Heat transfer analysis in wire bundles for aerospace vehicles

Abstract

Design of wiring for aerospace vehicles relies on an understanding of "ampacity" which refers to the current carrying capacity of wires, either, individually or in wire bundles. Designers rely on standards to derate allowable current flow to prevent exceedance of wire temperature limits due to resistive heat dissipation within the wires or wire bundles. These standards often add considerable margins and are based on empirical data. Commercial providers are taking an aggressive approach to wire sizing which challenges the conventional wisdom of the established standards. Thermal modelling of wire bundles may offer significant mass reduction in a system if the technique can be generalized to produce reliable temperature predictions for arbitrary bundle configurations. Thermal analysis has been applied to the problem of wire bundles wherein any or all of the wires within the bundle may carry current. Wire bundles present analytical challenges because the heat transfer path from conductors internal to the bundle is tortuous, relying on internal radiation and thermal interface conductance to move the heat from within the bundle to the external jacket where it can be carried away by convective and radiative heat transfer. The problem is further complicated by the dependence of wire electrical resistivity on temperature. Reduced heat transfers out of the bundle leads to higher conductor temperatures and, hence, increased resistive heat dissipation. Development of a generalized wire bundle thermal model is presented and compared with test data. The steady state heat balance for a single wire is derived and extended to the bundle configuration. The generalized model includes the effects of temperature varying resistance, internal radiation and thermal interface conductance, external radiation and temperature varying convective relief from the free surface. The sensitivity of the response to uncertainties in key model parameters is explored using Monte Carlo analysis.

A fast compact model to simulate the heat exchanges in a bundle of electric wires

“…In the automotive and aerospace fields, Chevrié [11], Benthem [12], Rickman [13], and Loos [14] studied models for one wire. They then extended their model to represent a bundle.…”

“…Benthem [12] organizes each wire in concentric layers. Rickman [13] developed a solution where thermal conductance between each neighboring wire must be known. The difficulty to know these conductances requires a simple wire disposition.…”

Improvements to Wire Bundle Thermal Modeling for Ampacity Determination

“…Reference [4] provided the derivation of the thermal network representing heat transfer within a wire bundle and noted wire-to-wire heat transfer between adjacent wire insulation jackets consisted of both radiative and conductive heat transfer paths. Heat transfer between adjacent wires can occur due to direct contact between adjacent insulation jackets, via radiation, and also via air conduction in the gaps between wires for cases where an atmosphere is present.…”

“…The Complex Wire Bundle Thermal Model Builder was developed due to the aforementioned limitations of the bundle spreadsheet model discussed in [4]. Specifically, due to Microsoft Excel ® matrix inversion limitations, a maximum of 50 wire bundle elements could be modeled.…”

“…Heat transfer considerations for wire-to-wire heat transfer within a bundle are presented. The capability to model wire bundles has been extended from the methodology presented in [4] in the form of a complex wire bundle thermal model builder. In this work, the model builder has been used to formulate three analytical configurations for use in comparison with a published derating standard.…”