Thermal Finite-Element Model of an Electric Machine Cooled by a Spray

TL;DR

This work addresses the challenge of increasing power density in electric machines by enhancing cooling with spray cooling. It introduces a practical quasi-3D finite-element framework that extrudes a 2D winding cross-section along the winding direction and represents spray cooling at the overhang with an impedance boundary, calibrated from experiments. The model uses a stationary conduction problem with heat sources $p=\dfrac{J^2}{\sigma_{\text{cu}}}$ and demonstrates that spray cooling can enable about a tenfold increase in achievable power density while maintaining insulation temperatures within class limits. The approach offers a tractable design tool for evaluating spray-cooled windings and informs spray-fluid choices and boundary-condition parameterization for realistic thermal predictions.

Abstract

The need for higher power density in electrical machines require better cooling strategies. Spray cooling is a very promising and relatively simple technology to apply, but involves extremely complicated physics. In this paper, a quasi-3D thermal finite-element model of a stator winding is created, by extrusion of a 2D cross-sectional finite-element model along the winding direction. The possible effects of spray cooling are simulated as a heat flux using an impedance boundary condition at the surface of the winding overhang. The results confirm the beneficial performance of spray cooling. The model indicates that spray cooling may allow a ten times larger power density than for standard air- or water-cooled machines.

Figures (13)

• Figure 1: Schematic view of an electric machine.
• Figure 2: Shadowgraphy image of spray impact onto a convex solid target.
• Figure 3: Typical outcomes of drop impact onto a wetted substrate. a) floating/bouncing (We = 0.62, Re = 24, $\delta =$ 0.33), b) deposition (We = 78, Re = 300, $\delta =$ 0.33) c) crown formation (We = 700, Re = 900, $\delta =$ 0.33, d) splash (We = 1224, Re = 604, $\delta =$ 0.04).
• Figure 4: Various types of splash observed in experiments: a) prompt splash, b) corona splash, c) corona detachment, d) Worthington jet.
• Figure 5: Effect of liquid temperature on the outcome of a Hexadecane drop impacting onto a Hexadecane wall film with $\delta =$ 0.1, $D_0$ = 2 mm and $U_0$ = 3 m/s.