Elastic bodies entering the water might experience Fluid-Structure Interaction phenomena introduced by the mutual interaction between the structural deformation and the fluid motion. Cavity formation, often misleadingly named cavitation, is one of these. This work presents the results of an experimental investigation on the water entry of deformable wedges impacting a quiescent water surface with pure vertical velocity in free fall. The experimental campaign is conducted on flexible wedges parametrically varying the flexural stiffness, deadrise angle, and drop height. It is found that under given experimental conditions cavity pockets forms beneath the wedge. Their generation mechanism is found to be ruled by a differential between structural and fluid velocities, which is introduced by the structural vibrations. Results show that the impact force during water entry of stiff bodies is always opposing gravity, while in case of flexible bodies might temporarily reverse its direction, with the body that is being sucked into the water within the time frame between the cavity formation and its collapse. Severe impacts might also generate a series of cavity generation and collapses.

Performing optimisation and scale-up studies of crystallisation systems requires accurate and computationally efficient mathematical models. The assumption of the ideal mixing conditions in batch reactors typically produce inaccurate results while the computational expense of CFD models is still prohibitively high. Therefore, in this work, a new intermediary approach is proposed that takes into account the non-ideal mixing conditions in the reactor and requires less computational resources than full CFD simulations. Starting with the Danckwerts concept of the intensity of segregation, an analogy between its application to chemical reactions and the kinetics of the crystallisation phenomena (such as nucleation and growth) has been made. As a result, the modified kinetics expressions have been derived which incorporate the effect of non-idealities present in stirred reactors. This way, based on the experimental measurements of the mixing time using the Laser Induced Fluorescence (LIF) technique, computationally more efficient mathematical models can be developed in two ways: (1) the accurate semi-empirical correlations are available for standard mixing configurations with the most often used types of impellers, (2) CFD simulations can be utilised for estimation of the mixing time; in this case it is necessary to simulate only the mixing process. The benefits offered by the LIF experimental technique have been demonstrated and some frequent problems in its application analysed. The mixing time results for configurations with and without baffles for three types of impellers and four different rotational speeds have been presented. The false shorter mixing times in the non-baffled configurations have been observed and this phenomena explained by the existence of two segregated zones in the reactor and confirmed by additional experiments. The precise measurements in these cases have been shown as difficult using the LIF technique, particularly for higher rpms. The experimental data has been compared to the preliminary simulation results obtained from the Smoothed Particle Hydrodynamics method and the standard k-ε turbulence model with the modest success. The shortcomings of the SPH model have been recognized and the directions for the future work discussed.

The second article in the series presents the application of the Smoothed Particle Hydrodynamics (SPH) method to modelling of batch crystallisation in stirred tanks. A methodology to integrate the population balance equations (PBE) in parallel and independently from the Navier-Stokes equations is demonstrated. The benefits of the proposed methodology in terms of computational requirements, accuracy and availability of the crystal size distribution are discussed. The specific formulation of the SPH equations where the resulting system of ordinary differential equations is solved using the weighted contributions rather than numerically by solving a linear system of equations allows for massive parallelisation and a very loose coupling of the population balance and the fluid dynamics. It has been demonstrated, that the population balance equations can be solved on a Shared Memory Architecture (SMA) system using the OpenMP interface while the fluid dynamics equations being computed independently on a General Purpose Graphics Processing Unit (GPGPU) using the NVidia CUDA technology. This way, a significant portion of the computational overhead due to the large number of additional transport equations resulting from the discretisation of the population balance was removed: the SPH simulation coupled with 200 population balance equations was only 40% slower compared to SPH-only simulation. Two methods for the solution of population balance equations that preserve full crystal size distribution were implemented: discretised population balance (DPB) and method of characteristics (MOCH). The DPB equations are solved using the high-resolution finite-volume method with flux limiter and the effect of a large number of different flux limiters have been investigated. Both methods were validated using the case studies from the literature where an analytical solution can be derived. The developed models were applied to a numerical solution of coupled computational fluid dynamics and population balance equations to model a batch crystallization process. The effect of the hydrodynamics on the local temperature/supersaturation and the resulting crystal size distribution was captured and compared to the ideal mixing case. The simulation results from the DPB and MOCH methods were compared in terms of computational requirements and accuracy and MOCH selected as computationally more efficient and accurate.

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions.

Smoothed particle hydrodynamics (SPH) is regarded as a pure Lagrangian approach, which can solve fluid dynamics problems without the creation of mesh. In this paper, a paralleled SPH solver is developed to solve particle-based computational acoustics (PCA). The aim of this paper is to study the feasibility of using SPH to solve acoustic problems and to improve the efficiency of solving processes by paralleling some procedures on GPU during calculating. A stand SPH code running serially in a CPU is proposed to solve wave equation. This is a wave propagating in a two-dimensional domain. After finishing the computation, the results are compared with the theoretical solutions and they agree well. So its feasibility is verified. There are two main methods for searching neighbor particles: all-pair search method and linked-list search method. Both methods are used in different codes to simulate an identical problem and their runtimes are compared to investigate their searching efficiencies. The runtime results show that linked-list search method has a higher efficiency, which can save a lot of searching time when simulating problems with huge amounts of particles. Furthermore, the percentages of different procedures’ runtimes in a simulation are also discussed to find the most consuming one. Then, some codes are modified to run in different GPUs and their runtimes are compared with those of serial ones on a CPU. Runtime results show that the paralleled algorithm can be more than 80 times faster than the serial one. The result shows that GPU paralleled SPH computing can achieve desirable accuracy and speed in solving acoustic problems.

Solid particles immersed in a fluid can be found in many engineering, environmental or medical fields. Applications are suspensions, sedimentation processes or procedural processes in the production of medication, food or construction materials. While homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics (SPH) as a simulation framework, we therefore present a modelling approach for Direct Numerical Simulations (DNS) of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid-solid interaction forces as well as the contact forces between solid aggregates. The focus of this contribution is the numerical modelling approach and its implementation in SPH. Since SPH presents a fully resolved approach, the construction of arbitrary shaped particles is conveniently realizable. After validating our model for single non-spherical particles, we therefore investigate the motion of solid bodies in a Newtonian fluid and their interaction with the surrounding fluid by analyzing velocity fields of shear flow with respect to hydromechanical and contact forces. Results show a dependency of the motion and interaction of solid particles on their form and orientation. While spherical particles move to the centerline region, ellipsoidal particles move and rotate due to vortexes formation in the fluid flow in between.

In this paper, we first discuss the research status and application progress of the finite element method and the smoothed particle method. By analyzing the advantages of the smoothed particle method and the finite element method, a new coupling algorithm, namely FEM-SPH algorithm, is proposed. By the method of comparison, it shows that finite element method and SPH method in the simulation of large deformation problems each have advantages and disadvantages, the finite element method smoothed particle coupling algorithm is effective to achieve the performance of high computational efficiency and can naturally simulate large deformation problems across. In the process of calculation, the large deformation unit can be freely into an algorithm to facilitate the calculation accuracy and efficiency of three methods of numerical simulation. Through the study found, FEM-SPH algorithm not only overcome the defect of smooth particle tensile instability, but also overcomes the problem of low efficiency of finite element computation. To further test the FEM-SPH algorithm has advantages in the practical engineering, we have carried out the actual test to the example of the super high speed collision, concluded that, since the target of most of the computational domain is always finite element, smoothed particle focused only in contact with the projectile and target of local area, particle number is not much, the whole calculation process just ten minutes, computational efficiency has been greatly improved, at the same time in the simulation of large deformation, the advantage is very obvious .This provides a criterion for the actual project, depending on the specific material deformation mode and choose a more appropriate conversion algorithm.

The proximal part of the colon offers opportunities to prolong the absorption window following oral administration of a drug. In this work, we used computer simulations to understand how the hydrodynamics in the proximal colon might affect the release from dosage forms designed to target the colon. For this purpose, we developed and compared three different models: a completely-filled colon, a partially-filled colon and a partially-filled colon with a gaseous phase present (gas-liquid model).The highest velocities of the liquid were found in the completely-filled model, which also shows the best mixing profile, defined by the distribution of tracking particles over time. No significant differences with regard to the mixing and velocity profiles were found between the partially-filled model and the gas-liquid model. The fastest transit time of an undissolved tablet was found in the completely-filled model. The velocities of the liquid in the gas-liquid model are slightly higher along the colon than in the partially-filled model. The filling level has an impact on the exsisting shear forces and shear rates, which are decisive factors in the development of new drugs and formulations.