Scaling Analysis of the Electromagnetic Powder Deposition Gun

The electromagnetic powder deposition (EPD) system employs high velocity gas flow to accelerate powder material to conditions required for high strength plating. The gas flow, however, is not continuous; rather it consists of bursts generated by an electromagnetic railgun and pulsed power system. Each gas burst is created by a high pressure plasma arc which fills a transverse section of the gun. This current carrying arc is driven by the railgun Lorentz force (magnetic pressure) and acts much like a piston, which via a snowplow process accelerates and compresses an ambient gas column to the flow speed required to accelerate powder particles. Analysis of the total system was carried out to provide scaling relations which give guidance in design of the system. Plating considerations define a desired powder velocity; this combined with the choice of working gas and ambient pressure determines the velocity and duration of each gas burst. Selection of gun geometry completes the definition of the pulsed power system requirements. An outline of the analysis is presented along with the physical models used. THE EPD PROCESS WAS DEVELOPED as a method of imparting high velocities to powder particles for creation of high mechanical strength surface platings. Like other coating processes, the high particle velocity is achieved by flowing supersonic gas past the particles; the viscous drag force associated with such flows is the mechanism used to accelerate the particles to desired final velocity. What is unique to the EPD approach is that use of electromagnetic railgun force means that the gas flow velocity can be as high as desired, and is not limited by any chemical or thermodynamic constraints. The railgun process is combined with a gasdynamic mechanism, called a snowplow, to produce controllable bursts of gas with the speed and duration required to accelerate finite segments of dispersed powder to the conditions required for plating purposes. Powder Acceleration General Considerations Gasdynamic generated viscous drag has a long history of use as a means of accelerating particles to high velocity. To apply simple theory to the design of our system, the assumption is made that the powder of interest is so finely dispersed that particles are far apart and the gas flow around any one particle is not affected by other particles. When this holds, the time and length scales for the gas flow are defined by the dynamics of a single particle. Again for simplicity, the process is taken to be one dimensional, which is a good approximation for describing the physical mechanisms involved, and is in fact a very good approximation to the actual system design. Each powder particle is assumed to be a solid sphere of diameter D p and density ρp . Gas of density ρg and (constant) velocity Vg streams by each particle. The force equation [1] is Mp dVp dt = CD A p Pk (1) where Mp = powder particle mass= π 6 ρp D p 3 Vp = powder particle velocity CD =drag coefficient Ap = powder particle projectedarea = π 4 Dp 2 Pk = gas kinetic pressure = 1 2 ρg (Vg − Vp) 2 The drag coefficient CD which appears in equation (1) is, in general, a function of both gas and particle velocity. From empirical data on supersonic flow[1] it is known that this parameter is close to unity for a wide range of Mach numbers ≥ 1. For design purposes we assume that CD = 1 at all times. It is convenient to work with dimensionless variables. Define the following new variables : f = Vp Vg and ξ = t τ where τ = 4 3 1 CD ρp ρg Dp Vg Then equation (1) takes the form df dξ = (1 − f )2 (2) which yields the solution