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Abstract
The premixed ethylene and oxygen flame that is burning in a narrow channel is investigated with digital holographic interferometry (DHI). Combustion in either a narrow tube or channel is quite different. This is caused by the significant effects of the boundary layer. The flame’s acceleration rate will be enhanced as the tube diameter decreases. Usually, flame and shock wave propagation, which occurs during the premixed ethylene/oxygen flame combustion in the measurement area, is less than few milliseconds, so that general camera can rarely capture this fast event. This paper demonstrates that, by introducing the high-speed camera to DHI, the propagation of weak compression wave, flame, and shock wave generated in the narrow channel is successfully measured with a temporal resolution of 10 μs. The ultrafast processes of the flame front changing, as well as the shock wave coupling and separating, are clearly shown from the reconstructed phase distributions of the recorded holograms; corresponding density variations are simultaneously calculated. The results could provide references for the micro-scale propulsion and power devices design and use, and this proposed configuration can also easily adapt to other kinds of ultrafast processes in fluids.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Combustion is a high-temperature exothermic chemical reaction widely existing in internal and external combustion engines as one of the main power sources for daily life and industrial production. Meanwhile, the combustion reaction process is also extremely complicated, because the characteristics of density, temperature, velocity, etc. in combustion are completely different when the fuels and external environment change [1–3]. In recent years, combustion in narrow tubes or channels have attracted intense research interests due to its potential applications in micro-scale propulsion and power devices [4]. This phenomenon is quite different from that in free space because of the significant effect of the boundary layer induced by the wall in small confined space [5]. Usually, the acceleration rate increases as the tube diameter decreases in combustion and the shock wave generates in a specific velocity fast enough. Therefore, it is of great significance to study the characteristics of the combustion in different environments for better optimization of combustion devices in energy and industrial areas, especially the combustion in narrow tubes or channels.
Normally, experiments and numerical simulations are the main ways for investigating the combustion [6,7]. The density, temperature and many other parameters of different kinds of flames can be obtained by numerical simulations with the characteristics of quick processing, low cost and wide range of applications [8]. Nevertheless, we need experimental data to verify the simulation results’ correctness [9–13]. Usually, a sensor (i.e. temperature sensor, pressure sensor) is positioned at a measurement point to monitor the changes in this selected point experimentally. However, it cannot get the full field information in the combustion area and the sensor itself has a certain volume which may disturb the combustion process. Non-contact optical measurement techniques, such as schlieren technique [14] and digital holographic interferometry (DHI) [15], are more effective as the two important full field techniques used in the study of combustion. Schlieren technique is sensitive to density variation during the combustion process but difficult to quantify this change [16]. Different from the schlieren technique, DHI can quantitatively and dynamically achieve the phase distribution of the object beam [17–19] and the density variation or any other parameters can be obtained by the phase distribution in different models. Many efforts have been done to investigate the structure and temperature distribution of flames with DHI, however, these works mainly concentrate on the combustion processes in large-scale space [20–23]. As we know, the premixed combustion in a narrow channel is an ultrafast process and traditional DHI is difficult for measuring this phenomenon clearly.
In this paper, we implement DHI to investigate the flames of premixed ethylene (C2H4) and oxygen (O2) in a millimeter-scale channel with a temporal resolution of 10 μs. During the combustion process, a high speed camera with 100,000 fps is applied to record the holograms. By reconstructing the complex amplitudes of the object waves from the recorded series holograms, the corresponding phase changes are obtained and the density variations of weak compression wave, flame and shock wave are calculated accordingly. The obtained results can be considered as references for designing and utilizing the micro-scale propulsion and power devices. And the proposed configuration can easily adapt to other kinds of ultrafast process in fluids.
2. Theory
In the combustion process, before igniting the mixture gases, the volume ratio of C2H4 and O2 in the narrow channel is taken as 1:3, and the initial density ρ of the mixture gases can be calculated according to the ideal gas law as following
where m, V, P and T are the mass, volume, atmospheric pressure and temperature of the mixture gases, respectively; R is gas constant; M is the relative molecular mass; Y is the volume fraction of each gas in the closed container and i denotes the kinds of the mixture gases.After igniting the mixture gases, the combustion reaction of C2H4 and O2 can be expressed as
During the combustion process, the density ρ is changing all the time in the narrow channel with the gases continually burning, and we cannot calculate it by Eq. (1) directly, because the pressure and temperature are all changed. For obtaining the density ρ, Gladstone-Dale equation is introduced and it can be expressed as [16]:where K is the Gladstone-Dale constant and n is the refractive index of the mixture gases. Because there is more than one kind of gases in the narrow channel, the Gladstone-Dale constant of mixture gases can be calculated by the Gladstone-Dale constant of each gas shown in Table 1. According to the volume ratio of C2H4 and O2 before igniting the mixture gases in the narrow channel and the corresponding combustion reaction, the values of the Gladstone-Dale constant of the mixture gases before and after burning are K(C2H4, O2) = 2.855 × 10−4 m3/kg and K(CO2, H2O) = 2.695 × 10−4 m3/kg, respectively, assuming the gases are well mixed and fully combusted.
Table 1. Gladstone-Dale constant of the involved gas mixtures
We use DHI to achieve quantitative measurement of the density variation Δρ during the combustion process in the narrow channel. The holograms, which carry the information of the density variation Δρ of the mixture gases, are recorded and numerically reconstructed by means of angular spectrum method [24-26]. Then, the phase change Δϕ of the object beam corresponding to the density variation Δρ of the mixture gases can be obtained. According to Eq. (3), the density variation Δρ and the refractive index variation Δn are closely related. Meanwhile, the phase change Δϕ to be measured is also determined by the refractive index variation Δn of the mixture gases in our experiment and the relationship between Δn and Δϕ can be expressed as
where λ and L are the wavelength and the thickness of the mixture gases, respectively. Then, according to Eqs. (3) and (4), the density variation Δρ can be given by3. Experimental setup
Figure 1 shows the experimental setup for measuring the combustion process of premixed ethylene/oxygen flames in a narrow channel based on DHI. The channel is manufactured by aluminum alloy and quartz glass mainly and its volume is 5.6 × 10−3 m3 with lengths of 400 mm, 7 mm and 2 mm in x, y and z directions, respectively. Meanwhile, the channel is full of C2H4 and O2 mixture with a volume ratio of 1:3 at room temperature and atmospheric pressure. The igniter located at the edge of the channel is used to ignite the gas in the container, which is controlled by a wireless controller to synchronize the combustion process and the camera recording. Usually, the early stage has an important influence on the combustion process, so the measured area is closed to the igniter. A continues laser with wavelength of 532 nm is used as the detection laser source to dynamically measure the ultrafast combustion process without contacting the combustion field. The detection laser beam is split into two parts via a fiber coupler C, and the two parts are acted as object and reference beams, respectively, after passing through the fiber connectors FC1 and FC2. The object beam is modulated by aperture A and collimated by lens L1 (f = 400 mm), respectively, and then passes through the combustion field. After carrying the information of the premixed ethylene/oxygen flame, the object beam is collected by a telescope system that consists of L2 (f = 400 mm) and L3 (f = 75 mm) with a magnification of 1/5.333. Then the object beam is combined with the reference beam which is collimated by lens L4 (f = 100 mm) via a beam splitter BS. The combined two beams are filtered by a polarizer P and then interfere with each other on the target of the high speed camera (Phantom V711, pixel size 20 μm). The polarizer P located between the beam splitter BS and the camera is used to modulate the intensity of the object and reference beams to form a high contrast ratio of interference fringes. The used high speed camera can record 100,000 frames per second with a resolution of 512 × 120, so a 10 μs time resolution can be achieved in the experiment.
Fig. 1 Experimental setup for measuring the combustion process in a narrow channel based on DHI. C: fiber coupler; FC1 and FC2: fiber connectors; A: aperture; L1, L2, L3 and L4: lenses; BS: beam splitter; P: polarizer.
4. Experimental results
In the experiment, after igniting the premixed gases, a weak compression wave is observed firstly in measured area and we set the time before this weak compression wave appears in measured area as the initial time (t = 0 μs). Figures 2(a)-2(h) show the reconstructed phase distributions of compression wave from 0 μs to 140 μs, where we can see the obvious variation of the phase distribution owing to the movements of compression wave and the propagation direction is indicated by the black arrows. At the initial time (t = 0 μs), as shown in Fig. 2(a), there is no obvious phase variation, which means that the mixture gases in this area is not disturbed at that moment. Then we can see clearly from the Figs. 2(b)-2(h) that the compression wave appears and continues to move forward (the right direction) as the time increases. Before the compression wave propagates to the other side of the measuring area, the mixture gases change no longer, so we can assume that the phase change Δϕ is 0 at the end of the right side in Figs. 2(a)-2(h). We extract all the phase distributions along the red line shown in Fig. 2(a), and the density variation Δρ can be calculated by Eq. (5) along x direction according to the phase change Δϕ, as shown in Fig. 2(i). In Figs. 2(a)-2(h), we cannot observe the burning flame, which means that the mixture gases are still C2H4 and O2 in the measuring area from 0 μs to 140 μs. So the Gladstone-Dale constant should be taken as K(C2H4, O2) = 2.855 × 10−4 m3/kg. From the curves shown in Fig. 2(i), it is obvious that before compression wave comes, there is no variation of the density, and as the time increases, the density variation Δρ caused by compression wave increases.
Fig. 2 (a-h) Phase images of the compression wave. (i) Density variation Δρ from 0 μs to 140 μs along the red line in (a). (The whole combustion process can be seen in Visualization 1.)
Figures 3(a)-3(f) show the phase distributions of the flame from 210 μs to 360 μs. Starting from 210 μs, an arc-shaped flame front shown in Figs. 3(a)-3(f) appears in the measured area,called finger flame. In Figs. 3(a)-3(f), we can see clearly that the curvature of the flame front increases as the flame continues to propagate along the direction of the white arrow. Usually, the flame front of premixed ethylene/oxygen flames combustion in a narrow channel is very thin and separates the burning products and unburned regions. In Figs. 3(a)-3(f), the phase distributions in both the burning products and unburned regions changes. We assume that the mixture gases have been fully burned, that means the substances in the region after flame front are only the burning products CO2 and H2O, and the unburned gases locate at the other part. Owing to the two different gas mixtures exist in the measured area and they have different Gladstone-Dale constants, we cannot calculate the density variation Δρ directly. Considering that, the two gas mixtures are positioned at different sides of the flame front, and the Gladstone-Dale constants of two gas mixtures can be calculated according to combustion reaction. So we can find the boundary between the two gas mixtures and calculate the density variation Δρ with different Gladstone-Dale constants in different regions. In burning products region, the Gladstone-Dale constant K(CO2, H2O) is 2.695 × 10−4 m3/kg, while in the unburned region, the Gladstone-Dale constant K(C2H4, O2) is 2.855 × 10−4 m3/kg. The density variation Δρ from 210 μs to 360 μs along the red line shown in Fig. 3(a) are depicted in Fig. 3(g) according to the phase distributions of Figs. 3(a)-3(f). It is obvious that there is a clear density difference between burned and unburned regions, and this density difference is decreasing as the flame continues to burn. In addition, the density difference in burned and unburned regions also have similarities. The density is smaller when the field is closer to the flame front both in burned and unburned regions.
Fig. 3 (a-f) Phase distribution of the finger flame. (g) Density variation Δρ from 210 μs to 360 μs along with the red line in (a).
Figure 4 shows the phase images of the flames from 380 μs to 740 μs and we can see that the flame front has been reversed. Similar to the finger flame, the reversed flame front is also the interface between the burning products and unburned regions. At t = 380 μs, as shown in Fig. 4(a), the flame front is a flat structure and it is quite different from that shown in Fig. 3, where the flame front is protruding outward. After a period of time, the flat flame front begins to inward concave and the concave field is increasing, as shown in Figs. 4(b)-4(g). The inward depression flame front is also an obvious sign of tulip flame, and it means that from t = 440 μs, the tulip flame is formed. The formation of the tulip flame is the result of the interaction of flow-flame and indicates the accomplishment of laminar-turbulent transition.
As the premixed gases burn rapidly and continuously, the shock waves are generated. The shock waves can be considered as the infinite superposition of weaker compression waves and the density has a clear difference across the shock wave. In the experiment, we record a meaningful process that two shock waves, reflected by different borders of the narrow channel, are coupled and separated in the measured area. Figures 5(a)-5(f) are the phase images of the coupled and separated shock waves, where the arrows denote the propagation directions of the two shock waves and the position pointed by the arrow is the shock wave. It is obvious that the two shock waves have opposite propagation directions and the phase has a dramatic change at the location where the shock wave is. Meanwhile, we cannot observe the flame front in the measurement area, which means that the measurement area is all burning products at that time.
Fig. 5 (a-f) Phase images of the shock wave coupling and separating. (g) Density variation Δρ along the horizontal direction in (c) and (d).
Figure 5(c) displays the time that the two shock waves first meet, where we can see obvious boundaries of the two shock waves. Figure 5(d) shows that the two shock waves are separated and prorated in their original directions, which means that the coupling of shock waves do not affect their original propagation directions. Figure 5(g) depicts the calculated density variation Δρ according to the phase distributions shown in Figs. 5(c) and 5(d) when the two shock waves are coupled and separated. Considering that there are all burning products in the observing area now, the Gladstone-Dale constant K(CO2, H2O) is 2.695 × 10−4 m3/kg according to the combustion reaction and the Gladstone-Dale constants of CO2 and H2O shown in section 2. In Fig. 5(g), the red curve depicts the moment that two shock waves meet, and it is clear that the density between the two shock waves is much lower than the other regions. However, the blue curve in Fig. 5(g) shows that when the two shock waves separate from each other, the density between the two shock waves is much larger than the other regions. Above all, we can know that when the two shock waves are coupling, the density of coupling area rises quickly and the original propagation directions do not change at the same time.
5. Conclusion
In summary, we have investigated the premixed C2H4 and O2 flame combustion in a narrow channel by exploiting DHI with a high-speed camera. With a 10 μs temporal resolution we have successfully obtained the phase changes and density variations caused by the premixed C2H4 and O2 combustion, and measured the processes of weak compression wave and flame propagation. We have also obtained the density variation in the coupling and separating process of two shock waves with the proposed configuration. The proposed optical setup can be applied to other types of fast processes measurements in fluids easily and the results can provide a reference to corresponding fields.
Funding
The Joint Fund of National Natural Science Foundation of China (NSFC) and China Academy of Engineering Physics (NSAF) (U1730137); Shaanxi Provincial Key R & D Program (2017KW-012).
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