Visualization of invisible phenomena is useful for understanding them. Fluid flow is one of the most popular targets for such visualization owing to its importance in various areas of engineering [1]. For visualizing the fluid flow, optical methods, including Schilieren and laser Doppler techniques [2,3], are commonly used [4] because they can observe a flow field without installing the measuring devices inside the field. In particular, particle image velocimetry, which observes the light scattered from tracer particles, is mainly used [5–7]. It is a well-established method for visualizing and measuring the distribution of the flow velocity recorded by the video camera. Interferometry is also the popular methodology for visualizing flow density. The recent development of parallel phase-shifting interferometry (PPSI) [8,9] enabled accurate measurement of the density, thanks to instantaneous observation of multiple phase-shifted interferograms [10,11].

Recently, simultaneous visualization of flow and sound in air has been realized [12]. The method proposed in that study, called the gas injection method, enables visualization of flow by using a gas whose density is different from the surrounding air. Although the gas injection method achieved high visibility of the incompressible flow, information of sound was hidden by the component of gas flow, since the phase change of light affected by the sound was much smaller than that of gas flow. For simultaneously visualizing multiple physical phenomena, including the fluid flow, the appearance of the flow must be adjusted so that the visibility of the phenomena of interest is arranged in the same order.

In this Letter, a method for optically visualizing a fluid flow by controlling the temperature of the fluid is proposed in order to realize the adjustment of the visibility of the fluid flow. In this method, the density change of a medium depending on its temperature is utilized. An experiment of simultaneous visualization of flow and sound using PPSI, which is the similar condition to Ref. [12], was conducted in order to verify the validity of the proposed method.

First, the theoretical relation between phase of light and temperature is considered. The phase of light passing through a medium is modulated by the refractive index of the medium which depends on the density. Hence, the temperature of the medium affects the phase of light through the relation between the temperature and the density of the medium. In order to investigate the amount of the phase change of light affected by temperature-controlled fluid, the phase of light modulated by the temperature difference between the fluid and surroundings is considered. The working fluid is often air in many practical engineering situations and, thus, air is assumed for the fluid and surroundings in this Letter.

The refractive index and the density of air follow the Gladstone–Dale relation [13]:

Figure 1 shows the relation between the phase of light and the temperature difference from surroundings. The horizontal axis shows the temperature difference from surroundings, and the vertical axis shows the phase of light. The phase of light was calculated from Eq. (6). For the calculation, the following values were used: $k=2\pi /\lambda =1.181\times {10}^7\mathrm{rad}/\mathrm{m}$ (the wavelength of the light $\lambda$ was 532 nm), $n_0=1.000273$, and $T_0=293.15\mathrm{K}$. The temperature $T$ is assumed to be constant on the optical path. The length of the optical path was set to 4, 6, 8, 10, 12, and 14 mm which are merely representative values. Figure 1 indicates that the phase change of about 0.5 rad can be obtained by the temperature difference roughly from $+5°\mathrm{C}$ to $+15°\mathrm{C}$.

 

Fig. 1. Relation between the phase of light and the temperature difference from surroundings. The phase of light was calculated from Eq. (6). ($k=1.181\times {10}^7\mathrm{rad}/\mathrm{m}$, $n_0=1.000273$, and $T_0=293.15\mathrm{K}$ were used for the calculation.) The temperature $T$ is assumed to be constant on the optical path, whose length was set to 4, 6, 8, 10, 12, and 14 mm.

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A basic experiment of visualization of a temperature-controlled fluid flow was conducted in order to verify the above theoretical consideration on the proposed method. First, air was supplied from the pump and heated by the heater installed in a flow path. Then air flow discharged from the hose was visualized in the test section. The temperature of fluid was set to $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$. PPSI was used as an optical measurement device in this experiment. The schematic diagram of the PPSI system is shown in Fig. 2 (see Ref. [12] for details). This system realizes a parallel phase-shifting method [8,9] by combining a polarization high-speed camera with a polarization interferometer. Hence, PPSI enables us to capture high-speed time-varying phenomena [14–16]. Fluid flow is a transient phenomenon; therefore, using PPSI is suitable for visualizing it. Note that the observed images are a projection of three-dimensional information, and we should be careful about that. There are several methods for reconstructing the three-dimensional information [17], including digital holography [11,18], where the proposed method can be combined with them for observing the three-dimensional phenomena.

 

Fig. 2. Schematic diagram of PPSI used in the experiment [12].

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Figure 3 shows the results of visualization and the comparison between theoretical and experimental values of the phase of light. The conditions of temperature correspond to $+5$, $+10$, and $+15°\mathrm{C}$ in order, from the top of Fig. 3. The right side of the figure shows visualized images of a fluid flow discharged from the hose. The color indicates the phase of light, and the range is from $-2$ to 2 rad. The left side of the figure shows the comparison between the theoretical and experimental values of the phase of light. The red line shows the theoretical value, and the blue line shows the experimental value. The theoretical value was calculated from Eq. (6), where the integral distance was determined from the inner diameter of the hose which was approximately 7 mm (that is, the maximum integral distance was 14 mm). The experimental value was extracted from one line near the hose of the visualized images. It can be seen from the left side of the figure that the experimental value approximately agrees with the theoretical value. As a result, obtaining the change of the phase of light due to the temperature-controlled fluid was experimentally confirmed.

 

Fig. 3. Comparing theoretical value with the experimental value. The temperature differences from surroundings were $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$, from top to bottom.

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Another experiment of simultaneous visualization of flow and sound using PPSI was conducted as an application of the proposed method. This experiment was conducted in a similar way to Ref. [12]. The experimental setup is shown in Fig. 4. Air was discharged from the air pump and heated by the heater installed in the flow path. The temperature of air at the test section was measured by the thermocouple and the thermometer. The electricity supplied to the heater was controlled by the power controller until expected fluid temperature in the test section was obtained. The distance between optical flats was set to 0.6 m. The whistle was chosen as a sound source because it can easily emit sound due to its resonant structure. The temperature of air was set to $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$ because a large adjustment of the temperature likely causes modification of the behavior of the fluid flow. In order to confirm the effectiveness of the proposed method, $+0°\mathrm{C}$ condition was also conducted. The frame rate of the high-speed polarization camera in PPSI was set to 42,000 frames per second, and the imaging size was $56\times 35\mathrm{mm}$.

 

Fig. 4. Experimental setup for realizing the proposed method.

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Figure 5 shows the positional relation and visualized images. The visualized images when the temperature differences from surroundings are $+0°\mathrm{C}$, $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$ in order from the second figure from the left are shown. The leftmost figure shows the positional relation of a whistle and visualized flow and sound. The color represents the phase of light, and the images are displayed in the range from $-0.2$ to 0.2 rad. The fluid was blown into the whistle from the left side of the visualized image. The sound wave can be seen on the upper side of the whistle as a circular phase distribution. The flow was observed along the whistle from the edge. In order to obtain the phase of light from data captured by PPSI, hyper ellipse fitting in a subspace method [19] was used because it can retrieve the phase accurately [20]. In addition, a time-directional high-pass filter with 1,000 Hz cutoff frequency [21] was applied to the data of the phase of light in order to remove undesired effects such as the fan noise of the PPSI system, natural convection caused by the temperature control, and vibrations of the optical elements (see Ref. [21] for details).

 

Fig. 5. Positional relation of the visualized image and visualized images. The left-most image indicates the positional relation between the whistle, flow, and sound. The temperature difference of air from room temperature was $+0°\mathrm{C}$, $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$ in order, from the second from the left to the right, respectively.

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As can be seen from the visualized images in Fig. 5, the circular wavefront around the edge was observed under all conditions. The flow along the whistle from the edge can be visualized except for $+0°\mathrm{C}$ condition. In addition, it can be seen from visualized images at $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$ conditions that the visibility of flow increases as the temperature difference increases. From these results, it was confirmed that flow and sound can simultaneously be visualized by the proposed method. Compared to the result of the experiment in Ref. [12], sound waves in a region of flow were visualized.

In order to evaluate the proposed method, the amount of the phase change of light due to flow was compared to that due to sound. As can be seen in Fig. 5, however, the component of sound was mixed in the flow region. Hence, separating the component of flow and sound was required. In order to separate them, we focused on the spatial frequency difference. The spatial frequency of the sound is lower than that of the flow. Therefore, applying a spatial high-pass filter [22] to these images can remove the component of sound, which is justified by the theory of the wave equation (a model of sound), as explained in Ref. [22]. A two-dimensional isotropic high-pass filter was used that was designed by subtracting the zero-mean bivariate Gaussian function from 1 in the spatial frequency domain. Images before and after applying the spatial high-pass filter are shown in Fig. 6. The four blocks in Fig. 6 correspond to $+0°\mathrm{C}$, $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$ conditions in order, from upper-left to lower-right. In those blocks, the left-side images are before applying a spatial high-pass filter that are the same images in Fig. 5. The right-side images are after applying the spatial high-pass filter. As can be seen from Fig. 6, the component of sound can be removed by applying a spatial high-pass filter.

 

Fig. 6. Images whose flow and sound were separated. The left-side images are visualized images, the same as in Fig. 5; the right-side images are images separated by the spatial high-pass filter.

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Figure 7 shows intensity histograms when the temperature difference was $+0°\mathrm{C}$, $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$ conditions in order from upper-left to lower-right. The blue bars are histograms of the flow region of the spatial high-pass filtered images, and the red bars are histograms of the sound region of the unfiltered images. The horizontal axis shows the phase of light, and the vertical axis shows the relative probability. The relative probability was obtained by dividing the number of each bin by the number of all elements in the data. These data were extracted from 50 visualized images. Focusing on the results of the histograms of the flow regions, the distribution is concentrated near 0 rad at $+0°\mathrm{C}$ condition. This means that the phase of light has a small variation in the flow region; that is, the component of sound in the flow region was correctly removed by applying the spatial high-pass filter. Comparing the width of the histograms of flow region at $+5°\mathrm{C}$, $+10°\mathrm{C}$, and $+15°\mathrm{C}$, the width of distribution increases as the temperature difference increases. The large width of distribution means that the difference of contrast is large; thus, it can be said that the visibility of flow is high. Yet, these histograms did not fully demonstrate our expectation (the visibility of flow increases as the temperature increases while that of sound stays the same) because the width of the histograms of sound for $+10°\mathrm{C}$ and $+15°\mathrm{C}$ conditions became broader than that of $+0°\mathrm{C}$. The reason for this might be the differences of the experimental conditions such as the position of the setting of the whistle and the condition of flow blown in the whistle. In addition, the room temperatures were not strictly the same for each condition, which should have affected the behavior of the sound. Although the temperature-controlled fluid might also have affected the sound, this effect should be relatively small because the fluid flow and the whistle have small integral distances (less than 7 mm), while the sound spread widely in the three-dimensional space.

 

Fig. 7. Intensity histogram of visualized images and separated images. The blue histogram shows the flow component chosen from separated images, and the red histogram shows the sound component chosen from visualized images.

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In conclusion, the temperature controlling method for optical visualization of the fluid flow was proposed. The effect of the proposed method to the measured phase of light was considered from both theoretical and experimental points of view, and its application to the simultaneous visualization of both flow and sound was demonstrated. The experiments suggested that the proposed method can adjust the visibility of the fluid flow, as expected from the theoretical consideration. In addition, the separation of the sound component from flow by the spatial high-pass filter illustrates the effect of the proposed method to the different physical phenomena through the histograms. The proposed method can be a useful tool for the field of experimental fluid dynamics.