Lagrangian-Eulerian Algorithm Research Articles

Tsunami Squares: Leapfrog scheme implementation and benchmark study on wave–shore interaction of solitary waves

Impulse waves are generated by rapid subaerial mass movements including landslides, avalanches and glacier break-offs, which pose a potential risk to public facilities and residents along the shore of natural lakes or engineered reservoirs. Therefore, the prediction and assessment of impulse waves are of considerable importance to practical engineering. Tsunami Squares, as a meshless numerical method based on a hybrid Eulerian–Lagrangian algorithm, have focused on the simulation of landslide-generated impulse waves. An updated numerical scheme referred to as Tsunami Squares Leapfrog, was developed which contains a new smooth function able to achieve space and time convergence tests as well as the Leapfrog time integration method enabling second-order accuracy. The updated scheme shows improved performance due to a lower wave decay rate per unit propagation distance compared to the original implementation of Tsunami Squares. A systematic benchmark testing of the updated scheme was conducted by simulating the run-up, reflection and overland flow of solitary waves along a slope for various initial wave amplitudes, water depths and slope angles. For run-up, the updated scheme shows good performance when the initial relative wave amplitude is smaller than 0.4. Otherwise, the model tends to underestimate the run-up height for mild slopes, while an overestimation is observed for steeper slopes. With respect to overland flow, the prediction error of the maximum flow height can be limited to ± 50% within a 90% confidence interval. However, the prediction of the front propagation velocity can only be controlled to ± 100% within a 90% confidence interval. Furthermore, a sensitivity analysis of the dynamic friction coefficient of water was performed and a suggested range from 0.01 to 0.1 was given for reference.

Dynamic response and performance assessment of subsea sandwich pipelines with different interlayer subjected to underwater explosion

The sandwich pipelines have been developed and applied in subsea due to their better resistance than single-layer pipelines. Explosive shock loads can cause fatal damage to subsea pipelines, thus the objective of this paper is to systematically evaluate the safety of subsea sandwich pipelines under explosion loading. The uniqueness of this study is to analyze the dynamic response of sandwich pipeline filled with different interlayer materials subjected to underwater explosion, especially considering the fluid-solid interaction (FSI) effect. Based on the Arbitrary Lagrangian-Eulerian (ALE) algorithm, the propagation of the blast shock wave in sea water and the FSI effect with the pipeline were investigated by using LS-DYNA code. The accuracy of the numerical method was verified, and then the evolution of the explosive pressure in sandwich pipes with different interlayer material was simulated. The energy absorbing capacity of each layer was analyzed. The structural dynamic response and deformation of the subsea sandwich pipelines was investigated by considering the influencing factors including the diameter-to-thickness ratio (λ) of the inner pipe and outer pipe, the interlayer material, and the explosive charge (Me). The results show that with the increase of λ and Me, the ovality of the pipe increase correspondingly. Moreover, the results demonstrate that with different material as the interlayer, each layer of the sandwich pipe shows different ability to absorb the internal energy caused by explosive shock wave, thus the deformation of the pipe differs significantly. This study can provide a reference for the optimized design of subsea sandwich pipelines to support the operational safety of deep-sea pipeline systems.

Investigations on geopolymer-based seawater sea-sand high performance concrete slabs reinforced with basalt FRP bars under direct contact explosions

Adopting locally available raw materials like seawater and sea-sand in coastal areas and oceanic islands has facilitated meeting the demands of marine engineering. However, these raw materials contain corrosive elements that could threaten the steel reinforcement in concrete structures, thus non-corrosive fibre-reinforced polymer (FRP) bars are proposed. In the present study, the geopolymer-based seawater sea-sand high performance concrete (G-SHPC) slab reinforced with basalt FRP bars was designed to preliminarily evaluate its dynamic behaviour under contact explosions. Tests were conducted on three large-sized slabs with different TNT charge weights, including 0.8 kg, 1.6 kg and 2.2 kg. To complement the experimental investigation, a numerical simulation was then performed in ANSYS-DYNA. A Continuous Surface Cap (CSC) model was developed to accommodate the unique characteristics of G-SHPC. Two different blast modelling methods, including the Arbitrary Lagrangian-Eulerian (ALE) algorithm and a hybrid Finite-Element (FE) and Smooth Particle Hydrodynamics (SPH) algorithm, were examined to faithfully reproduce the contact explosion phenomena. The structural models considered the bond-slip behaviour, and three bond-slip models were compared. The numerical results obtained through the ALE algorithm and the beam-in-solid bond-slip model exhibited fair agreement with the test results, with a maximum error of less than 6.3%. A parametric study was further conducted to establish the damage identification diagram. Formulas based on empirical data were formulated to anticipate the damage degrees of G-SHPC slabs exposed to contact explosions.

Effect of droplet diameter on oblique detonations with partially pre-vaporized n–heptane sprays

Liquid fuels have been widely used in propulsion systems for their higher energy density and easier storage, but there are few studies on oblique detonation engines (ODEs) using the liquid fuels. In this study, oblique detonation waves (ODWs) in partially pre-vaporized n–heptane sprays are simulated, using a hybrid Eulerian–Lagrangian algorithm with a skeletal chemical mechanism, to facilitate liquid fuels applications in ODE. A novel phenomenon has been observed, illustrating that the ODW initiation lengths in pre-vaporized n–heptane sprays firstly increase and then decrease with increasing fuel droplet diameters. It is found out that an increase of droplet diameter can increase the transferred heat amount caused by droplets evaporation and lower the inflow temperature, so leading to the increase of ODW initiation length firstly. However, extremely large droplet diameter can markedly reduce the heat transfer rate of the droplet and its surrounding mixture, and the compressed gas-stream behind oblique shock wave has a higher temperature that accelerate the induction chemical reaction and results in a decrease in the ODW initiation length. Furthermore, the unsteady oscillations of ODW initiation structures are also observed even for a steady inflow, which involves the periodic hot spots, normal detonation waves and their evolutions. Some factors causing the unsteady behavior of ODWs are tested through a sensitivity analysis method of the initiation lengths. Through the analyzation, the fluctuation of the post-shock temperatures is the main factor causing the fluctuation of initiation lengths, revealing that inhomogeneous heat loss by evaporation of dispersed liquid droplets is the main reason causing the unsteady behaviors of ODWs and the competition between heat release by chemical reactions and heat loss by evaporation determines the steadiness of ODWs.

Numerical analysis of interaction between flow characteristics and dynamic response of interlocked concrete block mattress during sinking process

Revetment can provide effective protection against wave overtopping and fluvial erosion along coastlines, estuaries, and rivers. The cost-effectiveness and rapid implementation make Interlocked Concrete Block Mattress (ICB mat) a viable alternative to unit armors. However, the intense hydrodynamic conditions may compromise the structural integrity of ICB mat during sinking construction, posing significant threats to both personnel and engineering safety. This study aimed to investigate the flow characteristics around the flexible mattress and its dynamic response. Recently, the fluid-structure interaction (FSI) method has been extended to multi-physics analysis in engineering applications due to its superior performance. A two-way coupling was employed to simulate the conceptualized cases of sinking process of ICB mat using the k-ω SST turbulence model, the Arbitrary Lagrangian-Eulerian algorithm, and the partitioned method in this study. The results indicated that the upstream surface velocity of the mattress increased exponentially with the growing water depth; meanwhile, the maximum velocity near the head beam was 23.8–31.2% larger than the average velocity. Additionally, the stress distribution on the mattress manifested transverse stripes influenced by the layout of interlocked blocks, with the highest stress primarily observed in the vicinity of the rotating plate and head beam. Furthermore, an estimation formula was proposed for the dynamic response of ICB mat considering the hydrodynamic conditions as well as structural properties. The current study can provide theoretical guidance for the structural design of ICB mat and engineering risk assessment during sinking construction.

Multi-scale characteristics investigation of sheet/cloud cavitation

Sheet and cloud cavitation involve the formation of large-scale cavities and microbubbles across a wide range of length scales. In this study, a two-way coupling Eulerian-Lagrangian algorithm was utilized to simulate the cavitating flow around a NACA66 hydrofoil at an incidence of 8 degrees and a cavitation number of 1.2. The large eddy simulation (LES) and volume of fraction (VOF) methods are used to capture the large scale vapor structures in Eulerian frame. Meanwhile, the discrete bubble model (DBM) and simplified Rayleigh-Plesset equation are implied to solve the dynamic of Lagrangian microbubbles smaller than local grid scale. The results indicate that large-scale cavities are periodically shed downstream, influenced alternatively by the re-entrant jet and shock wave mechanisms, resulting in periodic variations of both the number and Sauter mean diameter of microscale bubbles. During the quasi-periodic evolution process of sheet/cloud cavitation, the microbubbles scatter around the large scale cavities where have strong turbulence intensity and high vorticity, and the probability density function of discrete bubble diameter similarly conforms to Gamma distribution with the dominant bubble size between 30 and 70μm. During the growth of an attached cavity, the number density of bubbles follows a power-law scaling with a value of -5/3 on radius. For the other stages, the bubble size spectrum of smaller microbubbles exhibits a -2/3 power-law scaling when the diameter of the microbubble is less than 200 μm. For larger bubbles with a diameter greater than 300 μm, the bubble density is proportional to the bubble radius to the power of -6.

Vulnerability analysis of HSR bridge under near-field blast based on response surface method

In this paper, the vulnerability analysis of a high-speed railway (HSR) bridge system attacked by the near-field blasts is conducted using the response surface method. An “explosive-air-ground” coupling analysis model is established by the ANSYS/LS-DYNA software. Through a comparison of the numerical simulated and the experimental results, the effectiveness of the Arbitrary Lagrangian Eulerian (ALE) algorithm and the accuracy of the analysis model are verified. Then, the dynamic responses of an HSR simply-supported bridge subjected to four types of car-bomb blasts are calculated. The damage levels of the bridge components are evaluated using the residual bearing capacities of the pier and beam, and the shear displacement of the bearings. By adopting the central composite design method, the response surface models for the evaluation indices of the bridge components are fitted. Furthermore, the failure probabilities of each component at various damage levels are calculated, and the vulnerability of the bridge system is analyzed based on the Boundary Estimation Method. The proposed method could predict the damage probability of the bridge system under various car-bomb blasts, and provide a reference for exploring a probability-based evaluation method for the post-blast safety of the HSR bridges.

Comparative study on the forming characteristics and penetration effects of shaped charge jet in water and air

In order to analyze the influence of a water medium on the forming process and penetration performance of a shaped charge jet, a comparative study was carried out on an underwater shaped charge jet (USCJ) and a shaped charge jet (SCJ) in air. The virtual mass hypothesis is proposed to analyze the forming mechanism of USCJs. The arbitrary Lagrangian–Eulerian algorithm is adopted to carry out a series of simulation calculations considering the impact of standoff height and liner cone angle. The penetration test of the shaped charge jet in two media is carried out, and the experimental results verify the effectiveness of the theory and simulation. The differences of SCJ formation and penetration in air and water are analyzed. The results demonstrate that the USCJ exhibits a higher jet head velocity, higher cumulative kinetic energy, and a greater penetration ability than those of the jet in air. The depth of penetration (DOP) initially increases and subsequently decreases with an increase in the standoff height. The optimal standoff height of the USCJ is approximately 4–4.5 times greater than the charge diameter, whereas the SCJ in air is approximately 3.5–4 times greater than the charge diameter. Additionally, the DOP of the jet decreases at the optimal standoff height with an increase in the cone angle.

FE mesh density influence on blast loading analysis

To examine the influence of mesh density on the blast loads of anti-landmines (ALMs) and improvised explosive devices (IEDs) under an armored vehicle, models with different FE mesh densities were numerically analysed. The multi-material arbitrary Lagrangian-Eulerian (MM-ALE) algorithm was used to simulate under armored vehicle explosions. Explicit dynamic analysis was performed in LS-DYNA. Blast loading simulation was performed using the ConWep (conventional weapon) loading model, which is implemented in LS-DYNA. The material characteristics of high-strength steel were used to model the protective plates on the armored vehicle. Protective plates were modeled in a V-shape and as a deformable solid with the Johnson-Cook plasticity model. In this paper, the FE model with different mesh densities was numerically tested to analyse the influence of mesh density on the obtained results. For the purposes of the modeling, different types of finite elements were used for the FE models. The floor of the vehicle was modeled with 3D hexahedral eight-noded finite elements, and the protective plates were modeled with four-noded plate finite elements. The maximal value of plastic strain and the maximal value of the displacement of the central node on the protective plate was chosen as the parameters to compare the obtained results.

Reliability-based vulnerability analysis of bridge pier subjected to debris flow impact

In this paper, a finite element model of a highway bridge pier subjected to debris flow is established, which comprises a double-column pier, a gully channel, moving fluid and solid particles. By using the arbitrary Lagrangian-Eulerian (ALE) algorithm to calculate the fluid-solid coupling effect, the process of debris flow impacting on the pier is simulated. Based on the ‘two-phase flow’ theory, a simplified equation to calculate the impact force of debris flow containing both fluid and solid phases is proposed, and the variable parameters in the equation are determined through numerical simulation using the established FE model and the field-measured data. By comparing with the historical records of actual debris flows, the effectiveness of the numerical model and the proposed equation is verified. A reliability model of the pier subjected to debris flow is established, and the structural vulnerability is estimated by the MCS method. Using the site-observed data, the failure mode of a highway double-column pier subjected to impact of two-phase debris flow is studied. The critical velocities of debris flow causing the structure to have different modes of damage, and the critical impact height of debris flow on the pier suffering bending and shear failures are determined.

Study on explosion resistance process simulation and blast fracture failure of Ti[sbnd]6Al[sbnd]4V titanium alloy sheet

The application of high-strength and high-toughness titanium alloy in armour protection is increasing with its excellent properties. However, there is little research on titanium alloy in explosion protection, especially the dynamic response process under localised explosion load and finite element simulation of the explosion resistance process of titanium alloy sheet. In this paper, the deformation and fracture failure features of the 1.6 mm thick Ti6Al4V titanium alloy sheet during the blast loading process were studied by combining LS-DYNA finite element simulation and air explosion experiments. The error of the overpressure peak value of explosion shock wave between the value obtained by improved theoretical empirical formula calculation of cylindrical charge and the value obtained by numerical simulation is only 0.2%. By studying the influence of explosive shape and air domain mesh size on the overpressure value in the process of detonation wave propagation, the Structured Arbitrary Lagrangian-Eulerian (S-ALE) algorithm was selected for finite element simulation. When the air domain mesh size is 1 mm, the tensile failure criterion was introduced into the finite element simulation process. The results show that the numerical simulation results of the full-scale model and the test results were consistent. The destruction morphology of the target showed severe asymmetry. Under 50 g TNT blast load, the 1.6 mm thick Ti6Al4V titanium alloy target was damaged seriously, and the central area of the target was completely torn. The failure features were mainly petal-shaped warping tearing cracks and localised plastic deformation. The tensile stress is the main stress mode of the target failure. Therefore, dynamic tensile strength should be used as one of the selection criteria for explosion-resistant titanium alloy sheets. The target failure mode is dominated by adiabatic shear fracture.

G-UHPC slabs strengthened with high toughness and lightweight energy absorption materials under contact explosions

This study investigates the dynamic characteristics of geopolymer-based ultra-high performance concrete (G-UHPC) slabs strengthened with high toughness and lightweight energy absorption materials under the 1 kg TNT contact explosions. A total of four slabs were tested, including plain G-UHPC slab (G-UHPC-P), 20-layer basalt textile reinforced G-UHPC slab (G-UHPC-BFM), 20-layer steel wire mesh reinforced G-UHPC slab (G-UHPC-SWM) and 1.5 vol-% steel fibre reinforced G-UHPC slab with polyurethane coating (G-UHPC–SF–PU). The test results revealed that the steel wire mesh reinforcement was more effective in resisting contact explosions than the basalt textile reinforcement for G-UHPC. The polyurethane coating on the rear face of the slab exhibited its high tensile strength and deformability to absorb the blast-induced energy so as to enhance the anti-explosion performance of the slab, and additionally prevented the splash of slab fragments upon contact explosions to minimise secondary hazards. Based on the multi-material arbitrary Lagrangian-Eulerian (ALE) algorithm, local damage of G-UHPC-SWM and G-UHPC–SF–PU induced by contact explosions was reproduced using the explicit finite element software LS-DYNA. Fair agreement between the numerical and test results demonstrated that the numerical model could simulate the response of G-UHPC-SWM and G-UHPC–SF–PU with reasonable accuracy. Extensive numerical studies by varying polyurethane strain rate, coating thickness and the bonding between the polyurethane coating and the slab were further performed to analyse their effect on the maximum bulge depth of the polyurethane coating subjected to contact explosions.

Numerical study on load-shedding performance of a high-speed water-entry vehicle based on an ALE method

Aiming at the problem of load shedding in high-speed water entry of a vehicle, a composite structural buffer has been designed. Meanwhile, an accurate numerical model with the fluid-solid coupling is established to analyze the crushing process based on the arbitrary Lagrangian-Eulerian (ALE) algorithm and evaluate the effects of different schemes. The results show that the designed buffer can absorb the impact energy, leading to the damage and separation from the vehicle properly. The layered design of cushion foam changes the damage mode of the nose cap and causes it to be failure in advance. When the buffer is in contact with water, stress concentration occurs at the top of nose cap and preset groove. The groove effectively guides the destruction mode of the cap, such that the layered foam will not be too easy to be completely destroyed and the phenomenon of secondary cushion can occur. The velocity curve of the vehicle with the buffer changes more smoothly, the displacement is greater in the same time, and the load reduction rate of the layered foam scheme can reach 73.2% which is better than the single-layer foam scheme.

Design and optimization of multi-V hulls of light armoured vehicles under blast loads

To mitigate the blast loads of mines and improvised explosive devices (IEDs) under a vehicle and reduce the injury of occupants, three hull shapes have been designed according to the bottom structure of a light armoured vehicle: double-V hull (DVH), triple-V hull (TVH), and trapezoidal hull (TH). The multimaterial arbitrary Lagrangian-Eulerian (MM-ALE) algorithm was used to simulate vehicle bottom explosions. The simulation results show that DVH has the best load transfer path, rendering smaller occupant damage parameters with DVH installation and indicating that the best protection performance premised on meeting light weight requirements can be provided by DVH. Furthermore, multiobjective optimization of DVH has been carried out so that the protection performance can be further improved only by changing its dimension parameters. Compared with the performance of the original bottom structure of the vehicle, the optimized design of DVH could reduce the left and right lower tibia forces by 33.3% and 41.75%, respectively, and the mass decreased by 43.05%.

Dynamic simulation of sugarcane milling process based on Arbitrary Lagrangian–Eulerian algorithm

Understanding the process of the sugarcane milling is important for improving sugar extraction. The Arbitrary Lagrangian–Eulerian algorithm within LS-DYNA was successfully used for the first time to simulate the dynamic process of milling. The predictions of the numerical model were validated using experimental crushing data from a previous study and dynamic process of milling was examined in detail. The draining performance during milling needs to be carefully considered. It was found that the deformation of the sugarcane in the XY cross-section under loads consisted of two main phases; compression and expansion with reabsorption mostly occurring during the expansion phase. The feeding side of the nip is the main area for the draining of juice. A sensitivity analysis of parameters influencing load and pressure was conducted. This research method could be applicable to similar engineering problems where there is contact, collision, extrusion, large displacement, and large deformation.

Finite volume arbitrary Lagrangian-Eulerian schemes using dual meshes for ocean wave applications

For reasons of efficiency and accuracy, water wave propagation is often simulated with potential or inviscid models rather than Navier-Stokes solvers, but for wave-induced flows, such as wave-structure interaction, viscous effects are important under certain conditions. Alternatively, general purpose Navier-Stokes (CFD) models can have limitations when applied to such free-surface problems when dealing with large amplitude waves, run-up, or propagation over long distances. Here we present an Arbitrary Lagrangian-Eulerian (ALE) algorithm with special care to the time-stepping and boundary conditions used for the free-surfaces, integrated into Code_Saturne, and we test its capabilities for modeling a variety of water wave generation and propagation benchmarks, and finally consider interaction with a vertical cylinder. Two variants of the mesh displacement computation are proposed and tested against the discrete Geometric Conservation Law (GCL). The more robust variant, for highly curved or sawtoothed free-surfaces, uses a Compatible Discrete Operator scheme on the dual mesh for solving the mesh displacement, which makes the algorithm valid for any polyhedral mesh. Results for standard wave propagation benchmarks for both variants show that, when care is taken to avoid grids with excessive numerical dissipation, this approach is effective at reproducing wave profiles as well as forces on bodies.

Experimental and Numerical Study of the Hydroelastic Response of a River-Sea-Going Container Ship

The hydroelastic behaviour of a river-sea-going ship hull is analysed experimentally and numerically. A segmented ship model connected by a steel backbone is tested in regular waves, and its high-frequency vibrations such as springing and whipping responses are identified. The hydroelastic response of the ship is numerically calculated using a hydroelastic time domain method based on strip theory, which is extended to include an improved model of the slamming load. The slamming forces in the bow section are determined using the Modified Longvinovich Model (MLM) instead of the Von Karman model. The vertical motions and wave-induced loads are calculated and compared with the experimental results. The response amplitude operators of the vertical loads and the high-order harmonics are analysed under different speeds, showing good agreement with the experiments. The slamming loads on the bow section of a river-to-sea ship are predicted utilizing the MLM model and compared with the Arbitrary Lagrangian Eulerian algorithm by LS-DYNA and with the measured results.

An efficient numerical scheme for the thermo-hydraulic simulations of thermal grids

Renewable and smart energy systems require district heating and cooling grids able to operate with variable flow rates, to manage different supply temperatures, and to support distributed energy production involving bidirectional flows. Due to these requirements, accurate and effective thermo-hydraulic models are essential to correctly simulate the flow rates, the head drops and the temperature transients for supporting the design, management and optimisation of thermal distribution networks. In this article, an efficient numerical scheme for the simulation of thermal grids based on a thermo-hydraulic model with a quasi-dynamic approach is proposed. Global gradient algorithm of Todini together with a uniformly distributed representation of demand along the pipes is used for steady-state hydraulic simulations of the networks modelled according to the graph theory. The temperature distribution is computed by solving a first order hyperbolic PDE which accounts for heat advection in the flux term and heat dissipation in an algebraic source term. A very efficient second-order Eulerian-Lagrangian finite volume scheme is employed on a staggered mesh, which evolves in time the temperature distribution starting from the velocity distribution given by the hydraulic solver. The usage of a Eulerian-Lagrangian algorithm for the discretisation of the convective terms, allows the proposed model to be unconditionally stable for every time step size. As such, the main advantages of the proposed model are the flexibility due to the admissibility of any spatial-temporal discretisation, the second order accuracy provided by both the demand schematisation and the thermo-hydraulic solver, and the computational efficiency guaranteed by the decoupled modelling approach. The resulting algorithm is extensively validated on four tests consisting of thermal grids of various complexity that have been carefully designed in order to capture different features and behaviours of the model. The accuracy of the results in terms of velocity, pressure and temperature is tested by separately checking the symmetry, the advection term, the heat loss component and, finally, by simulating a complex grid configuration with multiple heat sources. The article aims to present a proof-of-concept concerning a breakthrough numerical scheme for the efficient thermo-hydraulic simulation of pipeline networks, which proves to be suitably implemented in the modelling of district heating and cooling networks.

Atomization and spray characteristics around an ERBS using various operational models and conditions: numerical investigation

The impetus of the current paper is to conduct numerical evaluations about the fundamental behaviors of the flow in an electrostatic rotary bell sprayer (ERBS) during the formation of the droplets and depositing on a target. The effect of operational parameters like bell rotational speed, shaping air and paint flow rate, electrical charge values and droplet distributions are considered precisely. Here, an Eulerian-Lagrangian algorithm that contains a model for airflow field, spray dynamics, electric charge field, droplet trajectory tracking and wall film dynamics has been extended by using the OpenFOAM package. The fluid dynamics is computed by using a large eddy simulation (LES) turbulence model. The mechanism of atomization is facilitated by the action of the centrifugal force that conducted the disintegrated droplets to the cup edge. Following that, the high-velocity droplets affected by the shaping airflow and electric force are transported towards the workpiece. The effect of the bell rotational speed in comparison with other parameters is dominant. The measured size of the droplets is controlled by increasing the bell rotational speed or decreasing the paint flow rate, in this case, promoting a reduction in droplet size. The droplet size near the bell cup was increased noticeably, however, their radius becomes more uniform at a longer lateral distance. Investigation of the various breakup models is one of the main goals of this work to predict the droplet size more precisely. The Reitz-KHRT, Reitz-Diwakar, Pilch-Erdman and the newly modified TAB model are examined in order to predict the breakup process in the ERBS. As the paint droplets are a viscous fluid a modification of the Taylor Analogy Breakup (TAB) approach taking non-linear influences for large viscosity into account is recommended. The use of the breakup models creates a smaller droplet size and this means they are more sensitive to recirculation regions flow pattern. The implemented wall film function was able to predict the transport in the boundary layer over the target. The numerical results describe exact values for the size, distribution, velocity and trajectory of the particles in ERBS, and these results are important for coating industries, in order to optimize their working conditions.

Numerical analysis of hydroplaning behaviour by using a tire–water-film–runway model

ABSTRACT Studying the hydroplaning behaviour is crucial for enhancing the safety of aviation during the landing stage. Due to the special nature of the aviation field, such as high aircraft velocity, wheel load and operating frequency, accurate numerical simulation is considered an effective method for investigating the tire hydroplaning behaviour. In this study, a fluid–solid coupling model was established using the coupled Eulerian–Lagrangian algorithm to analyze the hydroplaning behaviour. To reveal the influences of factors such as the runway texture, slip ratio, velocity and water-film thickness on tire hydroplaning, some parameters such as the skid number, water distribution, and tire inflation pressure were extracted. Moreover, the real pavement textures of stone mastic asphalt, an open-graded friction course, and asphalt concrete were determined to construct a real runway model and water-film thicknesses of 3, 7, and 10 mm were selected to study their effects on aircraft hydroplaning. The numerical simulation results were verified by calculating the braking distance and conducting trailer test, and the results prove that the numerical model can be applied for the multifactor analysis of tire hydroplaning behaviour.