Lead loss problem for a thermocouple imbedded in a burning propellant.

Abstract

A a flat solid-propellant surface has been ignited, and burning has gone on for a short time, a steady-state profile of temperature vs normal distance from the burningsurface is attained. When there is no reaction within the propellant up to the burning surface, and the solid has a constant thermal diffusivity, the temperature profile falls off exponentially; and, if the burning surface regresses at a constant rate toward a point within the propellant, that point will undergo an exponential increase in temperature with time. A very small thermocouple junction imbedded in the propellant also will undergo an exponential increase in temperature with time. To compute the heat losses through the thermocouple leads, one must consider the way in which the leads are directed outthrough the propellant. It is attractive to consider directing the leads away from the thermocouple junction along an isotherm to prevent heat loss through them. However, if we assume that an isotherm is represented by points equidistant from the burning surface, we can see that an isothermal surface could be very irregular because of the burning surface roughness in many propellants. Moreover, the full plane surface of a solid-propellant grain seldom is ignited all at once. These probable nonuniformities, coupled with the fact that the temperature gradient near the burning surface is very high (10°C/cm), lead one to conclude that the leads can not be directed from the junction parallel to the plane of the initial grain surface without the risk that the burning surface will reach the lead before the junction and preheat the junction by conduction through the lead. Therefore, one decides to direct the leads away from the burning surface, even though there may be a large heat loss through the leads. Since previous experimenters have used this path for the leads, it is important to compute the heat losses and, if necessary, make suitable corrections to previous work. The following analysis shows that these losses may be quite significant, and that use of a flattened junction parallel to the burning surface can appreciably reduce the loss.