Modeling of thermal enhancement and scaling analysis for omnidirectional magnetic field generator to actively detumble space debris

Abstract

An omnimagnetic field generator, or Omnimagnet, is a novel electromagnet that can potentially be used to remotely detumble electrically conductive, nonmagnetic space debris objects via eddy currents. Omnimagnets use three concentric, orthogonal copper solenoids wound around aluminum frames to generate magnetic fields. Operating an Omnimagnet generates large amounts of Joule heating in the solenoids, which can lead to overheating and device failure. Radiative cooling at the outermost surfaces is the only mechanism for heat dissipation. Heat dissipation of the innermost components is limited by the concentric geometry, causing elevated temperatures. Omnimagnet systems cannot be designed without understanding the relationships between Joule heating, Omnimagnet size, and detumbling capability, which are not adequately captured by existing models. The goal of this work is to calculate the detumbling capability of Omnimagnets in space while ensuring overheating does not occur. This work develops a finite element analysis (FEA) model to simulate Omnimagnet thermal behavior in space. Model results show that the innermost Omnimagnet components reach higher temperatures than the outermost components due to limited heat transfer pathways. Applying a high-emissivity coating to aluminum surfaces leads to increased radiative cooling, allowing for a 14% increase in applied current density without overheating. Scaling relationships between nondimensional Omnimagnet length and radiative cooling, maximum current density and magnetic dipole moment are developed to predict the detumbling capability of any size Omnimagnet. These scaling relationships show that radiative cooling scales approximately with nondimensional length squared. This relationship allows the prediction of the upper limit of heat generation via Joule heating. The applied current density scales with nondimensional length to the -0.686 power. Larger Omnimagnets must reduce current density because radiative cooling and Joule heating scale differently with nondimensional length. Magnetic dipole moment scales with nondimensional length to the 3.538 power, indicating that large Omnimagnets produce substantially stronger magnetic fields. Larger Omnimagnets are more efficient per mass than smaller Omnimagnets, which is critical for space applications. This work establishes the critical dependence of Omnimagnet size and detumbling capability on thermal behavior, marking the first step in thermally guided Omnimagnet design. Additionally, it identifies the significant role that surface radiative properties, such as emissivity, can play in enhancing thermal performance, further advancing the potential for successful detumbling missions in space.