Study On Extrapolation Method Based On Sapphire Fiber Blackbody Cavity Temperature Sensor

In aviation, weapons industry and some general industry, usually, the transient temperature accuracy measurement is essential. For example, the flame temperature in the end of aerospace engine, the inner surface temperature of artillery tubes and burning gas temperature in internal combustion engine, etc. These are transient temperatures that are high amplitude, rapidly changing, and need high measurement technology, its measurement conditions are poor.Under the background above, the sapphire fiber blackbody temperature sensor based on Planck blackbody radiation law is developed. When sapphire fiber blackbody temperature sensor is used to measure temperature, eventually the temperature can be obtained from temperature measurement system. But the temperature is obtained from thermal radiation signals of blackbody cavity inner surface, strictly speaking, the temperature is blackbody cavity inner surface temperature, rather than the measured object's real temperature. Because the outer surface of blackbody cavity directly contacts with the measured object, it is considered to be right that blackbody cavity outer surface temperature is consistent with the measured object's real temperature. In order to more accurately obtain the real temperature of the measured object, the blackbody cavity extrapolation theory based on heat transfer is proposed, analyzes the heat transfer law of blackbody cavity, and deduces blackbody cavity outer surface temperature by extrapolation method.Currently, the common temperature extrapolation methods are Analysis, Separation of variables and Finite difference method,ect. The derivation process of Analysis is easy, but n re indefinite integral in the extrapolation results is difficult to calculate, coefficient bn is not readily got, and there is the fitting error in extrapolation result. The extrapolation result of Separation of variables is easy to program by computer, but the derivation process is complex, and the extrapolation result is strictly limited on blackbody cavity film thickness, if the blackbody cavity film thickness x p< 18.6um, the extrapolation result of Separation of variables method is absurd, and not appropriate to analyze blackbody cavity heat transfer. Derivation process of Finite difference method is simple, and extrapolation result is easy to implement on the computer, but there is vibration in the Finite difference method, in order to eliminate vibration, it is necessary that the sample values of the blackbody cavity inner surface temperature are very smooth, and the sample curve are more smoother, vibration is more smaller, and the extrapolation result is more accurate, but the computation will be increasing and computing time will be longer, such balance usually appears in the numerical calculation.The results show that when the blackbody cavity film thickness are several hundred microns, Separation of variables or Finite difference method should be used, when the blackbody cavity film thickness is tens of microns, and the sample values of blackbody cavity inner surface temperature are not very smooth, Analysis should be used, if the sample values of blackbody cavity inner surface temperature are relatively smooth, Finite difference method should be used.