In this paper, discrete element method simulations were used to study the spreading of an idealised, blade based, powder coating system representative of the spreading of spherical, mono-sized, non-cohesive titanium alloy (Ti6AlV4) particles in additive layer manufacturing applications. A vertical spreader blade was used to accelerate a powder heap across a horizontal surface, with a thin gap between the blade and the surface, resulting in the deposition of a thin powder layer. The results showed that it is inevitable to deposit a powder layer with a lower packing fraction than the initial powder heap due to three mechanisms: shear-induced dilation during the initiation of powder motion by the spreader; dilation and rearrangement due to powder motion through the gap; and the inertia of the particles in the deposited powder layer. It was shown that the process conditions control the contribution of these three mechanisms, and that the velocity profile in the shear layer in front of the gap is critical to the final deposited layer packing fraction. The higher the mean normalised velocity in the shear layer the lower the deposited layer packing fraction. The gap thickness and the spreader blade velocity affect the properties of the deposited layer; with the former increasing its packing fraction and the latter decreasing it. The analysis presented in this study could be adapted to powders of different materials, morphologies and surface properties. Keywords Additive manufacturing (AM) • Powder spreading • Discrete element method (DEM) • Dilation • Metal powders • Powder bed fusion List of symbols d Particle diameter t Time v velocity x, y, z Cartesian coordinates δ Gap thickness Δ Change in packing fraction Packing fraction Subscripts 1, 2, 3 First, second and third packing fraction reduction mechanisms, respectively back Interrogation region at the back of the spreader front Interrogation region in front of the spreader p Particle w Spreader ∞ Final

Dilute particle-laden flows are encountered in various natural processes and manmade applications. To reduce the computational resources used to simulate such flows, the particle phase could be formulated using the Eulerian approach, resulting in a continuum hydrodynamic model. The aim of this paper is to present the analytical solution of a steady two-dimensional flow problem using that model. The dispersed solid particles, considered in this problem, are immersed in a uniform fluid flow field. The solid phase is coupled to the fluid using a linear Stokes-drag, which is valid for low slip velocities. The general solution of the solid phase velocity field is obtained by solving its quasi-linear hyperbolic momentum equations using the method of characteristics. For the case of a uniform inlet particle velocity, the solid phase velocity field is obtained in terms of Lambert W function. Subsequently, this velocity field is substituted in the solid phase continuity equation; transforming it to a semi-linear hyperbolic partial differential equation, which is solved to obtain the solid phase volume fraction field.

An experimental investigation is made to study the effect of different parameters affecting the process of natural air flowing through vertical ducts. The experimental setup has been designed and installed in the Air Conditioning Laboratory, Faculty of Engineering, Mansoura University. The test rig is consisted of mainly of rectangular cross-section duct of 25 cm width with different heights and gap thicknesses. The air gap thickness ranges from 3 to 20 cm while the height is ranged from 50 to 200 cm. All duct sides are well insulated with one side heated under heat flux density ranges from 191.04 to 440.75 ⁄. Experimental results are plotted to indicate the relation between air volume flow rate through the vertical duct and different parameters discussed, namely, gap thickness, duct height and heat flux density. Based on measured results the air volume flow rate increases with increasing both heat flux density and duct height. It is concluded also that, the air volume flow rate increases with increasing the gap thickness until it reaches maximum values, namely at gap thickness of 10 cm and then decreases with further increase in gap thickness. The results of the present study could be useful in the design and application of buoyancy-assisted natural ventilation systems.

Abstract