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Motivated by some discrepancies in the comparison between the rheometric viscosity function of shear-thinning fluids and the apparent Darcy viscosity function obtained in porous media simulations/experiments, we propose a model for the flow in porous media with a non-uniform pore distribution in the pore scale, i.e., inside the Representative Elementary Volume (REV). Since different pore sizes inside the REV would lead to different characteristic shear rates, the heterogeneity of the pores in the elementary scale can be responsible for the mentioned discrepancies. Indeed, simulations in a plug of a porous medium have shown that the apparent viscosity function decreases as we increase the standard deviation distribution of the diameter of idealized cylindrical pores. The ratio of the mobility of the heterogeneous pore distribution to the mobility of the homogeneous one is plotted as a function of the power-law index of the non-Newtonian viscosity function. The dimensionless analysis has shown to be a powerful tool in the investigation, collapsing the information in several cases. In addition, our results reveal that a non-uniform pore size distribution can be an important source of the discrepancy between the viscosity function obtained in a rheometric device and the one obtained from the Darcy equation, as reported in the literature.

Passive cooling reliability is crucial in nuclear and thermal systems, making single-phase natural circulation loops (SPNCLs) a vital mechanism for heat removal. However, their turbulent thermal–hydraulic behavior under strong buoyancy remains insufficiently quantified. This study experimentally assesses the thermal–hydraulic performance of a turbulent SPNCL operated under quasi-steady-state conditions. Experiments were performed using the large-scale FASSIP-02 Ver 02 facility with heat source temperatures between 50°C and 80°C. Dimensionless analysis was applied to characterize the dominant heat transfer regime and buoyancy-driven circulation. Increasing the heat source temperature intensified buoyancy forces, which enhanced circulation and improved heat removal. The system achieved a maximum temperature difference of 5.2°C and a low rate of 28.5 L/min at heat source temperatureT WHT = 80°C, with Re = 13,521– 33,850 and Gr = 2.997 × 10 12 –1.739 × 10 13 , confirming fully turbulent operation (Ra > 10 8 ). A correlation between Re and Gr/NG was obtained, with C = 0.00735 and r = 0.6534 (R 2 = 0.96), providing a quantitative model of buoyancy– low interaction. The results supply a validated dataset and correlation for predicting thermal–hydraulic behavior in support of passive cooling system designs.

Pressurized pipeline systems may have a wide operating regime. This paper presents the experimental analysis of the transient flow in a horizontal pipe containing an air pocket, which allows the ventilation of the air after the pressurization of the hydraulic system, through an orifice placed at the downstream end. The measurements are made on a laboratory set-up, for different supply pressures and various geometries of water column length, air pocket and expulsion orifice diameter. Dimensional analysis is carried out in order to determine a relation between the parameters influencing the maximum pressure value. A two equations model is obtained and a criterion is established for their use. The equations are validated with experimental data from the present laboratory set-up and with other data available in the literature. The results presented as non-dimensional quantities variations show a good agreement with the previous experimental and analytical researches.

Granular column collapse is a simple but important problem to the granular material community, due to its links to dynamics of natural hazards, such as landslides and pyroclastic flows, and many industrial situations, as well as its potential of analysing transient and non-local rheology of granular flows. This article proposes a new dimensionless number to describe the run-out behaviour of granular columns on inclined planes based on both previous experimental data and dimensional analysis. With the assistance of the sphero-polyhedral discrete element method (DEM), we simulate inclined granular column collapses with different initial aspect ratios, particle contact properties and initial solid fractions on inclined planes with different inclination angles ($2.5^{\\circ }\\unicode{x2013}20.0^{\\circ }$) to verify the proposed dimensional analysis. Detailed analyses are further provided for better understanding of the influence of different initial conditions and boundary conditions, and to help unify the description of the run-out scaling of systems with different inclination angles. This work determines the similarity and unity between granular column collapses on inclined planes and those on horizontal planes, and helps investigate the transient rheological behaviour of granular flows, which has direct relevance to various natural and engineering systems.

Spray cooling is influenced by many related parameters, making analysis of heat transfer mechanisms and prediction of cooling performance challenging. After summarizing and analyzing fifteen different forms of correlation in spray cooling literature, it appears that there are four expressions for spray cooling correlation. 2989 experimental data under different experimental conditions in twelve studies were collected to form an experimental database to evaluate the prediction of correlations. The prediction accuracy of Nusselt number correlations based on droplet diameter is considered the best, while that of correlations based on dimensionless heat flux is considered the worst. The factor analysis method was used to analyze the prediction differences of correlations and investigate the correlation between parameters and the heat transfer process. We found that the correlation with the best evaluation accuracy must contain more parameters with high correlation. A new correlation was derived based on this conclusion to predict the data better.

The present study deals with close-contact melting of a vertical cylinder on a horizontal isothermal superhydrophobic surface with an array of circular posts. A new numerical model for this phenomenon is formulated under several simplifying assumptions. For the limiting case of perfect slip and thermal contact, based on the model assumptions, it is demonstrated that superhydrophobic surfaces can enhance the melting time by no more than 30 %. Numerical solution of the new model reveals that the effect of superhydrophobic hydrodynamic slip can decrease the molten layer thickness. However, due to the dominant effect of thermal slip, the heat transfer rate can be decreased significantly, and the melting time can be roughly doubled. An approximate analytical model is developed for understanding the problem dynamics better. The analytical model predictions are compared extensively against the numerical model results. For sufficiently low surface volume fractions, the analytical model provides excellent estimations of the numerical model predictions. Dimensional analysis reveals that according to the analytical model, the ratio between the melting times for superhydrophobic and regular surfaces is governed by a single dimensionless group. Moreover, according to the analytical model, the melting time on a superhydrophobic surface is always longer than on a regular surface, which agrees qualitatively with the numerical model results. Based on this analysis, a dimensionless condition for the analytical model range of validity is formulated. Finally, a conservative criterion for the liquid–gas interface stability under a close-contact melting process is established.

Understanding the molten pool dynamics and accurately predicting its geometry are critical aspects of laser cladding. The molten pool depth is crucial for the metallurgical bond between layers, yet it remains difficult to determine. To address this challenge, this study developed a high-fidelity thermal-fluid model and utilized physics-informed machine learning to predict the molten pool depth in single-layer multi-track fiber laser cladding of 316L stainless steel. Initially, the thermal-fluid model was established and validated through experiments, followed by an analysis of the molten pool’s temperature and flow field. Dimensionless numbers such as dimensionless heat input, Peclet number, and Marangoni number were calculated to assess the impact of molten pool flow on its geometry. A physics-informed temporal convolutional network (TCN) model was then developed based on the dataset generated from the thermal-fluid model, incorporating physical information like Marangoni convection. The performance of the proposed prediction model was compared with other time series machine learning approaches, showing mean absolute error (MAE) improvements of 82.7%, 38.9%, and 31.3% over models using the same dataset and physical information but based on recurrent neural networks (RNN), long short-term memory (LSTM), and gated recurrent units (GRU), respectively. These findings highlight the potential of integrating physical insights into predictive modeling to enhance the accuracy and efficiency of laser cladding processes.

The profile of the laser beam plays a significant role in determining the heat input on the deposition surface, further affecting the molten pool dynamics during laser-based directed energy deposition. The evolution of molten pool under two types of laser beam, super-Gaussian beam (SGB) and Gaussian beam (GB), was simulated using a three-dimensional numerical model. Two basic physical processes, the laser–powder interaction and the molten pool dynamics, were considered in the model. The deposition surface of the molten pool was calculated using the Arbitrary Lagrangian Eulerian moving mesh approach. Several dimensionless numbers were used to explain the underlying physical phenomena under different laser beams. Moreover, the solidification parameters were calculated using the thermal history at the solidification front. It is found that the peak temperature and liquid velocity in the molten pool under the SGB case were lower compared with those for the GB case. Dimensionless numbers analysis indicated that the fluid flow played a more pronounced role in heat transfer compared to conduction, especially in the GB case. The cooling rate was higher for the SGB case, indicating that the grain size could be finer compared with that for the GB case. Finally, the reliability of the numerical simulation was verified by comparing the computed and experimental clad geometry. The work provides a theoretical basis for understanding the thermal behavior and solidification characteristics under different laser input profile during directed energy deposition.

Inkjet technology is a commendable tool in many applications including graphics printing, bioengineering and micro-electromechanical systems (MEMS). Droplet stability is a key factor influencing inkjet performance. The stability can be analysed using dimensionless numbers that usually combine thermophysical properties and system dimensions. In this paper, a drop-on-demand (DOD) inkjet experimental system is established. A numerical model is developed to investigate the influence of the operating conditions on droplet stability, including nozzle dimensions, driving parameters (the pulse amplitude and width used to drive droplet formation) and fluid properties. The results indicate that the stability can be improved by decreasing the pulse amplitude and width, decreasing the fluid density and viscosity or increasing the nozzle diameter and fluid surface tension. Based on case analysis and modelling, a dimensionless number ( $Z$ ), the reciprocal of the Ohnesorge number, is numerically determined for a stable droplet to lie in a range between 4 and 8. To explicitly combine the driving parameters, a new stability criterion, $Pj$ , is further proposed. A general rule taking into account both $Pj$ and $Z$ is proposed for choosing appropriate driving parameters to eject stable droplets for a known nozzle and fluid, which is further validated by experiments.

The slamming load acting on the bow of a large-bow flare ship is equivalent to a moving pulse time history with linear rise and exponential attenuation. The Abaqus finite element software is used to study the elastic dynamics of multiple stiffened plates under the action of the moving slamming load. Response calculations are conducted to analyze the influence of different load parameters on the dynamic response of the stiffened plate. The dynamic stress equivalent coefficient DLFps (Dynamic Load Factor of plate stress) of the plate is introduced, the change pattern and sensitivity between DLFps and the slamming load dimensionless parameters are analyzed, and the DLFps formula regression and verification are performed. A parameter determination method for the simplified slamming pressure model is proposed. Comparison with the results of the wedge-shaped body falling into the water test shows that the slamming stress equivalent formula DLFps of the plate proposed in this article has high accuracy and can be used to determine the slamming load of the ship structure.