Computer Simulation of Hydrodynamic and Thermal Processes in DLD Technology

This article deals with the theoretical issues of the formation of a melt pool during the process of direct laser deposition. The shape and size of the pool depends on many parameters, such as the speed and power of the process, the optical and physical properties of the material, and the powder consumption. On the other hand, the influence of the physical processes occurring in the material on one another is significant: for instance, the heating of the powder and the substrate by laser radiation, or the formation of the free surface of the melt, taking into account the Marangoni effect. This paper proposes a model for determining the size of the melt bath, developed in a one-dimensional approximation of the boundary layer flow. The dimensions and profile of the surface and bottom of the melt pool are obtained by solving the problem of convective heat transfer. The influence of the residual temperature from the previous track, as well as the heat from the heated powder of the gas–powder jet, taking into account its spatial distribution, is considered. The simulation of the size and shape of the melt pool, as well as its free surface profile for different alloys, is performed with 316 L steel, Inconel 718 nickel alloy, and VT6 titanium alloy

The geometric axial surface profiles of granular flows in rotating drums

SYNOPSIS A mechanistic description of axial segregation in rotating drum flows remains an open question. Consequently, optimal mixing of grinding balls and rocks for efficient breakage, maximum production of fines, and slurry transport is seldom achieved. Experimental and numerical studies of granular mixtures in rotating drums identify alternating axial bands that eventually coarsen in the long-term limit. Most models of axial segregation are limited to binary mixtures and cannot always predict the logarithmic coarsening effects observed experimentally. A key missing factor is a robust description of the axial free surface profile that is valid across a wide range of flow regimes. We present a practical model of the axial free surface profile by linking it to readily-derived geometric features of the cross-sectional S-shaped free surface profile. A parametric study shows good agreement with experimental measurements reported in the literature and heuristically valid trends. Keywords: rotating drum, granular flow, axial profile, comminution, mixing, segregation.

Effect of particle shape on particle breakage inside rotating cylinders

We study the influence of particle shape on the evolution of particle breakage process taking place inside rotating cylinders. Extensive particle dynamics simulations taking into account the dynamics of the granular flow, particle breakage, and polygonal particle shapes were carried out. We find that the rate of particle breakage is faster in samples composed of initially rounder particles. The analysis of the active flowing layer thickness suggests that for samples composed of rounder particles a relatively lower dilatancy and higher connectivity lead to a less curved free surface profile. As a result, rounder particles rolling down the free surface have a higher mobility and thus higher velocities. In consequence, the faster breakage observed for rounder initial particles is due to the larger particles kinetic energy at the toe of the flow.

Experimental Characterization of the Hydraulic Jump Profile and Velocity Distribution in a Stilling Basin Physical Model

The study of the hydraulic jump developed in stilling basins is complex to a high degree due to the intense velocity and pressure fluctuations and the significant air entrainment. It is this complexity, bound to the practical interest in stilling basins for energy dissipation purposes, which brings the importance of physical modeling into the spotlight. However, despite the importance of stilling basins in engineering, bibliographic studies have traditionally focused on the classical hydraulic jump. Therefore, the objective of this research was to study the characteristics of the hydraulic jump in a typified USBR II stilling basin, through a physical model. The free surface profile and the velocity distribution of the hydraulic jump developed within this structure were analyzed in the model. To this end, an experimental campaign was carried out, assessing the performance of both, innovative techniques such as the time-of-flight camera and traditional instrumentation like the Pitot tube. The results showed a satisfactory representation of the free surface profile and the velocity distribution, despite some discussed limitations. Furthermore, the instrumentation employed revealed the important influence of the energy dissipation devices on the flow properties. In particular, relevant differences were found for the hydraulic jump shape and the maximum velocity positions within the measured vertical profiles, when compared to classical hydraulic jumps.

Modified Babenko’s Equation For Periodic Gravity Waves On Water Of Finite Depth

Summary A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko’s equation considered in Kuznetsov and Dinvay (Water Waves, 1, 2019). Both operators in the proposed equation are nonlinear and depend on the parameter equal to the mean depth of water, whereas each solution defines a parametric representation for a symmetric free surface profile. The latter is a component of a solution of the two-dimensional, nonlinear problem describing steady waves propagating in the absence of surface tension. Bifurcation curves (including a branching one) are obtained numerically for solutions of the new equation; they are compared with known results.

Zredukowane współrzędne obrysu strumienia na trapezowym progu przepuszczalnym z przelewem o ostrej krawędzi na skarpie górnej

The purpose of the work was to develop a typical shape of water surface profi le above trapezoidal gabion sill with the sharpcrested weir on the upstream slope. Reduced co-ordinates of the water surface profile above trapezoidal gabion sill with a sharp-crested weir on the upstream slope were developed. The ordinate points of the contour were reduced in relation to the height of the upstream water level above the sharp-crested weir. The cut off points of the contour were reduced according to the length of the zone influencing the stream to the inside of the stone sill. In the analyzes, the results of laboratory tests were used, according to which the shape of the free surface profile reduced coordinates was developed. The analyzed sill consisted of the permeable part filled natural aggregates and the solid part in the form of an inclined sharp-crested weir. The sill had a symetrical trapezoidal shape with the slopes of 1 : 1. The shape of the stream flowing over the analyzed sill depends on the head of the upstream water level above the crest of the slope weir. As a result of the conducted analyzes, a uniform stream shape was obtained for both the free and wave flow of the disturbance zone. The profiles obtained have strong correlation dependence. The obtained results can be taken into account during design similar hydraulic structures.

Flow of a thin liquid-metal film in a toroidal magnetic field

We investigate the gravity-driven flow of a thin film of liquid metal on a conducting conical substrate in the presence of a strong toroidal magnetic field (transverse to the flow and parallel to the substrate). We solve the leading-order governing equations in a physically relevant asymptotic limit to find the free-surface profile. We find that the leading-order fluid flow rate is a non-monotonic bounded function of the film height, and this can lead to singularities in the free-surface profile. We perform a detailed stability analysis and identify values of the relevant geometric, hydrodynamic and magnetic parameters such that the flow is stable.

Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data

The objective of this study was to evaluate the applicability of a flow model with different numbers of spatial dimensions in a hydraulic features solution, with parameters such a free surface profile, water depth variations, and averaged velocity evolution in a dam-break under dry and wet bed conditions with different tailwater depths. Two similar three-dimensional (3D) hydrodynamic models (Flow-3D and MIKE 3 FM) were studied in a dam-break simulation by performing a comparison with published experimental data and the one-dimensional (1D) analytical solution. The results indicate that the Flow-3D model better captures the free surface profile of wavefronts for dry and wet beds than other methods. The MIKE 3 FM model also replicated the free surface profiles well, but it underestimated them during the initial stage under wet-bed conditions. However, it provided a better approach to the measurements over time. Measured and simulated water depth variations and velocity variations demonstrate that both of the 3D models predict the dam-break flow with a reasonable estimation and a root mean square error (RMSE) lower than 0.04, while the MIKE 3 FM had a small memory footprint and the computational time of this model was 24 times faster than that of the Flow-3D. Therefore, the MIKE 3 FM model is recommended for computations involving real-life dam-break problems in large domains, leaving the Flow-3D model for fine calculations in which knowledge of the 3D flow structure is required. The 1D analytical solution was only effective for the dam-break wave propagations along the initially dry bed, and its applicability was fairly limited.