Aero-Optical Measurement in Shock Wave of Hypersonic Flow Field

Abstract

Hypersonic flow field around a flight vehicle has density fluctuating elements such as shock wave and boundary layer. Since refractive index of light is related to density of medium, light propagation path changes while passing through the flow field. Influence of flow field property on optical characteristics is called aero-optics. As in Fig. 1, aero-optics distorts the image obtained by an optical instrument on the flight vehicle and degrades light intensity, displaces the position of an object, blurs the image, etc. To avoid these effects, various studies were conducted to relate optical characteristics with flow characteristics and to measure aero-optical aberration.

Introduction

Hypersonic flow field around a flight vehicle has density fluctuating elements such as shock wave and boundary layer. Since refractive index of light is related to density of medium, light propagation path changes while passing through the flow field. Influence of flow field property on optical characteristics is called aero-optics. As in Fig. 1, aero-optics distorts the image obtained by an optical instrument on the flight vehicle and degrades light intensity, displaces the position of an object, blurs the image, etc. To avoid these effects, various studies were conducted to relate optical characteristics with flow characteristics and to measure aero-optical aberration [1–3].

Fig. 1

Aero-optics induced by flow field near-flight vehicle

The optical instrument for aberration measurement is essential for aero-optics experiment, and recently a device called Shack-Hartmann sensor is developed. Wind tunnel experiment conducted at Arnold Engineering Development Center (AEDC) validated the performance of Shack-Hartmann sensor. In this research three devices were used to measure optical aberration. Imaging camera system (ICS) and X-Y detector were used to measure far-field pattern directly, and Point Spread Function (PSF) calculated from Shack-Hartmann sensor used to measure near-field pattern. Far-field pattern from ICS and PSF from Shack-Hartmann sensor were compared and both showed similar result [3].

Generally wind tunnel is used to demonstrate flow field on the ground. For hypersonic flight condition, enthalpy should be much higher than atmospheric temperature since nozzle expansion ratio is huge. Usually shock tunnel is used to increase enthalpy since the operation cost is relatively cheap and operating is simple than other high-enthalpy facility.

In this research aero-optical characteristics at shock wave in hypersonic flow field is studied. A wedge model is installed inside a hypersonic shock tunnel to demonstrate flow field on the ground. Optical aberration induced on light propagating through flow field is measured using Shack-Hartmann sensor.

Experiment Setup

Facility

AST-1 shock tunnel in the Aerospace Propulsion and Combustion Laboratory (APCL) at Seoul National University (SNU) is used to demonstrate hypersonic flow field on the ground [4]. Figure 2 is the image of AST-1 shock tunnel. Nitrogen is used for driver gas and air is used for driven gas. PET film is used as the diaphragm for both ends of the driven tube to split the gases. Thickness of PET film is varied to conduct experiment on different free-stream conditions. Two types of nozzle are used to produce Mach 7 flow. One is conical nozzle and another is contoured nozzle. A conical nozzle has constant wall inclination and a contoured nozzle has a different wall inclination designed by method of characteristics (MOC) [5]. The exit diameter of a conical nozzle is 150 mm and of a contoured nozzle is 189 mm. Flow property at each nozzle exit is validated using pitot rake and wedge model. Pitot rake measured stagnation pressure on nozzle radial direction, and wedge model validated the Mach at the nozzle exit. From pitot rake measurement, effective nozzle diameter is also conducted. Conical nozzle has Mach 6.8 flow at the exit and effective diameter is 120 mm. Contoured nozzle has Mach 7 flow at the exit and effective diameter is 144 mm. Size of a test section is 300 × 300 × 600 mm. The test section has a window on each side for flow visualization and one window on top for aero-optical measurement.

Fig. 2

AST-1 shock tunnel at SNU

Experiment Model

Aero-optics experiment model is installed in AST-1 as in Fig. 3. The left image in Fig. 3 is a schematic diagram of aero-optics experiment model, and the right image in Fig. 3 is an image of aero-optics model installed in shock tunnel test section. Aero-optics model consists of four parts: laser, optical components, sensor, and model. A laser beam becomes a plane wave through a collimation lens, propagates through flow field around wedge model, is guided with mirror, reduces to beam size appropriate for optical sensor aperture, and finally is captured by optical sensor, and optical aberration information is acquired.

Fig. 3

Aero-optics experiment model installed in AST-1

A wedge model with 10° angle is used to introduce oblique shock wave to hypersonic flow field. Thickness of the model is 66 mm and height is 50 mm. A window is installed on the surface of the wedge for laser beam path. Diameter of the model window is 45 mm and material is Pyrex. To analyze flow property, stagnation pressure and surface pressure are measured. Stagnation pressure is measured using pitot tube near the wedge front. Measurement result is used to verify Mach number of free-stream flow and pressure loss throughout the nozzle. Position of pitot tube is considered not to affect the flow field on the wedge model. For surface pressure measurement, a pressure hole is placed near the optical window.

Shack-Hartmann Sensor

Shack-Hartmann sensor is one of the optical sensors that measure wave front slope and intensity of incident beam. Figure 4 is schematic of the wave front measurement using Shack-Hartmann sensor. Shack-Hartmann sensor consists of a lenslet array and a Charge Coupled Device (CCD). Incident distorted wave is divided to each lens of the lenslet and focuses to a point. Since CCD is placed at the focal length of the lenslet array, the image of each focused point is captured with CCD. From captured image, position and intensity of the point are analyzed. Comparing the image with reference image, which is usually the image of plane wave captured before each measurement, position difference and intensity difference are obtained. The position difference of focused point is wave front slope at corresponding lens of the lenslet array. From wave front slope matrix at each point, wave front is reconstructed using various methods. Depending on the reconstruction method, the obtained wave front is different. In this thesis, wave front reconstruction is conducted with a modal method using Zernike polynomial. Since Shack-Hartmann sensor measures difference from reference data, only optical aberration is obtained from results. In other words, the effect of aberration induced by optical system itself is neglected during measurement.

Fig. 4

Principle of wave front measurement with Shack-Hartmann sensor

Shack-Hartmann sensor from Lumetrics (model: CLAS-XP) is used for the experiment. Data acquisition and analysis software is also provided from Lumetrics. The frame speed of Shack-Hartmann sensor is 30 hz and shutter speed in the experiment is 0.025 ms. Since the interval between each frame is 33 ms, only one frame is captured during shock tunnel test time. 635 nm diode laser is used as a light source for Shack-Hartmann sensor.

Results

Aero-optics experiment in hypersonic flow is conducted for three altitudes: 29.1, 32.3, and 38.6 km. For each altitude, pressure and temperature are as in Table 1. Since temperature is not controllable in current shock tunnel system, pressure is controlled to match each static pressure. For 29.1 km, p1, which is pressure of driven tube, is 0.76 Mpa and p4 is 8.3–8.5 Mpa (pressure ratio 11); for 32.3 km p1, p4 is same with 29.1 km altitude but conical nozzle is used so pressure loss is introduced. For 38.6 km, two kinds of pressure ratio are used. One condition is that p1 is 0.26 Mpa and p4 is 27.5–28.5 Mpa (pressure ratio 11). The other condition is that p1 is 0.09 Mpa and p4 is 6.9 Mpa (pressure ratio 76.7) which is the case for 1.5 higher temperature. But since there is not much difference between low temperature and high temperature, the temperature effect is neglected and condition two is considered as same altitude condition. For each experiment, wave front information is acquired, and PSF is calculated. From PSF Bore Sight Error (BSE), Strehl ratio is obtained. From wave front information, certain tilt induced by shock wave is observed. Figure 3.17 is typical wave front information acquired, and Table 3.4 is all of the aero-optics experiment data acquired with Shack-Hartmann sensor.

Table 1 General pressure and temperature of atmosphere at each altitude

All of the BSE, tilt, and Strehl ratio are plotted as in Fig. 5 and Strehl ratio is plotted as in Fig. 6. The error bar at each graph represents 95 % confidence interval on the mean. Standard deviation is acquired for each set of altitude population mean estimated. The average value and maximum value for each altitude are presented as Table 2.

Fig. 5

BSE and tilt depending on stagnation pressure

Fig. 6

Strehl ratio depending on stagnation pressure

Table 2 Average and maximum value of aero-optical characteristics

There seems no relation between maximum value and altitude. For the average value, BSE and tilt increase when altitude is decreased, and Strehl ratio is increased while altitude is increased. Since air is sparser at lower altitude, effect of aero-optics seems to be less. In hypersonic flow field, shock wave induces BSE of 80–150 μrad and it means that when the target is 10 km far away, 0.8–1.5 m position error will occur. Overall light system performance, which is Strehl ratio, will also decrease for 0.8.

Conclusions

Experiment is conducted to study hypersonic flow field characteristics. Shock tunnel is used to demonstrate hypersonic flow field on the ground. Conical nozzle and contoured nozzle is used to generate Mach 7 flow. Wedge model with pitot tube is used to measure Mach and pressure loss. Pitot rake is used to measure flow distribution by radial direction. Conical nozzle has Mach 6.8 flow at the exit and effective diameter is 120 mm. Contoured nozzle has Mach 7 flow at the exit and effective diameter is 144 mm.

Aero-optics experiment model is designed and installed inside shock tunnel test section to study shock wave effect on aero-optical characteristics. 10° wedge model is used to generate shock wave. 635 nm diode laser, which is the object of Shack-Hartmann sensor, is directed perpendicular to wedge model surface. Aero-optics experiment is held for conical and contoured nozzle. In hypersonic flow field, shock wave induces BSE of 80–150 μrad, and it means that when the target is 10 km far away, 0.8–1.5 m position error will occur. Overall light system performance, which is Strehl ratio, will also decrease for 0.8.