Determination of Real-Gas Stagnation Temperature Based on Mass-Flow Consideration

Abstract

ONE OF THE MAJOR PROBLEMS encountered in the operation of high-enthalpy test facilities is the determination of high stagnation temperatures (T > 4,000°R). Since these temperatures normally exceed the capabilities of available thermocouples, it is often necessary to resort to one of the various optical methods—such as pyrometry or the sodium-line reversal technique— for the determination of these temperatures. A method has been presented whereby real-gas stagnation properties in a highenthalpy system can be determined if the mass-flow rate through the system and the stagnation pressure are known. In the present analysis, this method was applied to determine stagnation temperature for stagnation pressures ranging from 100 to 1,000 atm. Nitrogen is considered to be the flow medium and the expansion of the gas from the stagnation chamber is assumed to be an isentropic and steady-state process. The maximum temperature dealt with (5,000°R) was low enough that the gas remained in an undissociated state; however, the method may be extended to other gases which may or may not be dissociated, provided the thermodynamic properties of the gas in the desired pressure and temperature range are known. A one-dimensional analysis of the flow is used to evaluate the mass flow per unit area at the throat of a nozzle for various stagnation pressures and temperatures. The evaluation of mass flow per unit area at the throat of a nozzle is a trial-and-error procedure and was performed in the following manner. Starting with an assumed stagnation pressure and temperature, an initial value of stagnation entropy was obtained from published data. , 3 The flow in the system was expanded by reducing the stagnation temperature at a constant value of stagnation entropy. At each assumed temperature the values of pressure, density, and enthalpy were obtained from Ref. 2 or 3; the velocity at each point was calculated from the energy equation. The result of the analysis is presented in Fig. 1, wherein mass flow per unit throat area is plotted against stagnation temperature. The dashed lines represent ideal-gas calculations. The spread between the ideal-gas and real-gas curves becomes larger as the stagnation pressure is increased. I t may be seen from Fig. 1 that a significant error in stagnation temperature could result by using the ideal-gas relationship. For example, a t a mass flow per unit throat area of 16,000 lb/ft-sec and a stagnation I7|-