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Modern shock-capturing schemes often suffer from numerical shock instabilities when simulating strong shocks, limiting their application in supersonic or hypersonic flow simulations. In the current study, we devote our efforts to investigating the shock instability problem for second-order schemes, which has not gotten enough attention in previous research but is crucial to address. To this end, we develop the matrix stability analysis method for the finite-volume Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) approach, taking into account the influence of reconstruction. With the help of this newly developed method, the shock instability of second-order schemes is investigated quantitatively and efficiently. The results demonstrate that when second-order schemes are employed, whether shock instabilities will occur is closely related to the property of Riemann solvers, just like the first-order case. However, enhancing spatial accuracy still impacts the shock instability problem, and the impact can be categorized into two types depending on the dissipation of Riemann solvers. Furthermore, the research emphasizes the impact of the numerical shock structure, highlighting both its role as the source of instability and the influence of its state on the occurrence of instability. One of the most significant contributions of this study is the confirmation of the multidimensional coupled nature of shock instability. Both one-dimensional and multidimensional instabilities are proven to influence the instability problem, and they have different properties. Moreover, this paper reveals that increasing the aspect ratio and distortion angle of the computational grid can help mitigate shock instabilities. The current work provides an effective tool for quantitatively investigating the shock instabilities for second-order schemes, revealing the inherent mechanism and thereby contributing to the elimination of shock instability. [ABSTRACT FROM AUTHOR]

In this paper, the cavitation and flow characteristics of the unsteady liquid nitrogen (LN2) cavitating flow in a submersible pump are investigated through both experimental and numerical approaches. The performance curve of the LN2 submersible pump is obtained via experimental measurement. Numerical simulations are performed using a modified shear stress transport k–ω turbulence model, incorporating corrections for rotation and thermal effects as per the Schnerr–Sauer cavitation model. The numerical framework is verified by comparing the cavitation morphology features with previously reported visual data of the LN2 inducer and aligning pump performance data with those obtained from experimental tests of the LN2 submersible pump. The results indicate that cavitation at the designed flow rate predominantly manifests as tip clearance vortex cavitation in the inducer. Increased flow rates exacerbate cavitation, potentially obstructing the flow passage of the impeller. The vortex identification method and the vorticity transport equation are employed to identify the vortex structures and analyze the interaction between cavitation and vortices in the unsteady LN2 cavitating flow. The vortex structures primarily concentrate at the outlet of the impeller flow passage, largely attributed to the vortex dilation term and baroclinic torque. The influence of thermal effects on the cavitation flow of submersible pumps is analyzed. An entropy production analysis model, comprehensively involving various contributing factors, is proposed and utilized to accurately predict the entropy production rate within the pump. This study not only offers an effective numerical approach but also provides valuable insight into the cavitation flow characteristics of the LN2 submersible pump. [ABSTRACT FROM AUTHOR]

Cavitation-induced vortex and energy loss are critical topics in the field of hydraulic machinery. Through a combination of experimental and numerical analysis, this paper investigates how blade loading affects vortical structures and energy loss during cavitation in a waterjet pump. The flow rate and cavitation conditions changed blade tip pressure loading, which significantly affected the trajectories of the primary tip leakage vortex cavitation and secondary tip leakage vortex cavitation. A considerable pressure gradient at the attached cavity closure region leads to a wall reentrant jet and a side-entrant jet, resulting in an attached vortex under the cavitation developing stage and severe stage. The development of the attached vortex leads to the shedding of attached cavities. Furthermore, the blade tip pressure difference loading significantly alters the distribution of tip leakage vortex and gives rise to a perpendicular leakage vortex (PLV). The PLV entrains the shedding cavities and forms a perpendicular cavitation vortex. These complex vortical structures induced by cavitation inevitably enhance enstrophy and lead to entropy production in the pump. The entropy production terms of viscous dissipation, turbulent dissipation, and the wall effect react differently to the development of cavitation. As the cavitation stages developed and became more severe, wall entropy production (S3) decreased. While turbulent dissipative entropy production S2 due to mixing losses occurring in the tip region increased sharply, which dominates the total entropy production S and results in an increase in S. [ABSTRACT FROM AUTHOR]

This paper analyzes the liquid atomization mechanisms of an N-heptane spray jet emerging from a swirl simplex atomizer using numerical and experimental techniques. In particular, a direct seamless coupled Volume of Fluid and Lagrangian Particle Tracking approach together with adaptive mesh refinement within the Large Eddy Simulation framework offers a suitable way to accurately simulate the complex behavior of spray atomization, spray evolution, and droplet dispersion as a whole while using manageable computational cost. The achieved simulation results are first presented in terms of qualitative properties, characteristics of liquid sheet, air core generation, flow recirculation zones, and vortex patterns. For validation purposes, the numerical results are then compared with detailed experimental data obtained by a two-component Phase Doppler Anemometry technique. The assessment includes especially droplet statistics which strongly determine subsequent possible spray combustion process and related product and species emissions. The overall reported agreement demonstrates the capability of the adopted methodology in predicting and comprehensively investigating the complex phenomena associated with a pressure swirl fuel atomizer. In particular, it is found out that the normalized number-based probability density function of droplet size fits well with a lognormal distribution. [ABSTRACT FROM AUTHOR]

This paper's goal is to investigate if a gob-side entry retention technique combined with a surrounding rock support system is feasible in three soft coal seams. Field engineering confirmed the results of numerical simulation tests and similar simulation tests, which were conducted in accordance with the actual geological conditions of Zhaojiazhai Mine. The following conclusions are reached after studying the technology and process parameter of the gob-side entry retaining in three soft coal seams in conjunction with theoretical calculations: the coal seam of Zhaojiazhai Coal Mine's 12 209 working face is a part of the soft coal seam, and its loose circle is approximately 1.8 m. The expansion roadway size is 3.5 m, and the potential loose circle range is 1.32 m, according to the same model and numerical simulation test. The support scheme after the expansion of the road working face is determined to be the "anchor rod + anchor cable + hydraulic lifting shed" support method. Furthermore, this article suggests a building method for the reinforcement and enlargement of gob-side entry retaining in three-soft thick coal seam by theoretical analysis and numerical simulation. Roadway shotcrete, advance grouting, building of a large deformation anchor cable and continuous resistance, single column lifting shed, hydraulic lifting shed, and roadway enlargement in advance are all steps in the procedure. Furthermore, an analysis is conducted on the deformation features of the surrounding rock in gob-side entry retention. The study highlights the significance of actively supporting the surrounding rock, fortifying the roof support, guaranteeing the stiffness compatibility between the shoulder filling body and the surrounding rock on the roof, boosting the wall's strength and stability, and enhancing the roadway's stability. [ABSTRACT FROM AUTHOR]

The development of hydrodynamic instabilities has a significant impact on the operation of laser fusion systems. During radiation compression, the shells of a target are accelerated, resulting in the growth of perturbations at their interfaces. In this paper, we study the influence of density perturbations on the stability of the contact boundary during accelerated motion. The analysis is performed in a two-dimensional planar formulation using the linear approximation and assuming a weak spatial dependence on the temperature near the contact boundary. Due to the consideration of small time intervals, the phenomenon of heat conduction is not taken into account. The cases of acceleration of a medium described by the Mie–Grüneisen equation of state (EoS) into a vacuum and of acceleration of two contacting media, each described by the ideal plasma EoS, are considered. The time dependence of the amplitude of the boundary perturbation on time is obtained. The obtained values are in agreement with the results of numerical analysis. It is shown that the boundary curvature occurs independently of the acceleration direction. The theoretical results are compared with numerical results for laser fusion systems. [ABSTRACT FROM AUTHOR]

This paper investigated the differences for the hydraulic characteristics in a single fracture between using the Navier–Stokes (N–S) equation and Darcy's law, which would be benefit to understand the seepage mechanism in the fracture. A numerical model of the radial flow was established considering the aperture size and water injection flow rate. Some conclusion could be given. First, the Darcy's law only described the seepage characteristics when the flow rate was small when the flow rate and pressure response have a linear relationship. While the N–S equation could describe the linear and nonlinear seepage characteristics, resulting in a better model of the actual fracture seepage flow. Second, the aperture size had a limited influence on the water pressure and seepage velocity inside the fracture when the flow rate was small. It began to have a significant impact influence on the seepage characteristics inside the fracture with the aperture increased. Third, the flow–pressure response conformed to the Forchheimer equation in the fracture. The critical Reynold number would decrease from 1.2 to 0.0116 when fracture aperture decreased from 3 to 0.5 mm using the N–S equation. The degree of nonlinearity of the fluid flow increases with fracture roughness increasing. This work gave a guidance to the difference in the two seepage theories and correction for the result by Darcy law, which was widely used in the engineering calculation. [ABSTRACT FROM AUTHOR]