensional examples.

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In this article we propose an efficient method to compute the friction factor of helically corrugated hoses carrying flow at high Reynolds numbers. A comparison between computations of several turbulence models is made with experimental results for corrugation sizes that fall outside the range of validity of the Moody diagram. To do this efficiently we implement quasi-periodicity. Using the appropriate boundary conditions and matching body force, we only need to simulate a single period of the corrugation to find the friction factor for fully developed flow. A second technique is introduced by the construction of an appropriately twisted wedge, which allows us to furthermore reduce the problem by a further dimension while accounting for the Beltrami symmetry that is present in the full three-dimensional problem. We make a detailed analysis of the accuracy and time-saving that this novelty introduces. We show that the swirl inside the flow, which is introduced by the helical boundary, has a positive effect on the friction factor. Furthermore, we give a prediction for which corrugation angles the assumption of axisymmetry is no longer valid. It then has to make place for Beltrami-symmetry if accurate results are required.

The motivation of the investigation is the critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, two-equation turbulence models (k−ϵ and k−ω) are used in the computations. First, the fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions, and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, the turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: The friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric, which is wrapped around the spiral.

Hypervelocity impacts (HVIs) are collisions at velocities greater than the target object’s speed of sound. Such impacts produce pressure waves that generate sharp and sudden changes in the density of the materials. These are propagated as shock waves. Previous computational research has given insight into this shock loading for the case of homogeneous materials. Shock-wave propagation through materials with discontinuous density distribution has not been considered in depth yet. Smoothed Particle Hydrodynamics (SPH) is a numerical technique, which has been extensively used for the simulation of HVIs. It is especially suitable for this purpose as it describes both the solid and fluid-like behavior effectively as well as the violent breakup of the material under impact. In previous studies on SPH, impact loading of composite materials was modeled by homogenization of the material, or under assumption of being a so-called functionally graded material (FGM). Both these models neglect the reflection-transmission effects on the interface between materials of different density. In this paper the shock loading of layered materials is studied. A modification to the standard SPH method is developed and tested, that incorporates materials with purely discontinuous density distribution. The developed method’s performance at simple shock loading cases is investigated; reflection-transmission patterns of shock-waves through layered materials are discussed, along with a parametric study of the governing parameters.