Velocity measurements in a flow field have attracted significant attention in the development of aerospace technology and aerodynamics.^[1,2] Previous measurement systems have tended toward hot wire/hot film anemometry,^[3] time-resolved particle image velocimetry (TR-PIV),^[4] and laser Doppler velocimetry (LDV).^[5,6] Hot wire/hot film anemometry, along with contact gauges, has always been used in subsonic and transonic speed fluidic velocity measurements. The TR-PIV and LDV, which are based on tracer particles, have been developed for steady flow velocity measurement. However, their precision is affected by particle-adding technology and trace particle-following features, which restricts their development and application in unsteady flow velocity measurements.

Knowledge of interferometric Rayleigh scattering (IRS) dates back to the 20th century. It is mainly based on a Fairy– Pérot (F-P) interferometer, which is used to discriminate the Rayleigh scattering (RS) spectrum accurately.^[7–10] Then, IRS can be used for the non-contact measurement of flow velocity, flow temperature, and gas density.^[11–14] Recently, many institutes have successfully used photomultiplier detectors to achieve RS signals. The Glenn Research Center of NASA reported that interferometric rings that corresponded to RS were imaged by using different photomultipliers, and the spectral profile and flow velocity were then acquired via complicated picture-processing arithmetic.^[15–20] Although the amplification factor of a photomultiplier was large, spectral rings were obtained by using only a few photomultipliers, thereby reducing the spatial sampling rate of the IRS apparatus. To improve the spatial sampling rate, an intensified charge-coupled device (ICCD) was used to image interferometric rings for measuring the instantaneous velocity of flow.^[21,22] However, the systematic temporal sampling frequency was only 10 Hz.

In this study, we demonstrate a measurement system with a high temporal and spatial sampling rate. This system is mainly fabricated based on an F-P interferometer and an electron-multiplying charge-coupled device (EMCCD). Temporal sampling frequency can increase up to 10 kHz, ensuring high spatial sampling frequency. The spectral results suggest that this system can be generalized to the measurement of high-precision velocity and turbulence intensity in supersonic flow.

An incident light interacts with an atom or a molecule, thereby inducing a dipole moment that oscillates and radiates at the frequency of the incident field. This phenomenon is considered as an elastic scattering process because the internal energy of molecules remains unchanged, whereas the frequency of light is changed only via the Doppler effect given bulk motion of molecules. Doppler shift Δv _D can be given by^[21]

(1)

Fig. 1.

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	Fig. 1. Geometric sketch of Doppler frequency-shift.[20]

The minimal variation between the wavelengths of the incident light and the scattered light is attributed to Doppler shift. Taking gas velocity V_k = 100 m/s for example, when the incident light wavelength λ = 532 nm and the angle θ = 90°, the wavelength shift from the incident light is only 2.5 × 10⁻⁵ nm according to Eq. (1). An F-P interferometer was recently used to resolve the RS spectrum.^[23–26] When a parallel beam irradiates the F-P interferometer, sharp interferometric rings can be imaged once the condition is fulfilled, i.e.,^[21]

(2)

(3)

The radius of the ring of the scattered light can be inferred using Eq. (3) as follows:

(4)

Flow velocity turbulence intensity I is then given by^[16]

(5)

The optical arrangement of the time-resolved IRS (TIRS) system is shown in Fig. 2. A coherent 10-W continuous-wave (CW) 532-nm laser with a 2-mm-diameter and 5-MHz linewidth output beam provides the incident light for the system. A small portion of laser energy is extracted by using a beam splitter, to serve as the reference light during measurements. Most of the laser beam is focused by using a 1000-mm focal length lens (L1) into a spot with a diameter of 100 μm at the probe volume. The beam is oriented at an angle of 45° with respect to the primary flow direction, whereas the scattered light is collected at an angle of 90° relative to the incident laser beam. A finite length of the scattered light is imaged by using a pair of lenses (L2 and L3) onto the face of a multimode optical fiber with a diameter of 1 mm. The scattered light and the reference light are then combined via the Y fiber and irradiated parallel to the F-P interferometer. Subsequently, interferometer rings are focused and imaged on EMCCD as shown in Fig. 3(a). The radius of the ring clearly varies between the scattered light and the reference light because of Doppler shift. The corresponding flow velocity V_k can be finally obtained according to Eqs. (1), (3), and (4).

Fig. 2.

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	Fig. 2. (color online) Sketch of the TIRS system.

Fig. 3.

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	Fig. 3. (color online) (a) Interference rings consist of the reference laser (black dotted lines) and the Rayleigh light (black solid lines) scattered simultaneously at different levels (k, k−1). (b) Computational one-dimensional (1D) intensity distributions of F-P interference rings at different laser wavelengths. The inset shows a partially enlarged view.

To characterize the interferometric information according to different wavelengths, 1D distributions of interferometric rings at different wavelengths (532.0000, 532.000025, and 532.00025 nm) are simulated as shown in Fig. 3(b). The aperture and surface reflectivity of the F-P interferometer are set to be 50 mm and 90%, respectively. The focal length of the L5 lens is 1000 mm. The laser linewidth and the angle θ are determined to be 5 MHz and 90°, respectively. The ring radius decreases with the increase of wavelength. Taking the wave-lengths 532 nm and 532.000025 nm for example, the peak separation between the two spectra is approximately 13 μm as shown in the inset of Fig. 3(b), whereas the optimized pixel size is approximately 1.6 μm in the EMCCD image. Hence, velocity resolution in the designed TIRS system can theoretically reach up to 1.23 m/s.

Then, the property of the designed velocity and turbulence intensity measurement system (as shown in Fig. 2) is experimentally realized. Hot wire anemometry is performed and the results are compared with those of the designed system by measuring velocity and turbulence intensity in the same Laval nozzle (Mach number: 1.8). In the measurements, the two apparatuses are independently operated at the same position, that is, 80 mm away from the entrance of the nozzle and 1.5 mm away from the axis of flow. Then, the sampling rate and the sampling time are set to be 5 kHz and 3 s, respectively. Furthermore, inlet pressure is approximately 0.7 MPa. The difference in measured velocity between the hot wire system and the designed system, and the corresponding power results are clearly seen in Figs. 4 and 5, respectively. The distinction between the two apparatuses is small, that is, the velocity and turbulivity results are (280 m/s, 7.08%) and (291 m/s, 6.9%), respectively (as listed in Table 1). Therefore, the designed TIRS system can be used further to measure the flow velocity and turbulence.

Fig. 4.

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	Fig. 4. (color online) (a) Velocity pulsation and (b) power spectrum density (PSD) measured via hot wire anemometry.

Fig. 5.

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	Fig. 5. (color online) (a) Velocity pulsation and (b) PSD measured by using the TIRS system.

Table 1.

Table 1.

Table 1. Measured velocity and turbulence relating to Figs. 4 and 5. . Hot wire Designed apparatus Average velocity/(m/s) 280 291 Turbulence 7.08% 6.98%

Table 1. Measured velocity and turbulence relating to Figs. 4 and 5. .

Subsequently, TIRS measurement is performed during the testing of a supersonic free jet produced by a Laval nozzle with a Mach number of 1.8. The sampling rate is set to be 10 kHz, and the other evaluation parameters are the same as those mentioned earlier. Prior to the measurement, the schisophone result of the nozzle is obtained to display its flow structure (Fig. 6). A stable flow can be achieved by reducing the distance to the entrance of the nozzle d ₁. Then, the TIRS apparatus is used to measure the velocity and turbulence intensity distribution of the nozzle (Table 2). The detecting position is on the axis of flow. First, the change in flow velocity is slow at d ₁ smaller than 30 mm, and turbulence intensity is relatively stable (< 1.5%). Second, flow velocity clearly decreases with the increase of distance d ₁. Third, turbulence intensity is well consistent with the increasing rule. That is, turbulence intensities are at 2.33%, 2.63%, and 4.98% for distance d ₁ values of 40, 50, and 60 mm, respectively.

Fig. 6.

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	Fig. 6. (color online) Shadow graph of the free jet.

Table 2.

Table 2.

Table 2. Measured velocity and turbulence intensity results relating to distance d 1. . d 1/mm 10 15 20 30 40 50 60 70 80 90 100 110 Velocity/(m/s) 518 546 509 518 471 422 402 386 336 318 295 279 Turbulence/% 1.25 1.4 1.2 1.25 2.33 2.63 4.98 5.39 6.98 8.98 9.0 10.27

Table 2. Measured velocity and turbulence intensity results relating to distance d 1. .

A TIRS apparatus for measuring flow velocity and turbulence intensity is designed in this study. The systematic sampling rate can increase to 10 kHz because of EMCCD. The theoretical results show that the velocity resolution of TIRS can reach 1.23 m/s. Further experiments verify that this test system can be used to measure flow velocity and turbulence. Moreover, this apparatus is used to quantitatively measure the velocity and the turbulence distribution of the Laval nozzle. The result is similar to that of a schisophone. By further studing the change in Rayleigh-scattered signals influenced by flow temperature and gas density, the multifunctional apparatus will be used to measure various flow parameters, such as temperature and gas density.