We propose a simple yet effective method for estimating the minimum internal pressure, denoted as Pb, min, within an oscillating bubble at its maximum size. In controlled explosion-generated bubble experiments, Pb, min is estimated at approximately 3 000 Pa, with the partial pressure of non-condensable gas being below 1 000 Pa. Numerical simulations using accurate initial parameters derived from Pb, min accurately reproduce the bubble behaviors for the first two cycles, particularly the significant energy damping in nonspherical bubbles. For spark-generated cavitation bubbles, increasing the discharge energy from 10 to 62.5 J leads to a reduction in Pb, min from approximately 10 000 to 4 000 Pa. The analysis further shows that low Pb, min and high mv/m trigger a violent collapse, leading to a pronounced increase in acoustic radiation, which in turn suppresses the bubble rebound. Within this regime, the radiation is acutely sensitive to variations in both parameters.

This study experimentally and numerically investigates the dynamics of a high-speed liquid jet generated from the interaction of two tandem cavitation bubbles, termed bubble 1 and bubble 2, depending on their generation sequence. Although the overall collapse pattern and jet orientation are well documented, the underlying mechanisms for supersonic jet acceleration, tip fragmentation and subsequent penetration remain to be elucidated. In our experiments, two near-identical, highly energised cavitation bubbles were generated using an underwater electric discharge method, and their transient interactions were captured using a high-speed camera. We identify three distinct jet regimes that emerge from the tip of bubble 2: conical, umbrella-shaped and spraying jets, characterised by variations in the initial bubble-bubble distance (denoted as $\gamma$ ) and the initiation time difference (denoted as $\theta$ ). Our numerical simulations using both volume of fluid and boundary integral methods reproduce the experimental observations quite well and explain the mechanism of jet acceleration. We show that the transition between the regimes is governed by the spatio-temporal characteristics of the pressure wave induced by the collapse of bubble 1, which impacts the high-curvature tip of bubble 2. Specifically, a conical jet forms when the pressure wave impacts the bubble tip prior to its contraction, while an umbrella-shaped jet develops when this impact occurs after the contraction. The spraying jets result from the breakup of the bubble tip, exhibiting mist-like and needle-like morphologies with velocities ranging from 10 to over 1200 m s-1. Remarkably, we observe that the penetration distance of spraying jets exceeds ten times the maximum bubble radius, making them ideal for long-range, controlled fluid delivery. Finally, phase diagrams for jet velocity and penetration distance in the $\gamma -\theta$ parameter space are established to provide a practical reference for biomedical applications, such as needle-free injection and micro-pumping.

This paper investigates the interaction dynamics and propulsion mechanism of a cavitation bubble and a projectile with a coaxial concave tail employing experimental, numerical, and theoretical approaches. The bubble undergoes near-piston-like pulsations in the concave, which changes the interaction markedly relative to a solid projectile. For the same input energy, the concave-equipped projectile achieves maximum velocities exceeding five times those of its solid counterpart. A theoretical model integrating bubble pulsation dynamics and projectile motion was developed to elucidate the propulsion enhancement mechanism. Theoretical analysis confirms that the concave prolongs expansion and slows the decay of internal pressure, yielding a stronger and more sustained propulsive force. Furthermore, the influences of key governing parameters including equivalent maximum bubble radius Rm, concave length ratio θ, and bubble initiation location σ on propulsion characteristics were systematically investigated. Scaling laws correlating maximum projectile velocity with these governing parameters were derived and validated. Our findings establish the bubble initiation location σ as the key determinant of propulsive efficiency. Control over σ provides a practical means to regulate projectile velocity, opening new possibilities for manipulating bubble-propelled systems.

Combining experimental and numerical methods, we investigate the dynamics of a cavitation bubble between two parallel cylinders. The results reveal that the bubble motion is highly dependent on the distance parameter gamma, cylinder size ratio lambda and deviation distance eta [gamma = d/R-max, lambda = R-c/R-max, eta = (gamma(1) - gamma(2))/2, d is the vertical distance from the bubble's initial center to the cylinder walls, R-c is the radius of cylinder, R-max is the maximum radius of the bubble]. Experiments are conducted using a high-speed camera to capture the morphology of a transient bubble with an electric discharge method. A three-dimensional model is established based on the boundary integral method. We employ a weighted moving least squares method, a density potential method, and an edge swapping method to maintain the mesh regularity. When the bubble is located in the middle between the two cylinders, three collapse patterns are identified as splitting, counter jet, and spherical collapse, indicated by the magnitudes of three distinct velocities. A phase diagram of the symmetric bubble collapse patterns in the lambda-gamma range is obtained. If the bubble deviates from the middle point of the two cylinders, two collapse patterns are observed, i.e., splitting and directed jetting. Finally, larger eta enhances the Kelvin impulse and drives centroid migration toward the nearer cylinder. The Kelvin impulse undergoes rapid negative growth, a plateau phase, and a second phase of rapid negative growth.

This study examines the impact of hydrostatic pressure on the dynamics of underwater explosion bubbles near a steel plate through numerical and experimental studies. We conduct underwater explosion experiments in a pressure tank, altering the air pressure within the tank using a pressure pump to change the hydrostatic pressure around the bubbles. The interaction between the bubbles and the plate is recorded with a highspeed camera, and we extract and analyze the jet velocity, bubble radius, and plate displacement as functions of hydrostatic pressure. Building on this, we design a numerical framework that encompasses hydrostatic pressures varying from 0.2 MPa to 20 MPa and dimensionless bubble-plate standoff parameters gamma from 0.6 to 2.5 for a more thorough investigation on the bubble-plate interaction. We find that both the maximum jet velocity and the maximum jet volume exhibit scaling relationships with hydrostatic pressure p(infinity) when p(infinity) > 1 MPa. Additionally, the dimensionless maximum jet volume shows a non-monotonic relationship with gamma, depending on the degree of bubble-plate interaction at the moment of jet impact. Across a certain span, the maximum plate displacement also follows a scaling relationship with p(infinity), where the exponent differs according to gamma. This work is intended to offer a foundation for the study of underwater explosion bubble dynamics and fluid-structure interaction characteristics under high hydrostatic pressure or deep water environments.

The supercritical carbon dioxide (sCO2) cooled Lithium–Lead (LiPb) dual function blanket is an advanced blanket concept design proposed by Chinese Fusion Engineering and Test Reactor (CFETR), which has the characteristics of high inherent safety and high thermoelectric conversion efficiency. In order to study the operational safety characteristics of the fusion reactor blanket Auxiliary Cooling System (ACS) and ensure the safe and stable operation of the system, this paper establishes a dynamic simulation model of key equipment for the fusion reactor blanket ACS, and develops a system analysis program. Based on the self-programming system program, this paper analyzes the thermal safety effects of various heating powers and flow rates on the sCO2/LiPb dual function blanket, and conducts research on the operational safety characteristics of the system under expected shutdown transient events and varying degrees of Unprotected Loss of Heat Sink (ULOHS) accidents. The results indicate that sCO2 and LiPb can effectively remove plasma radiation heat flux and nuclear thermal power, ensuring the thermal safety of the blanket. When the LiPb mass flow rate is 60

Cavitation inside the regulating valve significantly affects the control accuracy, causing vibration, noise, and structural failure. The periodic distribution characteristics of cavitation flow fields were investigated through visualization experiments, numerical simulations, and theoretical analysis. The coupling relationship between the periodic evolution of cavitation and re-entrant jet was analyzed, and a quantitative method to evaluate cavitation flow instability was also proposed. The findings indicate a strong correlation between the re-entrant jet and the periodic evolution of the cavitation flow field as well as flow instability. Under the influence of re-entrant jet, cavitation was divided into attached cavitation and free cavitation. Furthermore, the spatiotemporal distribution characteristics of both attached and free cavitation change periodically, accompanied by four distinct processes: inception, growth, shedding, and collapse. The collapse of cavitation generates re-entrant jet at the trailing end of the cavitation collapse region. The re-entrant jet ascends and interacts with the cavitation structure, accelerating the contraction of attached cavitation, the shedding and collapse of free cavitation, thereby promoting the transition of cavitation to the next cycle. The re-entrant jet interacts with the cavitation structure at t0+3T/7 and t0+5T/7, respectively, destabilizing the cavitation flow in the regulating valve and leading to the first and second cavitation shedding events. This research reveals the periodic evolution of cavitation flow field and the mechanism of flow instability in the regulating valve, providing a significant theoretical reference for the warning technology of the cavitation flow instability.

Direct contact condensation of steam bubbles with non-condensable gas is common in nuclear safety equipment. It was insufficient research on the direct contact condensation heat transfer model of steam bubbles with noncondensable gas at high Reynolds numbers (Re > 22000) in previous works. To study the effect of noncondensable gas on heat transfer of steam-air bubbles at high Reynolds numbers, a high-speed camera was used to capture the behavior of bubbles and used image processing and bubble reconstruction to obtain size and dynamic parameters of bubbles. The size and upward motion behavior of bubbles were analyzed. The heat transfer coefficient during the bubbles condensation experiment were calculated and experimental results were compared with correlations proposed by previous works. In order to better explain the heat transfer characteristics and predict the heat transfer coefficient of bubbles at high Reynolds numbers, a modified heat transfer correlation based on the correlation of rigid sphere was proposed which are functions of bubble Reynolds number, liquid Prandtl number, Jacob number, and dimensionless time. This correlation considers the influence of both forced convection around bubbles and variations in steam fractions on bubble condensation. Comparison of experimental data and the corresponding predicted values shows that the deviation between the experimental data and predicted values is within +/- 25 % which indicates the modified correlation accurately predicts the experimental data in this paper.

We examine how ambient temperature $T$ (23–90 $^\circ \mathrm{C}$ ) alters the dynamics of spark-induced cavitation bubbles across a range of discharge energies. As $T$ rises, the collapse of an isolated spherical bubble weakens monotonically, as quantified by the Rayleigh collapse factor, minimum volume and maximum collapse velocity. When the bubble is generated near a rigid wall, the same thermal attenuation is reflected in reduced jet speed and diminished migration. Most notably, at $T \gtrsim 70\,^\circ \text{C}$ , we observe a previously unreported phenomenon: secondary cavitation nuclei appear adjacent to the primary bubble interface where the local pressure falls below the Blake threshold. The pressure reduction is produced by the over-expansion of the primary bubble itself, not by rarefaction waves as suggested in earlier work. Coalescence between these secondary nuclei and the parent bubble seeds pronounced surface wrinkles that intensify Rayleigh–Taylor instability and promote fission, providing an additional route for collapse strength attenuation. These findings clarify the inception mechanism of high-temperature cavitation and offer physical insight into erosion mitigation in heated liquids.

We investigate the influence of ambient temperature on the dynamics of spark-generated cavitation bubbles over a broad temperature range of 23 to 90^∘C. Increasing temperature, the attenuation of collapse intensity of a bubble in a free field is quantitatively characterised through the Rayleigh factor, minimum bubble volume, and maximum collapse velocity. In scenarios where the bubble is initiated near a rigid boundary, this temperature-dependent weakening effect manifests further as a reduction in jet velocity and bubble migration. Additionally, our findings demonstrate that when ambient temperature exceeds 70^∘C, secondary cavitation forms near the bubble surface around the moment of maximum bubble expansion, followed by coalescence-induced surface wrinkles. These perturbations trigger Rayleigh-Taylor instability and enhance bubble fission. We determine the internal gas pressure of the bubble at its maximum expansion via the Rayleigh-Plesset equation with the input of bubble radius from experimental measurements. It reveals that the secondary cavitation is derived from the gas pressure descending below the saturated vapor pressure, which provides nucleation-favorable conditions. This study sheds light on the physics behind erosion mitigation in high-temperature fluids from the perspective of cavitation bubble dynamics.

This paper employs a combined experimental and numerical approach to investigate the influence of airflow characteristics—specifically air velocity νa and air density ρa—on the evolution of water-entry cavities at low Froude numbers (Fr<13). A custom-designed test platform enables control over air density ρa and water-entry initial velocity V0. The velocity V0 influences the cavity expansion rate, which in turn determines the air inflow velocity νa into the cavity. Based on the experimental results, a critical condition for surface seal is proposed: ρ*·Fr 2.62 =315, where ρ*=ρa/ρ0, ρ0 is the ambient density. For constant air density, deep seal dynamics exhibit negligible direct sensitivity to airflow when the Fr < Frc, aligning with classical inertial theories and a 1/2-power scaling law during radial collapse. As ρ* or Fr increases beyond the critical threshold, the cavity closure mode transitions from deep seal to surface seal. Numerical simulations, based on finite volume method, reveals that when the flow field is approximately uniform, the ratio of air flow velocity νa to projectile velocity ν is 1.5. Furthermore, the airflow-induced pressure difference basically satisfies Δp = ρaua2/2, driving inward splash motion. Neglecting the change in projectile velocity, there is Δp ∝ ρaV02/2. When the splash is about to close, the flow field distribution is relatively complex, and the pressure relationship no longer holds consistently. Surface seal blocks the connection between the cavity and the external atmosphere, directly impacting the internal pressure dynamics and further influencing the deep seal characteristics.

The collapse of an initially spherical cavitation bubble near a free surface leads to the formation of two jets: a downward jet into the liquid, and an upward jet penetrating the free surface. In this study, we examine the surprising interaction of a bubble trapped in a stable cavitating vortex ring approaching a free surface. As a result, a single fast and tall liquid jet forms. We find that this jet is observed only above critical Froude numbers ( $Fr$ ) and Weber numbers ( $We$ ) when ${Fr}^2 (1.6-2.73/{We}) > 1$ , illustrating the importance of inertia, gravity and surface tension in accelerating this novel jet and thereby reaching heights several hundred times the radius of the vortex ring. Our experimental results are supported by numerical simulations, revealing that the underlying mechanism driving the vortex ring acceleration is the disruption of the equilibrium of high-pressure regions at the front and rear of the vortex ring caused by the free surface. Quantitative analysis based on the energy relationships elucidates that the velocity ratio between the maximum velocity of the free-surface jet and the translational velocity of the vortex ring is relatively stable yet is attenuated by surface tension when the jet is mild.

In this paper, we present a theoretical, experimental, and numerical study of the dynamics of cavitation bubbles inside a droplet suspended in another host fluid. On the theoretical side, we provided a modified Rayleigh collapse time and natural frequency for spherical bubbles in our particular context, characterized by the density ratio between the two liquids and the bubble-to-droplet size ratio. Regarding the experimental aspect, experiments were carried out for laser-induced cavitation bubbles inside oil-in-water (O/W) or water-in-oil (W/O) droplets. Two distinct fluid-mixing mechanisms were unveiled in the two systems, respectively. In the case of O/W droplets, a liquid jet emerges around the end of the bubble collapse phase, effectively penetrating the droplet interface. We offer a detailed analysis of the criteria governing jet penetration, involving the standoff parameter and impact velocity of the bubble jet on the droplet surface. Conversely, in the scenario involving W/O droplets, the bubble traverses the droplet interior, inducing global motion and eventually leading to droplet pinch-off when the local Weber number exceeds a critical value. This phenomenon is elucidated through the equilibrium between interfacial and kinetic energies. Lastly, our boundary integral model faithfully reproduces the essential physics of nonspherical bubble dynamics observed in the experiments. We conduct a parametric study spanning a wide parameter space to investigate bubble-droplet interactions. The insights from this study could serve as a valuable reference for practical applications in the field of ultrasonic emulsification, pharmacy, etc.

In the operation of nuclear power plants, the accurate prediction of power change trends is crucial for ensuring safety and stability. In this work, a ML-GRU-RS method, based on model-agnostic meta-learning (MAML), gate recurrent unit (GRU), and random search optimization, is proposed for the long-term prediction of key parameters of nuclear power plants. This method combines the fast adaptability of MAML, the time series data processing capability of GRU, and the optimization efficiency of random search to achieve high-precision predictions under varying power conditions. The results demonstrate that this method can effectively predict the future trends of key parameters in nuclear power plants. The ability of operators to anticipate these trends has been significantly enhanced, contributing to the overall safety of the nuclear power plants.

Accurately quantify the complex structure of cavitation in pressure relief valve by experiment remains a challenging task. In this research, a quantitative method for assessing the vapor volume fraction in cavitation images by void fraction experimentally is proposed, this method is less affected by environmental interference and could achieve rapid and accurate characterization of cavitation. The results show that void fraction effectively represents changes in vapor volume fraction under different conditions. The influence of the grid division numbers on the vapor volume fraction is investigated, the optimal number of grid division is 93 in X direction, with a misjudgment number of 130 and a misjudgment rate of 1.62 %. The effects of grid numbers on vapor volume fraction under different cavitation image pixels is also discussed, the optimal number of grid division is 112 in flow direction, with a misjudgment number of 144 and a misjudgment rate of 1.21 %. Through processing the vapor volume fraction image using the Proper Orthogonal Decomposition (POD) method under different cavitation numbers, the results show that the cavitation number has an important influence on the proportion of reentrant jet area and cavitation collapse area, when the cavitation number decreases to 0.047, the proportion of re-entrant jet area and cavitation collapse area achieve the maximum that 6.41 % and 8.68 %, respectively. Such quantitative analysis of the cavitation degrees under various working conditions can contribute to a better understanding of the impact of cavitation on valve dynamics mechanisms.

Marine physical data are currently derived mainly from satellite remote sensing, sparsely distributed buoys, and mobile observation platforms. The buoys and mobile observation platforms are more suitable for acquiring deep ocean data. Traditional methods for dealing with such observations rely on linear and Gaussian assumptions in the assimilation of nonlinear marine characteristics, which may introduce bias in analysis and forecasting. The particle-filter assimilation method is of increasing interest because it has advantages in dealing with nonlinear assimilation problems, although it has limitations with sparsely distributed observations. To address this problem, we introduced inverse distance-weighted interpolation into the localization scheme of the localized equivalent-weights particle fi lter with time-distributed statistical observations method based on data from sparsely distributed buoys and mobile platforms. This improved the utilization rate of observations and increased forecast accuracy. Theoretical experiments were undertaken to highlight the characteristics of the improved method, using reanalysis data from the European Centre for Medium-Range Weather Forecasts as evaluation criteria in comparing the method with the localized weighted ensemble Kalman fi lter method}a hybrid particle-filter method. Results indicate that the method effectively improves assimilation and the accuracy of state estimation and forecasts of ocean temperature and salinity. SIGNIFICANCE STATEMENT: This paper addresses the problem of assimilating sparsely distributed observations in processing ocean elements. We improved the localization scheme to deal with the sparse-observation problem based on the localized equivalent-weights particle fi lter with time distribution statistical observation (LEWPF-T-Sobs). This method can effectively handle the assimilation problem with sparse observations while retaining the advantages of traditional particle fi ltering assimilation, thus improving the accuracy of estimates of physical ocean data.

In the current field of nuclear energy, the development of the third generations nuclear power plants(NPPs) are the mainstream, and its safety and economy are the important direction of nuclear energy development. Therefore, the normal, stable and safe operation of the nuclear reactor system is particularly important. In order to improve the safety and stability of the nuclear power system, this paper proposes a life prediction model of a NPP based on a comprehensive framework. In this study, an integrated framework based on BP, LSTM, Informer and other models is built, and the model is verified by the running data of Qinshan simulator. The results show that, compared with the traditional BP and LSTM, the long-term trend prediction model of NPP based on integrated framework has lower MAE and MSE values, indicating that the long-term trend prediction model of NPP based on integrated framework has lower error, which provides strong support for the safe and stable operation of nuclear power system.