Acoustic Resonance Considerations for a Lined Induction Furnace

The implementation of ultrasonic resonators of standing wave and travelling wave type has undergone lengthy development for applications including grain refinement of alloys, removal of gas from liquid metals prior to foundry pouring, and sequestration of radio-toxic byproducts of activated coolants in generation IV nuclear reactor systems. While advantages over competing mechanical treatments include reduced treatment times, improved degassing effectiveness, and more favorable carbon footprints due to a reduction in recycled material streams, technical challenges remain owing to the difficulties of transmitting and dispersing high-powered ultrasound to far-field locations within the insonated volume. Within the last few years, concepts have been proposed which rely on action-at-a-distance processes, including electromagnetic induction, for purposes of overcoming these obstacles. The focus of this paper is to present: (i) an acoustic field model of ultrasound generation in an induction furnace system, (ii) an assessment of the role played by the furnace liner in controlling the retention and distribution of acoustic energy within the furnace volume, and (iii) a delineated set of operational parameters and design constraints consistent with favorable degassing action within a given furnace system.  A first principles approach is used to solve for a consistent set of acoustic field variables which account for the mechanical response of a fluid susceptor excited by the electromagnetic field, as well as the manner by which the susceptor response is coupled to the characteristics of the liner. To obtain the field variables in terms of parameters which are pertinent to the evaluation of effective degassing, solutions are obtained via both a finite element methodology as well as a lumped mass approach.  For the finite element approach, the governing equations for mass and momentum are solved for both the liquid metal and the liner, along with constitutive and property equations appropriate for treatment of each as a slightly compressible medium; this results in linearized system sets that can be resolved for the vibration amplitudes, eigenfrequencies and eigenmodes.  Favorable modes and amplitudes for promoting the most effective degassing are identified as well as operating conditions needed to accelerate degassing.  From the modal information, a Rayleigh-type methodology is used to develop lumped mass equivalents for the melt and liner system.  Operational envelopes are outlined within which the approaches overlap.  Results are presented in terms of acoustic field variables that relate directly to standard criteria currently in use for assessing the effectiveness of conventional ultrasonic degassing.  A novel method for exciting the system by means of both AC and DC fields is discussed.  Estimates are provided for how this duplex method can effectively be extended to high strength magnetic field applications.