MEASUREMENT OF GAS VELOCITY AND PRESSURE IN A ROCKET FLAME USING A FABRY–PEROT INTERFEROMETER*)

To measure the velocity and pressure of gases in a rocket flame, the authors made use of the change in wavelength of the sodium \(D\)-line (in two experiments, the lithium line 6707 Å), emitted by the flame as a result of the presence of sodium in the rocket fuel. The gas velocity was determined from the magnitude of the Doppler shift when observing the flame at two different angles. The change in wavelength caused by the change in pressure was determined, in order to exclude the Doppler shift, by observing the flame at a right angle to the direction of gas motion.

Since the expected change in wavelength is less than 0.1 Å, it is extremely important that the intrinsic width of the spectral line be as small as possible. In the case of a sufficiently thin flame, when absorption in it can be neglected, the line width is determined by the thermal motion of the emitting atoms (Doppler effect) and by perturbing collisions with neighboring atoms and molecules. It is interesting to note that, as the temperature rises, these two factors affect the half-width of the line in opposite ways. As calculation shows, beginning at 1600° K, the half-width of the sodium \(D\)-line should practically no longer depend on temperature. However, the line broadening due to absorption, as is known, depends on the shape of the line. Therefore, at low temperature and high pressure, when the line shape is determined chiefly by perturbing collisions, the half-width of the line proves to be greater than at high temperature and low pressure, when the Doppler effect plays the main role. Obviously, in order to reduce the broadening of the line under the influence of absorption, the concentration of sodium vapor in the flame must be minimal. Usually, to obtain radiation of the required intensity, the amount of sodium present in the rocket fuel (alcohol) as an impurity is sufficient.

For measuring the velocity and pressure of the gases, an apparatus was assembled as shown in Fig. 1. The change in wavelength of the sodium \(D\)-line was determined with a Fabry–Perot interferometer. Since the sodium \(D\)-line is a doublet, the distance between the plates of the interfero-

*) F. P. Bundy, H. M. Strong and A. B. Gregg, J. Appl. Phys. 22, No. 8 (1951).

Fig. 1.

Fig. 2.

was selected so that the interference maxima of both lines (5890 Å and 5896 Å) coincided. To eliminate the effect of vibrations, unavoidable during rocket combustion, the interferometer was placed in a protective chamber mounted on an antivibration support. In front of the interferometer there was placed a filter transmitting the sodium \(D\)-line but opaque to extraneous light.

The gas velocity was determined from two photographs of the interference pattern, obtained when observing the flame in two different directions \(\theta_1\) and \(\theta_2\) (Fig. 2). These directions were chosen so as to reduce as much as possible the influence of the complex structure of the flame on the measurement results. The change in wavelength \(\delta\lambda\) was calculated, as usual, from the change in the diameter of the interference rings in the two photographs, compared with the aid of a recording microphotometer, after which, from the relation

\[ \frac{\delta\lambda}{\lambda}=\frac{v}{c}(\cos\theta_1-\cos\theta_2), \]

where \(c\) is the speed of light, the gas velocity \(v\) was determined. On the basis of the average of 12 experiments, the gas velocity was found to be

\[ (2.3 \pm 0.15)\cdot 10^5 \ \text{cm/sec}. \]

To measure the pressure, the flame was observed in a direction perpendicular to the direction of gas motion, so that the Doppler shift was excluded. As in the measurement of the gas velocity, two photographs of the interference rings were compared: one corresponding to a definite region of the flame; the other obtained when the interferometer was illuminated by a standard sodium lamp, in which the pressure is very low. The change in wavelength of the sodium \(D\)-line found in this way made it possible to determine, from the calibration curve, the gas pressure in the corresponding portion of the flame. The calibration curve, giving the relation between the change in wavelength and the absolute gas pressure, was obtained by determining \(\delta\lambda\) in a flame with a known gas pressure of the same composition.

The results of measuring the pressure in various parts of the rocket flame are given in Fig. 2.

The accuracy of the pressure measurement is estimated by the authors as \(\pm 0.3\) atm.

I. L.