Analytic Thermal Design of Bitter-Type Solenoids

Abstract

We describe an analytic approach to designing axially water-cooled Bitter-type electromagnets with an emphasis on heat dissipation considerations. The design method here described aims to enhance the efficiency of the design process by minimizing the role of finite element analysis (FEA) software. A purely analytic design optimization scheme is prescribed for establishing the cooling hole placement. FEA software is only used to check the accuracy of analytic predictions. The analytic method derived in this paper predicts the required heat dissipation rate by approximating the volumetric joule heating profile with a smooth, continuous profile. Equations for turbulent convective heat transfer in circular ducts are generalized to model the cooling capacity of elongated cooling passages. This method is currently in use at the University of Maryland Baltimore County Dusty Plasma Laboratory to design a Bitter magnet capable of generating fields of 10 T.

Design and experimental results of the 1-T Bitter Electromagnet Testing Apparatus (BETA)

“…7 The conductors' cooling hole wall temperatures are analytically calculated to predict the temperature profile of the Bitter arc conductors as a function of the optimal operating current. 1 Cooling holes are placed to produce an approximated average conductor temperature that results in the prescribed conductor resistivity of the electromagnetic optimization. If the water's temperature from the cooling channels' outlets are below boiling and peak temperatures on the conductors do not change the mechanical properties of the material, then the design moves to the mechanical stress stage.…”

“…The magnet core design of BETA was determined by analytical design methodologies developed at DPL. 1,2 Presented here are the essential design specifications and analyses of BETA including the magnet core design, fabrication processes, scalable subsystems, and initial experimental results. The experimental results of BETA are used to validate and verify DPL design methodologies.…”

Development of a Bitter-Type Magnet System

“…A heat transfer analytical method is then used to optimally place cooling holes after the design parameters are obtained from ohmic heating optimization [12]. Placement of these cooling holes is very important to reduce the thermal load on the conducting plates.…”