Free Surface Velocity Research Articles

Optimization Design of Submerged-Entry-Nozzle Structure Using NSGA-II Genetic Algorithm in Ultra-Large Beam-Blank Continuous-Casting Molds.

To achieve uniform cooling and effective homogenization control in ultra-large beam-blank molds necessitates the optimization of submerged-entry-nozzle (SEN) structures. This study employed computational fluid dynamic (CFD) modeling to investigate the impact of two-port and three-port SEN configurations on fluid flow characteristics, free-surface velocities, temperature fields, and solidification behaviors. Subsequently, integrating numerical simulations with the non-dominated sorting genetic algorithm II (NSGA-II) and metallurgical quality-control expertise facilitated the multi-objective optimization of a three-port SEN structure suitable for beam-blank molds. The optimized parameters enabled the three-port SEN to deliver molten steel to the meniscus at an appropriate velocity while mitigating harmful effects such as SEN port backflow, excessive surface temperature differences, and shell thickness reduction due to fluid flow. The results indicated that the three-port SEN enhanced the molten-steel flow pattern and mitigated localized shell thinning compared with the two-port SEN. Additionally, the optimized design (op2) of the three-port SEN exhibited reduced boundary layer separation and superior fluid dynamics performance over the initial three-port SEN configuration.

Fundamental influence of irreversible stress–strain properties in solids on the validity of the ramp loading method

The widely used quasi-isentropic ramp loading technique relies heavily on back-calculation methods that convert the measured free-surface velocity profiles to the stress–density states inside the compressed sample. Existing back-calculation methods are based on one-dimensional isentropic hydrodynamic equations, which assume a well-defined functional relationship P(ρ) between the longitudinal stress and density throughout the entire flow field. However, this kind of idealized stress–density relation does not hold in general, because of the complexities introduced by structural phase transitions and/or elastic–plastic response. How and to what extent these standard back-calculation methods may be affected by such inherent complexities is still an unsettled question. Here, we present a close examination using large-scale molecular dynamics (MD) simulations that include the detailed physics of the irreversibly compressed solid samples. We back-calculate the stress–density relation from the MD-simulated rear surface velocity profiles and compare it directly against the stress–density trajectories measured from the MD simulation itself. Deviations exist in the cases studied here, and these turn out to be related to the irreversibility between compression and release. Rarefaction and compression waves are observed to propagate with different sound velocities in some parts of the flow field, violating the basic assumption of isentropic hydrodynamic models and thus leading to systematic back-calculation errors. In particular, the step-like feature of the P(ρ) curve corresponding to phase transition may be completely missed owing to these errors. This kind of mismatch between inherent properties of matter and the basic assumptions of isentropic hydrodynamics has a fundamental influence on how the ramp loading method can be applied.

Effects of microstructures on dynamic deformation and spallation damage of high-entropy alloy Al0.3CoCrFeNi under plate impact loading

Plate impact experiments are conducted on high-entropy alloy Al0.3CoCrFeNi with different microstructures to investigate the effects of grain size, precipitates and heterogeneous structure on dynamic response. Free surface velocity histories are obtained. All initial and postmortem samples are characterized with transmission electron microscopy and electron backscatter diffraction. Nanoscale L12 precipitates result in a considerable increase in dynamic yield stress. Spall strength is higher for the heterogeneous structure, the large grain size (200 μm) and small grain size (63 μm) with L12 precipitates by ∼4%, 19% and 10% than for the small grain size (77 μm) without precipitates. After shock compression, dislocation slip, stacking faults, the Lomer-Cottrell locks and nanotwins are found in the samples without the L12 precipitates. L12 precipitates increase the energy barrier and inhibit deformation twinning. Spall damage is ductile in Al0.3CoCrFeNi. For the homogeneous structures, intragranular voids are predominant. Voids are preferentially distributed in the fine-grain domains or at the fine-grain–coarse-grain domain boundaries of the heterogeneous structure.

Kinematics of nonlinear waves over variable bathymetry. Part I: Numerical modelling, verification and validation

Fluid particle kinematics due to wave motion (i.e. orbital velocities and accelerations) at and beneath the free surface is involved in many coastal and ocean engineering applications, e.g. estimation of wave-induced forces on structures, sediment transport, etc. This work presents the formulations of these kinematics fields within a fully nonlinear potential flow (FNPF) approach. In this model, the velocity potential is approximated with a high-order polynomial expansion over the water column using an orthogonal basis of Chebyshev polynomials of the first kind. Using the same basis, original analytical expressions of the components of velocity and acceleration are derived in this work. The estimation of particle accelerations in the course of the simulation involves the time derivatives of the decomposition coefficients, which are computed with a high-order backward finite-difference scheme in time. The capability of the numerical model in computing the particle kinematics is first validated for regular nonlinear waves propagating over a flat bottom. The model is shown to be able to predict both the velocity and acceleration of highly nonlinear and nearly breaking waves with negligible error compared to the corresponding stream function wave solution. Then, for regular waves propagating over an uneven bottom (bar-type bottom profile), the simulated results are confronted with existing experimental data, and very good agreement is achieved up to the sixth-order harmonics for free surface elevation, velocity and acceleration.

Dynamic response of equiatomic and non-equiatomic CrMnFeCoNi high-entropy alloys under plate impact

A typical Fe-rich non-equiatomic CrMnFeCoNi high-entropy alloy (HEA), Cr10Mn10Fe60Co10Ni10, and the equiatomic Cr20Mn20Fe20Co20Ni20 HEA, are investigated via plate impact experiments along with in situ free surface velocity measurements. Both the initial and postmortem samples are characterized with transmission electron microscopy and electron backscatter diffraction. These two HEAs contain a single face-centered cubic phase, are texture-free, and have similar grain sizes. Dynamic yield stress and spall strength of the non-equiatomic CrMnFeCoNi are lower by ∼55 % and 15 % than those of its equiatomic counterpart, respectively. After shock compression, dislocation slips, stacking faults, Lomer-Cottrell locks and nanotwins are found in the postmortem samples of both HEAs. Due to the reduced stacking fault energy in the non-equiatomic HEA, more deformation twins and newly formed hexagonal close-packed phases are found. For spallation, intergranular voids are larger in size but smaller in quantity than intragranular voids for both HEAs. Both intragranular or intergranular voids show strong dependence on grain boundary misorientation.

Effect of grain size on spall fracture of CrCoNi medium-entropy alloy under Taylor-wave loading

The effect of grain size on spall properties of medium-entropy alloy CrCoNi under Taylor-wave loading is investigated. Three different grain sizes, 300 μm, 20 μm, and 3 μm, are explored. The free surface velocity histories are measured to obtain such quantities as dynamic yield strength and spall strength. With decreasing grain size, there is a slight decrease in spall strength, but a significant increase in damage rate. The shock-recovered samples are characterized with scanning electron microscopy and electron backscatter diffraction. In coarse-grained samples, voids tend to nucleate within grain interiors, while in fine-grained samples, voids nucleate preferentially at grain boundaries (GBs). Molecular dynamics simulations show that the nucleation of intergranular or intragranular voids is dominated by GB–slip and slip–slip intersections, respectively. The higher GB density results in more extensive GB–slip intersections, consistent with the experimental results.

Analytical solution to a coupled system including tuned liquid damper and single degree of freedom under free vibration with modal decomposition method

This research focuses on employing a linear analytical approach to transform free surface waves and velocities into mode coordinates, with the aim of investigating the free vibration behavior of a coupled system consisting of a Single Degree of Freedom and a sloshing tank. Through a series of manipulations and simplifications of the coupled equations, a fourth-order ordinary differential equation is derived to showcase the overall response of the system, highlighting the contribution of each odd mode. Key concepts explored include system stability, mode-specific natural periods, establishment of initial boundary conditions, and formulation of the complete system response. The analytical method applied to study Tuned Liquid Dampers, a type of elevated sloshing tank, reveals that in higher modes, the lower frequency aligns with the structural natural frequency, while the higher frequency is approximately n times the structural natural frequency (where n is the odd mode number). This approach also elucidates why the system's response does not exhibit a higher-frequency component in higher modes. The study further investigates concepts such as employing an initial perturbation to excite higher frequencies and the potential for approximating the system through the first mode. Additionally, a numerical model was developed using variable separation and modal decomposition methods to complement and validate the analytical approach. Finally, further verification of the model was performed using the Preismann scheme applied to the relevant equations and the central upwind applied to nonlinear equations.

Integrated monitoring method of flood free surface and surface velocity in a laboratory compound channel

River flooding can pose a significant threat to people's lives and properties on the floodplain. Due to the difficulty and potential danger of monitoring field river floods, laboratory experiments have become the main and key method for exploring flood propagation and evaluating potential flood risks. However, the complex three-dimensional flow state of floods in the compound channel makes current measurement techniques inadequate for meeting monitoring requirements. To this end, a new technique is developed in this study that can simultaneously monitor the flood free surface and the surface velocity in the laboratory compound channel. The developed measurement technique combines stereoscopy and the particle tracking velocimetry (PTV) method through the pixel coordinate fitting method, so that the coordinates of the tracer particles can be reconstructed in the three-dimensional state. This method can not only increase the basic data in the free surface construction but can also capture the complex three-dimensional flood flow behavior. The proposed technology was applied to measure the free surface of flood propagation in a laboratory compound channel. Water level, flow velocity, wave velocity, and wave height were simultaneously measured. The measurement accuracy was verified using wave probes, spatial planes, and fringe projection techniques. The results indicate that the water level measurement error is approximately 1.6 mm, and the flow velocity measurement error is around 3 %. The developed measurement system is simpler than previous methods based on light reflection or absorption. Most importantly, it can simultaneously measure both the flood free surface and surface velocity by only sowing tracer particles on the water surface. The current measurement technology offers a new tool for studying flood propagation in a laboratory compound channel.

Numerical simulation of surf-zone turbulence beneath plunging breakers using Reynolds stress models

This study applied Reynolds transport models (RSMs) to simulate turbulence under waves and plunging breakers. A simplified analysis that disregarded the diffusion effect on turbulence revealed a two-way energy transfer between waves and turbulence. Moreover, the Stokes drift was a crucial factor for enhancing the turbulence intensity, and the growth rate of the turbulence was directly proportional to the square of the wave steepness. Regarding plunging breakers, we observed that RSMs and the stabilised k−ω model yielded similar performances in simulating the free-surface displacement and velocity. However, in terms of turbulence intensity, RSMs demonstrated better accuracy. The differences in the pressure rate of strain tensor within the model formulae insignificantly affected the turbulence intensity beneath the plunging breakers.

RECURSIVE NEURAL NETWORK AS A HIGH-SPEED PLATE COLLISION EMULATOR

Based on a database obtained using a high-speed plate impact model that relates impact parameters and material model parameters to the free surface velocity profile, the study compares the learning process and accuracy of a feedforward artificial neural network and a recursive neural network. A recursive neural network provides a significantly greater accuracy and requires less training time. Using a recursive neural network as a fast model emulator and Bayesian calibration can make it possible to solve the inverse problem of determining the substance model parameters from the free surface velocity profile with a greater accuracy.

Identification of spatially distributed rheological parameters for viscoplastic gravity currents

The rheology of a fluid is often difficult to measure in situ and in real time. This work investigates whether it is possible to recover rheological information from direct field observations. We present a closed-form analytical solution for inverse problem of identification of the mobility coefficient in gravity-driven fluid flowed down an inclined plane. The lubrication approximation is used to model the three-dimensional thin film of fluid and the governing equation is solved numerically by the explicit finite difference method to calculate the fluid thickness. We show in this study that using very straightforward measurements of fluid thickness at only a few points and only two successive instants, the mobility coefficient of fluid flow can be estimated accurately. Then as an important application in Bingham fluids we show that the knowledge of the mobility coefficient together with velocity measurement at only one point and instant enable us to estimate temperature-dependent viscosity and yield stress of the Bingham fluid. Unlike other methods, the proposed method allows the local identification of the rheology which is particularly useful when the rheological parameters are functions of the local temperature and/or composition. The proposed inverse analysis is a non-iterative approach with negligible computational cost since our analysis revealed closed form formulae relating the rheological parameters to the local flow depth, its derivatives, and the local free surface velocity.

Using double pulse laser ablation in air to enhance the strength of laser-driven shocks

In the process of multi-pulse laser ablation, inter-pulse delay time, Δt, is known to be an important parameter for maximizing ablation efficiency as well as impulse imparted to the target. In this work, using photon Doppler velocimetry, we show that for single pairs of colinear pulses (1064 nm, 8 ns, ∼ 60 J cm-2 per pulse) in air, the peak free surface velocity of the back surface of an aluminum target (125 µm thick) is increased, by a factor of nearly 3, when Δt = 10 microseconds, compared with both pulses arriving simultaneously (Δt = 0). Fast imaging of the ablation process suggests this enhancement is due to rarefaction of the contiguous air in the passage of the leading shock produced by ablation, which then in turn allows a larger fraction of the energy of the second pulse to reach the target surface. This interpretation is strengthened by additional experiments in which the two pulses do not overlap on the target surface, but the shock strength is nevertheless enhanced. Given a fixed energy budget this work suggests a prescription for maximizing laser-driven shock strength by judicious choice of inter-pulse delay.

Spallation damage of tungsten heavy alloy under shock loading

In this study, plate-impact experiments are conducted using tungsten heavy alloy (WHA) to obtain the free-surface velocity profiles under shock stress of 6–23 GPa. By analyzing the velocity wave profile, it is demonstrated that the spall strength is weakly dependent on the peak stress. The microstructure of the recovered WHA is well characterized and it’s observed that intergranular fracture and cleavage are the primary fracture mechanisms. Deformation twins are sparsely distributed near the cleavage crack. The existence of twin boundary not only affects crack propagation but also regulates the crack path and reinitiates the cleavage propagation direction on the twin boundary. The macroscopic cleavage facet planes are detected to be {100}, {110} and {111} at all shock stress.

Impact Velocity-Dependent Patterns and Mechanisms of Spalling Behavior in Single Crystal Nickel

To reveal the impact velocity (U<sub>p</sub>) effect on the spalling and fracture behavior of single crystal nickel, a non-equilibrium molecular dynamics approach is performed to investigate the free surface velocity curve, radial distribution function, atomic crystal structures, dislocations, and void evolution process. The results show that the critical U<sub>p</sub> for spalling behavior in single crystal nickel is 1.5 km/s, the spallation mechanism is classical spallation damage (U<sub>p</sub>≤1.5 km/s) and micro-spallation damage (U<sub>p</sub>＞1.5 km/s). The number and distribution area, and stress distribution area under micro-spallation damage much higher than those under classical spallation damage. Analyzed the influence of impact velocity on the classical spalling damage behavior (U<sub>p</sub> ≤ 1.5 km/s) and obtained the corresponding spalling strength, an accident of spalling strength occurs at the U<sub>p</sub> of 1.3 km/s. The spalling strength of single crystal nickel is influenced by the combined effects of stacking faults, phase transformation, and dislocation mechanisms. The nucleation and emission of dislocations increase lead to a decrease in the spalling strength. When U<sub>p</sub> <1.3 km/s, spalling damage is primarily influenced by stacking faults. When U<sub>p</sub> =1.3 km/s, spalling strength is mainly affected by the competition between stacking faults and phase transformation. When U<sub>p</sub> >1.3 km/s, spalling strength is predominantly influenced by the body-centered cubic (BCC) phase transformation mechanism (transformation path: FCC → BCT → BCC). This study reveals the impact velocitydependent patterns, mechanisms, and effects on spalling damage and fracture, providing a theoretical basis for the protective application of nickel-based materials under extreme impact conditions.

Spall strength of additively repaired 304L stainless steel

Additive manufacturing has the potential to repair damaged parts, but the performance of additive materials under high strain rate loading is still uncertain—especially with the added complexity of an interface with an existing wrought material. In this work, 304L stainless steel samples were intentionally damaged and then repaired with wire-fed laser additive manufacturing. The samples were subjected to shock loading to generate incipient spall. Velocimetry and post-mortem metallography results show that when the additive repair process parameters are optimized to reduce porosity and match the equation of state of the original material, the influence of the repair region on the shock propagation is negligible. The free-surface velocity profile and internal damage morphology of the repaired sample are shown to be practically identical to the pristine material.

Anisotropic dynamic response of AlSi10Mg fabricated via laser powder bed fusion under plate impact

The effects of structural anisotropy on dynamic yield and spallation damage of an AlSi10Mg alloy manufactured via laser powder bed fusion are investigated via plate impact experiments along the build direction (BD) and the transverse direction (TD). Free surface velocity histories are measured to deduce its dynamic mechanical properties. The as-received and postmortem samples are characterized with scanning electron microscopy, metallograpic microscopy, electron backscatter diffraction and synchrotron X-ray computed tomography. The Hugoniot elastic limit for loading along TD is about 40% higher than that along BD, given the initial 〈100〉∥BD texture. For spallation, voids prefer to nucleate at melt pool boundaries. Spall strength for loading along TD is about 18% higher than that along BD, as a result of higher critical stress for void nucleation and less nucleation sites due to the melt pool morphology. The damage evolution features are also correlated well with melt pool morphology and grain morphology within the pool interior, demonstrating the “ductile” interpool and “brittle” intrapool fracture modes for loading along BD and TD, respectively.

Examination of machine learning method for identification of material model parameters

In this work, we compare two methods of using artificial neural network (ANN) to determine the optimal parameters of material model by results of high-speed plate impact experiments. The first ANN is trained to determine the free surface velocity history based on the impact parameters and material model parameters; this ANN is used as a fast emulator of model to speed-up the statistical Bayesian calibration of the model parameters. The second ANN directly determines the material model parameters based on the impact parameters and the free surface velocity history, because this ANN is trained by inverse data set; this approach for inverse problem is proposed for the first time and can be more preferable for fast-track expert systems in engineering applications. Both approaches are successfully used to determine the optimal parameters of material model in the case of impact of copper and aluminum plates at different temperatures and impact velocities with experimental data from the literature. A simple relaxation plasticity model with a constant relaxation time is used in the present research as an example; more accurate coincidence with the experimental data and wider applicability of the ANN-based approach can be expected for a more realistic plasticity model.

Numerical Investigation of Critical Hydraulic Parameters Using FLOW-3D: A Case Study of Taunsa Barrage, Pakistan

Hydraulic structures, such as barrages, play an important role in the sustainable development of several regions worldwide. The aim of this novel study is to identify the critical hydraulic parameters (CHPs) of Taunsa Barrage, built on the Indus River. These CHPs, including free surface profiles, flow depths, Froude number, velocity profiles, energy dissipation and turbulence kinetic energy, were investigated using simulation via FLOW-3D numerical models. Incompressible Reynolds-averaged Navier–Stokes (RANS) equations on each computational cell were solved using the numerical methods available in FLOW-3D. The simulation results indicated that the locations of hydraulic jumps (HJs) were lower than that were reported in the previous one-dimensional study. Similarly, the distances of the HJs from the downstream toe of the glacis were reached at 2.97 m and 6 m at 129.10 m and 130.30 m tailwater levels, respectively, which deviated from the previous studies. In higher tailwater, the sequent depth ratio also deviated from the previous data. The maximum turbulent kinetic energies were observed in the developing regions of HJs, which were found to be decreased as the distance from the HJ was increased. The results of this research will be highly useful for engineers working in the field of design of hydraulic structures.

Development of the global tsunami forecasting system considering the dynamic interaction of tide-tsunami around the Korean Peninsula

Tsunamis are extreme natural events that pose a significant threat to coastal communities, making a comprehensive understanding of tsunami propagation mechanisms necessary for forecasting and evacuation purposes. While previous forecasting models have successfully examined several factors influencing tsunami propagation, the impact of the dynamic interaction between tides and tsunamis has yet to be investigated thoroughly. The Yellow Sea is characterized by high tidal elevations and strong tidal currents, which can accelerate the tsunami impacts on the Korean coasts. This study developed a regional tide-tsunami interaction model based on the shallow water equation model to quantitatively investigate the dynamic tide-tsunami interaction and evaluate its influence on tsunami propagation and amplification mechanism. High-resolution numerical tests were conducted for two worst-case tsunami scenarios that occurred in the Korean Peninsula, including the 2010 Chilean tsunami (far-field forecasting) and the 2011 Tohoku tsunami (near-field forecasting). The performance of the numerical model was validated utilizing the observational tide data collected along the Korean coasts. The numerical model effectively reproduces the horizontal distribution of instantaneous free surface displacement and velocity. The results reveal that the dynamic tide-tsunami interaction induced by these tsunamis generally reduces the water level and velocity in the ocean while amplifying these quantities as the tsunamis approach the coastal regions. However, due to the complex and arbitrary features of the topography, the impact of the dynamic tide and tsunami interaction on water elevation and velocity is inconsistent even compared with measurements from the adjacent tidal gauges, which suggests that the dynamic interaction can play an opposite role during the propagation and amplification process. Furthermore, the different arrival times of tsunamis along the Korean coasts are dominated by the corresponding phase of the local tidal currents that develop in each region.

Correlation between grain size and dynamic response of NiTi alloy during intense shock-induced multi-spallation

This work committed to performing non-equilibrium molecular dynamics simulations to explore the influence of grain size on multi-spall performance of nanocrystalline nickel-titanium (NiTi) alloy. By comparing the calculated Hugoniot relationship with present experimental results, the Finnis-Sinclair (FS) type potential used in this work was verified to be suited for reproducing the shock behavior of NiTi alloy at high strain rate. During shock wave evolution, a single plastic wave was clearly observed in the sample with grain size of 5 nm, while there was a more pronounced elastic-plastic double wave structure at larger grain size. According to the free surface velocity history, the predicted spall strength exhibited a decreasing tendency and subsequently increased when the grain size decreased from 50 to 5 nm, indicative of a critical grain size (10 nm). Correspondingly, there were multiple spall planes appearing in the sample, the grain size of which was not smaller than the critical one. Contrarily, a single spall plane was observed at 5 nm. By counting the void distribution statistic, we found that as the grain size increased, the void-nucleation behavior changed from the intergranular to intergranular/transgranular coexisting pattern. In consequence, more nucleation sites were provided to promote an increase in the number of voids. Interestingly, for intergranular, there were much more voids involved in spallation at smaller grain size, which was attributed to grain boundary effect. The results demonstrated that void evolutions rarely occurred at the grain boundaries parallel to the loading direction. Moreover, when the grain size was larger than 5 nm, the B19 phases were found to be produced around those potential void-nucleation sites. After void nucleation, these B19 phases decreased till disappearance, accompanied by the proliferation of a large number of [100] dislocations. Such dislocations accumulated in the region without voids could block the void growth in this region, which was expected to be the reason for the formation of multiple spall planes. On the contrary, the absence of dislocations at 5 nm was inclined to the fact that the space for dislocation emission and aggregation was preoccupied by nucleated voids.