1 Introduction

Flow visualization techniques are of great interests in fluid mechanics, because these techniques can provide useful information about complex three-dimensional structures which have been recognized to play an important role in turbulent flows and would help further understand the physical mechanisms of turbulence. In the compressible regime, widely used techniques, such as shadowgraph and schlieren methods, are limited to investigate the three-dimensional feature of coherent structures, due to the spatial integration of such methods. The development of laser-based techniques, which avoid the spanwise integration effects of schlieren and shadowgraph, provide more powerful tools to visualize the instantaneous three-dimensional structures in compressible turbulence. For example, Smith and Smits (1995) observed the large-scale motions in a supersonic turbulent boundary layer using planar laser Rayleigh scattering. Huntley and Smits (2000) used CO2-enhanced filtered Rayleigh scattering (FRS) to visualize the boundary layer transition on a sharp-nosed elliptic cone at Mach 8, and found that the transition begins with the emergence of small-scale structures near the centerline axis of the cone. Danehy et al. (2009) used the planar laser induced fluorescence (PLIF) to acquire qualitative data about the flow structures of a Mach 5 transitional boundary layer over a discrete hemispherical roughness element. The recently developed Nano-tracer planar laser scattering (NPLS) technique has provided another useful tool to visualize the coherent structures in supersonic and hypersonic flows (Zhao et al. 2009; He et al. 2011).

Though these flow visualization techniques have been applied widely in the studies of compressible flows, flow visualization results are not sufficient and improved quantitative parameter measurements are needed. For example, PLIF could perform instantaneous non-intrusive planar measurement of many flow parameters including density. Hence, it plays an important role in visualization and diagnosis of flow and combustion (Danehy and O’Byrne 1999; Geng et al. 2006). Miles and Lempert first performed Rayleigh scattering flow visualization, discussed and then validated the feasibility of this method to measure flow parameters (Miles and Lempert 1990). Subsequently, Rayleigh scattering has been applied widely, especially in measuring density distribution of the flow field (Panda and Seasholtz 1998, 1999; Wang et al. 2001; Mielke et al. 2006). Tian et al. (2009) also performed a density measurement based on the NPLS images of supersonic flows. In addition, He et al. (2013) performed simultaneous density and velocity measurements in a supersonic turbulent boundary layer based on NPLS images.

However, these are still many difficulties for flow visualization quantitative measurements, as most measurements are based on the image gray-level information which are determined by the intensity of the scattered light. Scattered light is affected not only by the parameters of the tracer (such as the concentration, diameter and refractive index) but also influenced by the intensity of the incident light. If the incident light intensity is nonuniform (as in most cases) or fluctuates with time, the scattered light intensity as well as image gray-level information is affected, and modify the measurement. Even if the experiment has been designed very carefully, it is still very difficult to ascertain whether the intensity of the incident light is uniform and does not fluctuate with time.

To improve the flow visualization technique and provide more accurate quantitative information, the polarization properties of the light scattered by the tracers can be taken into account. Compared with traditional imaging techniques, polarization imaging provides information of degree and angle of linear polarization, instead of just the intensity information.

Polarization imaging has been widely used in target detection, atmospheric detection, earth resources investigation, medical diagnostics, material classification and many other applications. However, its use in flow visualization has been rare. For example, Porcar and Prenel (1976) successfully visualized the effect of a parietal injection on the flow inside an ejector operating without an induced stream by using the polarization properties of the scattered light. Desevaux et al. (1994) took advantage of the polarization properties of the light scattered by the particles in a flow, to investigate the mixing of a supersonic jet with a subsonic induced stream inside an induced flow ejector.

Other methods only used the polarization properties to separate different scattered light sources. For example, Ganapathisubramani et al. (2005) used three cameras to measure velocity components in two differentially separated planes, and used orthogonal polarizations to separate the scattered light from the two planes onto the respective cameras. Kim et al. (2006) studied the three-dimensional topology of a zero pressure-gradient turbulent boundary layer, using the polarization characteristics to minimize the spurious particle images of the two orthogonal planes. A similar application has also been performed by Hellström et al. (2015) to investigate the evolution of large-scale motions in turbulent pipe flow. While the information from the degree and angle of polarization has been widely applied in other fields, it has seldomly used for flow visualization studies.

The limitation of polarization imaging in flow visualization is partly due to the fact that the tracer usually used has a diameter of micrometer scale and the scattered light is unpolarized. On the other hand, the nanoscale tracers used in supersonic or hypersonic flow are in the Rayleigh scattering regime, and the scattered light contains polarization information. Traditionally, the real-time measurement of the polarization is prevented due to the limits of conventional hardware.

Due to the development of the real-time polarization imaging sensor and the NPLS technique which uses nanoparticles as tracers, the application of polarization imaging in flow visualization has now become possible. The purpose of this paper is to verify the polarization imaging technique for flow visualization of compressible flow, and compare its effect with traditional imaging methods. We select the interaction between a shock wave and a boundary layer (SWBLI) as the target flow, because this flow is a common occurrence in supersonic and hypersonic flow, which includes not only complex flow structures such as shock wave, expansion wave, boundary layer and shear layer, but also because the density and velocity of this field change strongly. This target flow is very suitable for verifying the validation of the polarization imaging technique for supersonic and hypersonic flow.

2 Experimental details

2.1 Flow facility

These experiments were performed in a low-noise supersonic wind tunnel at the Aerodynamics Laboratory of the National University of Defense Technology. Figure 1 shows the arrangement of the equipment. The tunnel operates in a vacuum-indraft mode, and the Mach number can be set from 2 to 4 by changing different nozzles. The test section is 250 mm long, 120 mm high and 100 mm wide, and each wall has a glass window along the entire test section length which provides ample optical access from either side. In this present study, the tunnel was operated at Mach 3.4 with a stagnation pressure of 0.1 MPa and a stagnation temperature of 300 K. Table 1 shows the flow parameters that were used.

Fig. 1
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Photograph of the supersonic wind tunnel

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Table 1 Flow conditions
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2.2 NPLS technique

To visualize the flow structure of the SWBLI, the NPLS technique was applied which has been used in many previous experimental studies, such as a supersonic mixing layer (Yi et al. 2009), supersonic flow over double ramp (Zhang et al. 2013), a shock wave/turbulent boundary layer interaction (He et al. 2014), as well as a compression ramp (Wu et al. 2015). This technique is based on the planar laser scattering technique and uses nanoscale particles as tracers, which provides a good flow-following ability in supersonic or even hypersonic flows. Since the nanoscale particles have a characteristic size less than the wavelength of the incident lights, the scattering by the tracers is in the Rayleigh regime, therefore, the scattered light is mostly polarized light, which is suitable for polarization imaging.

In the present experimental study, titanium dioxide (TiO2) particles with a manufacturer-specified nominal diameter of 5 nm were used as tracers. A nanoparticle generator broke up the large agglomerated nanoparticles, and then selected and delivered nanoscale particles into the upstream of the setting chamber of the wind tunnel. The seed particles were illuminated by a double-pulsed Nd:YAG laser in the test section, with a 350 mJ pulsed energy and a 6 ns pulse duration at a wavelength 532 nm. The linearly polarized laser beam was delivered by an articulated mirror arm and formed into a laser sheet with a minimum thickness of about 0.5 mm using cylindrical and spherical lenses. A half-wave plate was used to change the polarization direction of the beam to maximize the scattering signals in the imaging plane, due to the polarization dependence of Rayleigh scattering. A polarization camera instead of an ordinary CCD camera was used as the imaging system. A detailed description of this polarization camera is given in Sect. 2.3. The laser and the polarization camera were connected to a host computer via a synchronizer which controls the timing of laser illumination and image acquisition. Figure 2 shows a schematic depicting the NPLS system.

Fig. 2
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Schematic of the NPLS system

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2.3 Polarization imaging system

A polarization camera with a resolution 2448 × 2048 pixels was used as the imaging system. Acquisition of polarization information with a normal camera allows only changes in intensity as a polarization filter rotates in front of the camera. In this specialized camera, each 2 × 2 group of pixels are covered with a pixel pitch-matched micro-polarization filter with four different orientations that are each offset by 45°. The orientations of each filter are defined in Fig. 3. Therefore, this polarization camera is able to obtain simultaneously the light from four different polarization directions, without mechanically adjusting the polarization filter or any other parameters. Both the degree and angle of linear polarization can be computed across the entire imaging array for group, with a total resolution of 1224 × 1024 pixels. This camera is connected to the host computer via a USB3 connector. The readout is 75 frames per second.

Fig. 3
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Schematic of the micro-polarization filter array on a neighborhood of 2 × 2 pixels

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2.4 Shock wave generator

The test boundary layer developed in a nominally zero pressure gradient along the bottom floor of the test section, with transition occurring naturally upstream in the nozzle section. A wedge with a flow deflection angle of 15° was used to generate the incident shock wave which was placed in the freestream and spanned approximately the entire test section width. A schematic representation of the experimental arrangement and a photograph of the model in the test section are shown in Fig. 4a, b respectively. A Cartesian coordinate system is adopted with the x, y, and z axis directed along the streamwise, wall normal and spanwise direction, respectively. The origin is located on the extrapolated wall impact point of the incident shock wave. In the present studies, the flow visualization of the SWBLI was performed in the streamwise-wall-normal plane (xy-plane) along the centerline of the test section.

Fig. 4
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Experimental arrangement of the SWBLI

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3 The effectiveness of polarization imaging for flow visualization

To prove the effectiveness of polarization imaging in flow visualization of supersonic flows, a validation experiment was initially performed to determine the range in which the polarization imaging can be applied. It is important to note that light scattering characteristics from particles in the moving air flow in the test section of wind tunnel and the still water are nearly the same. In validation experiments, particles were added to still water in a rectangular glass box. Therefore, the polarization imaging of particles added in the still water is the same as that in the moving air.

Here, two types of particles were used for this study. The first type was hydrophilic TiO2 which are nanoparticles with a nominal diameter of 5 nm (the same as adopted in the NPLS technique), which corresponding to Rayleigh scattering. The second type were hollow glass spheres with a nominal diameter of 20 μm, which corresponding to Mie scattering.

The gray-scale images obtained from different polarization filters of two different particle types are shown in Figs. 5 and 6, respectively. In Fig. 5, the obvious difference in the gray scale of these four images can be observed. The gray scale from the 0° polarization filter is at the maximum (average gray value is 143), while the gray scale from the 90° polarization filter is at the minimum (average gray value is 13). The gray scale from the 45° and 135° polarization filters are nearly the same (average gray values are 83 and 92, respectively). However, there were still some large particles in the water, which corresponded to the white points in these images. The four images in Fig. 5 show that the light scattered from the nanoparticles has obvious polarization characteristics, and this measurement agrees with the theory of Rayleigh scattering. The degree of linear polarization (DOLP) and the angle of linear polarization (AOLP) can be calculated from these four images according to Eq. (1).

$$\begin{aligned} P & = \frac{{\sqrt {\left( {I_{0} - I_{90} } \right)^{2} + \left( {I_{45} - I_{135} } \right)^{2} } }}{{I_{0} + I_{90} }} \\ \theta & = \frac{1}{2}\arctan \frac{{I_{45} - I_{135} }}{{I_{0} - I_{90} }} \\ \end{aligned}$$
(1)

Here P is the DOLP value, which is a quantity used to describe the portion of the linear polarized light in the total scattered light. While θ is the AOLP value, it is stands for the angle of scattered light at which the light is all polarized. Circularly polarized light is neglected for these measurements.

Fig. 5
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Original pictures of nanoparticles obtained from filters with four different orientations

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Fig. 6
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Original pictures of hollow glass spheres obtained from filters with four different orientations

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Compared with Fig. 5, there are no obvious differences between the gray-scale images from different polarization filters in Fig. 6. The average gray values for these four images are 185, 146, 116 and 168, respectively. Because the light scattered from micron particles corresponds to Mie scattering, the polarization characteristics of the scattered light is weak, and therefore, the difference among the scattered light from different polarization filters are relatively small. This statement is also reflected in the DOLP results (Fig. 7).

Fig. 7
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DOLP results calculated by images from different polarization filters

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Figure 7a, b are the DOLP results calculated from the four images in Figs. 5 and 6, respectively. The distribution of DOLP is nearly uniform in Fig. 7, because the hydrophilic TiO2 nanoparticles were distributed uniformly in the water. The average DOLP result of Fig. 7a is 0.86, while the average DOLP of Fig. 7b is only 0.29. This result again shows that the light scattered from nanoparticles has obvious polarization characteristics compared with the micron particles.

Figure 8a, b are pseudo-color images (using the colormap ‘jet’) calculated from Figs. 5a and 6a, respectively. These images are used for quantitative comparison with DOLP results. Unlike the uniform distribution of the DOLP result, a slight nonuniform distribution of gray scale in Figs. 5a and 6a can be observed clearly from the color change. These results are probably due to the nonuniform distribution of the incident light, as the particles were distributed uniformly in the water. To quantitatively compare the gray-scale image with the DOLP results, a statistical analysis is shown in Table 2. The coefficient of variation (CV%) of the DOLP result of nanoparticles is 8.33%. This value is nearly one-third of the gray-scale result. This result reveals that the nonuniform distribution of incident light has a lesser effect on the DOLP result than the gray-scale information. However, the CV% of DOLP result of the micron particles is larger than the CV% of Fig. 6a. This comparison can also explain why the polarization imaging is seldom applied to flow visualization, as the micron particles usually used in flow visualization have little polarization characteristics, and therefore, the DOLP results have no advantage over the gray images. But when nanoparticles were adopted as tracers for supersonic/hypersonic flow visualization, the effect of using polarization imaging can easily be seen, and the influence of nonuniform spatial distribution of the incident light will be weakened.

Fig. 8
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Pseudo-color images calculated by images obtained from the 0° polarization filter

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Table 2 Statistical information of experimental results
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4 Results and discussions

4.1 Visualization of the structures of the SWBLI using polarization imaging

To verify the practical effect of polarization imaging, an experiment that measured SWBLI was performed. Figure 9a is the gray-scale image of the instantaneous structures of the SWBLI in the xy-plane obtained from the 0° polarization filter, while Fig. 9b is the image of Fig. 9a after a contrast adjustment that was used to enhance the visual effect. The flow is from left to right, and the field of view is x = − 70–10 mm and y = 0–40 mm. The digital resolution is approximately 84.2 µm/pixel. In Fig. 9b, the incident shock wave is clearly discernible in the upstream region. The shock-wave angle measured from the image is 29.8°, and the theory value calculated from the oblique shock relations has a deflection angle of 15° is 29.71°. However, the expansion wave generated from the tail of the shock wave generator affects the incident shock wave, and a slight bend of the incident shock wave can be observed. The incident shock is strong enough to induce a separation of the incoming turbulent boundary layer. Besides, the scattered light from the wall can also be observed, which influences the flow visualization in the near wall region.

Fig. 9
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Flow visualization of SWBLI using gray-scale images (obtained from the 0° polarization filter)

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The DOLP results calculated from the gray-scale image of Fig. 9a and gray-scale images from the other polarization filters at the same time are shown in Fig. 10, which have been normalized from these uncalibrated gray-scale images. Figure 10a is the DOLP image using the “GrayScale” color map, to compare with the gray-scale images of Fig. 9a. Figure 10b is the DOLP image using the “Small Rainbow” color map, where the variation of the DOLP can be visualized more clearly. It can be seen that the instantaneous structures of SWBLI displayed by the DOLP result is the same as the gray-scale image of Fig. 9, showing that the polarization imaging is also suitable for the flow visualization of supersonic flows. However, the incoming turbulent boundary layer is clearer in the DOLP image than that in the gray-scale image. The scattered light from the wall is weaker obviously in the DOLP image, because the scattered light from the wall is not polarized light so that the DOLP result will be small.

Fig. 10
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Flow visualization of SWBLI using the DOLP

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As mentioned by Tian et al. (2009), there is a proportional relationship between the gray scale of image and the local gas density. From Fig. 10b we can find that the DOLP result will increase through the incident shock wave, where the local gas density is increased. Through the reflected shock wave, the DOLP result is increased again. The DOLP results are relatively small in the turbulent boundary layer and the separation bubble, where the local gas density is low. Although it has not been confirmed, there should also exist a relationship between the DOLP results and the local gas density. This effect may provide a new way for local gas density measurement using the DOLP technique.

4.2 Image fusion of the DOLP result and the gray-scale image

Image fusion is a signal processing technique that can combine information received from different sensors into a single composite image in an efficient and reliable manner (Stathaki 2008), which has been widely applied into many fields such as the defense industry, robot vision, digital camera application, medical imaging and satellite image. In the present experiments, both the gray-scale images and the DOLP images of the same object are obtained using the polarization imaging. It makes the image fusion possible without additional image obtained by other sensors. Because the DOLP image are calculated from the gray-scale images, both the gray-scale image and the DOLP results have the same size and the same spatial location. Therefore, the procedure of image registration during image fusion can be skipped.

In this section, examples of image fusion of the present results are shown below, and a subjective assessment and a quantitative analysis of the original images and the fused images are discussed to compare the effect of image fusion. Figure 11a is the original gray-scale image of SWBLI at another moment obtained from the 0° polarization filter. The reason why we selected the original image instead of the normalized image is that different normalization methods would affect the quantitative analysis results of image fusion. Figure 11b is the gray-scale image converted from the DOLP results, where the DOLP value 1 corresponds to gray level 255 while the value 0 corresponds to gray level 0, to ensure that the histogram of the polarization information will not be changed. The calculation of DOLP not only normalizes the image, but also enhances the image. When the DOLP information is converted to gray information again, the resulting image of Fig. 11b is obviously brighter than the original gray image of Fig. 11a, c, d are fused images from Fig. 11a, b, using 2-D wavelet decompositions at level 2 using ‘db2’ by taking two different fusion methods. Figure 11c is fused by taking the mean value of the coefficients for both approximations and details, while Fig. 11d is fused by taking the mean value of the coefficients for approximations and the maximum value of the coefficients for the details.

Fig. 11
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Image fusion of the gray-scale images and the DOLP images

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From a subjective assessment, the fused images are clearer than both the gray-scale image and the DOLP image. The image in Fig. 11d is clearer than Fig. 11c as the details are enhanced. Because both the original gray-scale image and the DOLP image display the same coherent structures as the other images, they can also further increase the definition of these structures, such as the small-scale structures in the incoming boundary layer and the separation zone.

Some common quantitative analysis parameters of these images are calculated and presented in Table 3. In this table, the maximum value of each parameters is indicated in bold type. The average value, standard deviation and information entropy of Fig. 11b (DOLP image) are larger than those of Fig. 11a (original gray-scale image). This difference indicates that the image quality of DOLP image is better than that of the gray image. Even if both images are enhanced after contrast adjustment, the same result can still be obtained. The average gradient, edge intensity and contrast of Fig. 11d are larger than those of DOLP image and gray-scale image. This observation shows that the sharpness of the fused image is enhanced compared with the original images, and the visual effect of the fine structure in flow visualization is improved through image fusion. However, the average gradient, edge intensity and contrast of Fig. 11c are still smaller than those of the DOLP image, suggesting that the selected method of image fusion plays an important role in improving image quality. There still are many other quantitative parameters for image quality evaluation that are not discussed, and there will be better methods of image fusion to improve the image quality in future analyses. The present results show that polarization imaging provides an opportunity for the fusion of polarization information and gray information. When the fused images are enhanced by a suitable method, they will further provide more information of interest and be convenient for image analysis and processing from the viewpoint of digital image processing.

Table 3 Quantitative analysis parameters of images
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4.3 The quantitative comparison of the polarization result and the gray-scale image

Besides flow visualization, the quantitative measurement based on the visualization results is also very important. Usually the gray information is used to calculate quantitative parameters, such as the density of gas. However, there are many factors would affect the gray information, such as the variation of the incident light at different times. To compare the influence of incident light variation on the DOLP results and the gray information, a statistical analysis of the gray information and the DOLP results with time have been performed. First, two regions of the field of view are selected as shown in Fig. 12. Region 1 is located upstream of the incident shock wave, while Region 2 is located downstream of the shock. The size of both two regions is 50 × 50 pixels (about 4.2 × 4.2 mm2). These two regions are in the uniform area. If the incoming conditions are not changed, the local gas density in Region 1 and Region 2 should not change over time. Ideally, the parameters (gray information for example) obtained from the flow visualization should be nearly identical.

Fig. 12
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Schematic of the selected regions through the incident shock wave

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The statistical analysis of gray-scale information and DOLP results in Region 1 and Region 2 from 33 samples (with 5 Hz sample rate) were carried out for comparison. The results are shown in Figs. 13 and 14 and in Table 4. Here, \(I_{1}\) and \(I_{2}\) represent the mean gray information of each sample in Region 1 and Region 2, respectively, and the mean values \(\bar{I}_{1}\) and \(\bar{I}_{2}\) represent the mean gray information obtained by statistical analysis of these 33 samples. The mean values are used to nondimensionalize the results. The definition of the DOLP is the same as for the gray information.

Fig. 13
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Comparison of the gray information and the DOLP results in Regions 1 and 2 of each sample

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Fig. 14
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Comparison of the ratio of DOLP and the gray-scale values through the incident shock wave of each sample

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Table 4 The coefficient of variation of different parameters
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As shown in Fig. 13, there are obvious variations of \({{I_{1} } \mathord{\left/ {\vphantom {{I_{1} } {\bar{I}_{1} }}} \right. \kern-0pt} {\bar{I}_{1} }}\) and \({{I_{2} } \mathord{\left/ {\vphantom {{I_{2} } {\bar{I}_{2} }}} \right. \kern-0pt} {\bar{I}_{2} }}\) with time. The CV% of \(I_{1}\) and \(I_{2}\) are 2.9% and 2.91%, respectively (Table 4). The variations of gray information may be due to the variation of the incident light intensity, as the energy of each laser pulse is not exactly the same. Besides, the variation of the tracer concentration in the upstream of the wind tunnel can be another reason for the variation. As a result, if a gas density measurement based on the gray information was made, the variation of gray information would affect the result. However, the variations of the DOLP results with time are less than the gray information. As shown in Fig. 13, the maximum of \({{I_{1} } \mathord{\left/ {\vphantom {{I_{1} } {\bar{I}_{1} }}} \right. \kern-0pt} {\bar{I}_{1} }}\) is about 1.08%, while the maximum of \({{{\text{DOLP}}_{1} } \mathord{\left/ {\vphantom {{{\text{DOLP}}_{1} } {\overline{\text{DOLP}}_{1} }}} \right. \kern-0pt} {\overline{\text{DOLP}}_{1} }}\) is less than 1.02%, while the CV% of DOLP1 and DOLP2 are 0.69% and 0.47%, which are about one-fifth of the variation of the gray information. Figure 14 shows that the ratio of DOLP and the gray information in the selected regions through the incident shock wave also have the same tendency. The CV% of I1/I2 (1.12%) is less than the CV% of I1 (2.9%) or I2 (2.91%), and the CV% of DOLP1/DOLP2 (0.36%) is about one-third of the CV% I1/I2. Though there are only 33 samples, the tendency that the variation of DOLP is much less than the variation of the gray-scale results can still be identified.

The variations of the incident light intensity with time would affect the gray information of the flow visualization images. However, these variations would affect the gray information from the micro-polarization filter with four different orientations simultaneously. That is why the DOLP results, calculated from these four gray-scale images, would suffer less from the variation of incident light intensity than the gray information. It is implied that the quantitative measurement such as density based on the DOLP results would provide a higher accuracy than that the gray information, because the influence of the fluctuation of incident light with time is weakened by polarization imaging. If the DOLP results instead of the gray information are used in the particle image velocimetry (PIV) technique to perform the velocity measurement through cross-correlation calculation, it is possible that the accuracy of velocity measurement can be improved.

5 Conclusions

The flow visualization of a SWBLI has been performed using the polarization imaging method, which uses the DOLP information instead of the gray information to visualize the instantaneous structures of supersonic flows. To use this technique, first a validation experiment was performed to determine the application range of polarization imaging. The experimental results showed that polarization imaging will be effective when using nanoparticles instead of microparticles as tracers, and weaken the influence of nonuniform spatial distribution of the incident light.

Visualization results of the instantaneous structures of a SWBLI show that the DOLP results are the same as the gray-scale images. This observation shows that polarization imaging is suitable for the flow visualization of supersonic flows. And the DOLP results have been normalized without any image calibration. In addition, the polarization imaging provides an opportunity to combine gray information with the polarization information through image fusion. Through appropriate image fusion techniques, the flow visualization effect will be further improved.

A quantitative comparison of the information of the polarization images and the gray-scale images indicates that the DOLP information would suffer less than the scattered light itself, when the intensity of the incident light fluctuates with time. Though further investigations of polarization imaging are still needed, the present results demonstrate that quantitative measurement based on polarization information can provide a higher accuracy than that only based on gray information.