Turbulent premixed combustion is of great interest for industrial applications where low pollutant emissions are sought. It is well-established that most premixed turbulent flames that have been studied to date are composed of wrinkled “flamelets” [1]. In the so called flamelet regime, the thickness of the chemical reaction layer (flame front) is smaller than the Kolmogorov scale [2]. The flame can be regarded as behaving similarly to the laminar case and described independently of the turbulent flow field. Fundamental parameters such as the flame surface density, flame brush thickness, and turbulent burning velocity are calculated based on the turbulent flame front [3]. These parameters are not only significant to a better understanding of the underlying mechanisms of turbulent premixed combustion, but also useful for validating computational models.

The measurement of flame front position relies on laser based optical diagnostics techniques. The laser induced fluorescence (LIF) signal from radicals such as OH and CH, which are generated during combustion, is frequently used for flame front tracking [4–7]. Another common approach adapts particle image velocimetry (PIV, also called Conditioned PIV when it was first proposed for flame front extractions and in some later publications) [8,9]. It works by detecting the sharp particle number density gradient in the Mie-scattering images of the seeding particles, caused by the temperature change between the unburned and burned regions. It was proposed as a low-cost and reliable alternative for flame front detection, and has been applied widely [8–13]. Besides, the PIV method can achieve simultaneous measurement of flame front position and flow velocity field, enabling relatively simple determination of flow–flame interaction and flame displacement speed without needing an additional LIF system [10,11]. In principle, flame front measured by PIV is in the preheat layer where the sharp temperature gradients exist (slightly toward reactants). Radicals like OH and CH are post-flame species (slightly toward products).

Conventionally, the above-mentioned techniques deliver single-plane measurements. Efforts have been made to capture the three-dimensional (3D) information of flame front structure. One representative example is volumetric LIF imaging based on tomographic reconstruction [14,15]. In a combustion device where optical access is limited, such as the optically accessible internal combustion engine described in this Letter, deploying a camera array for an accurate tomographic reconstruction is impractical. Alternatively, researchers record signals from multiple planes by laser sheet scanning across the volume of interest, thereby recovering the 3D structure of the flame or investigating correlations between planes [16–19]. The sequential nature of scanning measurement may restrict the application to moderate flow rates and turbulence levels. Simultaneous multi-plane measurements have been attempted, by using the polarization and wavelength differences of the light [20,21]. They can achieve simultaneous measurements with high spatiotemporal resolution, but the number of measurement planes is limited.

In this Letter, we present a simultaneous two-plane flame front measurement using PIV. It is based on a standard single-plane PIV system in combination with an image splitting device. Our previous work validated the feasibility and accuracy of using this configuration for a simultaneous two-plane velocimetry of non-reacting flows [22,23]. By using a non-polarizing beam splitter and mirrors with adjustable optical path lengths, each half of a camera sensor is focused to a different depth plane. With a shallow depth of field, the overlapping image that is not in-focus is significantly defocused. Based on a high-pass filter and a novel two-step filter we have devised, the out-of-focus particle images can be effectively removed while the in-focus particle images remain. Potentially, by fuzther splitting the images, or combining our method with conventional polarization/wavelength discrimination, simultaneous flame front detection on more planes could be achieved. The focus of this Letter is to demonstrate our method, and to assess the flame front detection uncertainty caused by two-plane cross talk.

The image splitting optics design is shown in Fig. 1 (a). A 2-in. 50/50 non-polarizing beam splitter (Thorlabs BSW42-532) splits scattered light from two parallel depth-offset planes into two paths. Mirrors are used to direct light traveling along each path to a different half of the camera sensor. Since both optical paths share the same camera lens and image distance, by adjusting the positions of the mirrors (therefore the optical path length of each path), the two measurement planes can be placed at different depths along the optical axis. For either side of the camera sensor, the image from one plane is in-focus, while the other plane’s image is out-of-focus. By using a large aperture camera lens (f = 85mm, f/2), a shallow depth of field is achieved.

 

Fig. 1. (a) The image splitting device (adapted from [22]). (b) Two-plane flame front detection in the optical engine.

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The two-plane flame front measurement was performed in a single-cylinder, optically accessible gasoline direct injection engine (Fig. 1 (b)). The engine ran at 1000 revolutions per minute (RPM) with stoichiometric isooctane-air mixtures. A LaVision aerosol generator was used to seed olive oil droplets into the intake plenum. A pair of coaxial laser beams, generated by a dual-cavity Nd:YLF laser (Photonics Industries DM20-527-DH), were split into two pairs by a 50/50 non-polarizing beam splitter (Edmund Optics 35959). A fused silica annulus provided optical access for the laser sheets, illuminating two horizontal planes in the engine. The upper plane was 2.5 mm below the firing deck. The lower plane was 22 mm below the upper plane. A Bowditch piston and 45$^\circ$ mirror arrangement enabled the planes to be imaged through the piston crown window onto a high-speed CMOS camera (Phantom VEO 710L). A dichroic filter (Elliot Scientific CDG-5051) was used to reject chemiluminescence emission from the flame, and transmit the green Mie scattering from the PIV particles. The field of view on each plane was 35 mm $\times$ 107 mm. Restriction of the field of view size, caused by the image splitting optics, is discussed in [22].

Figure 2 presents two examples of detecting flame fronts on the two planes. To improve visualization, all PIV images presented in this Letter are rotated so that the upper-plane image and lower-plane image are vertically arranged. Row 1 shows images at 75 crank angle degrees (CAD) after Top Dead Centre (aTDC), and Row 2 shows images at 80 CAD aTDC, in the same cycle. The first column shows background subtracted images. The second column presents images processed with a high-pass filter, which subtracted the images’ low-frequency content generated using a 2D Gaussian smoothing kernel (32 $\times$ 32 pixels in this work). It is noticed that the high-pass filter is able to remove a substantial fraction of the out-of-focus particle images, but some still remain. Here we propose a two-step filter to clean up the blurry particle images. The first step is called a ratiometric coefficient of variation filter (RCOVF). First, a 5 $\times$ 5 window is used to calculate the local coefficient of variation for each pixel:

Algorithm 1. Ratiometric coefficient of variation filter (RCOVF)

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Fig. 2. Two-plane flame front detection examples.

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In practice, the RCOVF performs well in removing the central part of an out-of-focus image “blob”, but it is not able to effectively remove the edges of the out-of-focus particle images. Therefore, a second step called ratiometric sliding maximum intensity filter (RSMIF) is applied. It is based on the observation that for those bright out-of-focus particles which survive high-pass filtering, there should be corresponding bright in-focus particles on the other plane. The filter is defined in Algorithm 2, where $S$ is the sliding maximum intensity value of each pixel calculated using a 13 $\times$ 13 window:

In this filter, the ratio of the sliding maximum intensity value is used to evaluate if a pixel is a part of the edge of an out-of-focus particle image. Due to the inherent brightness difference of in-focus particle images, caused by, e.g., the different physical sizes of in-focus particles and the spatial distribution of laser sheet energy, the second condition on the coefficient of variation ratio is used to prevent removing pixels in regions where in-focus particles exist on both planes.

Algorithm 2. Ratiometric sliding maximum intensity filter (RSMIF)

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The effect of the proposed two-step filter is visualized in the third column of Fig. 2. Direct observation of the images shows that the out-of-focus particles were removed satisfactorily. Based on the filtered images, turbulent flame front contours were determined using the automatic histogram-based threshold approach proposed by [8].

To evaluate the flame front detection uncertainty caused by two-plane cross talk, single-plane illumination images were numerically added, so that we are able to compare the flame front contours generated from the numerically added “two-plane illumination” images and from the ground-truth single-plane illumination images. In Fig. 3, a single-plane (upper and lower) illumination image was selected and numerically added to 100 others to create 100 “two-plane illumination” images. In the last row of Fig. 3, the probability density map of the unburned region of each plane calculated from the numerically added images is presented, and the flame contour generated from the single-plane illumination image is overlaid. We observe that despite the cross talk imposed during numerical addition, the algorithm remains able to extract the structure of the flame front highly reproducibly.

 

Fig. 3. Evaluation of flame front detection uncertainty caused by out-of-focus images. The last row shows the probability density map of the unburned region of each plane calculated from the numerically added images, overlaid with flame contour generated from the single-plane illumination image.

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In summary, we have proposed a simultaneous two-plane flame front detection method using defocusing based PIV. It could be applied alone as an inexpensive approach to extend a standard single-plane PIV system for two-plane measurement, or combined with conventional polarization/wavelength discrimination to achieve simultaneous multi-plane flame front reconstruction. Our previous work [22] indicated that reliable flow velocity field reconstructions of non-reacting flows could be achieved with plane separation as small as 15 mm, with the same optical hardware and similar field of view size to this work. In future work we will systematically investigate the impact of plane separation on flame front measurement and study the achievable improvement by narrowing camera depth of field and optimizing image processing steps.