1 Introduction

For many combustion systems, unburned gas temperature is arguably one of the most influential parameters defining combustion. Within internal combustion (IC) engines, gas temperature controls mixture preparation, auto-ignition, pollutant formation, and thermal transport to solid boundaries. The bulk gas temperature changes drastically during compression, while solid boundaries of the combustion chamber are typically cooled and exhibit fewer temperature variations than the gas [1, 2]. Near the end of the compression, gas temperatures are significantly higher than wall temperatures, and the interaction between the hot gas and colder boundaries has been argued as the leading cause of natural thermal stratification in IC engines [3–5]. Large temperature stratifications can affect combustion performance; particularly in homogeneous charged compression ignition (HCCI) systems where temperature plays a dominant role in determining the combustion phasing and maximum peak release rate [6]. Recent engine development has led to the downsizing of engine geometries in which greater surface-to-volume ratios will further advance temperature stratification and affect thermal transport. Therefore, within the combustion community, there is a strong effort to measure the in-cylinder gas temperature to better understand the thermal transport in IC engines [3–7].

Tracer-based laser-induced fluorescence (LIF) thermometry is a common technique used to spatially resolve unburned gas temperatures in IC engines [3–13]. LIF thermometry measures the red-shifted temperature dependent fluorescence spectrum of a given tracer molecule following its excitation from UV light [14]. Although there are several tracers used for LIF thermometry [14–16], the emission spectrum for 3-pentanone and toluene has been extensively characterized for high temperatures and pressures [13, 14, 17–22] and are two primary LIF tracers used in IC engines. Although 3-pentanone has provided noteworthy temperature measurements in IC engines [6, 8, 9, 13] and has provided similar findings to works employing toluene [6], this manuscript focuses on fundamental aspects of common toluene LIF detection strategies to appropriately interpret the results of local temperature distribution measurements in IC engines.

A primary focus of toluene LIF thermometry within IC engines has been investigating the development of natural thermal stratification during compression and expansion [3–5, 7]. Most measurements revealed that the temperature distribution becomes more heterogeneous during compression [3–5], especially in the near wall regions where cold gases appear to extend from solid surfaces [4, 5]. Such results suggest that thermal stratification develops due to heat transfer from the hot gas to the relatively cold walls. During early expansion for motored engine operation, additional findings revealed that temperature stratification significantly progresses from outgassing of relatively cold crevice volumes [5, 7].

Although toluene LIF measurements have provided insight into the development of thermal stratification, an improved understanding of the LIF detection limitations is needed to successfully interpret LIF temperature signals in complex environments such as IC engines.

1.1 Toluene LIF thermometry detection

Toluene planar LIF thermometry encompasses two detection strategies denoted as the one-color and two-color detection. The one-color detection records a fluorescence image that spectrally integrates the fluorescence signal (S) originating from a volume located at position x, y, which is characterized by:

$$S(x,y,T) = \eta E_{\text{laser}} \left( {x,y} \right)n_{\text{tol}} \left( {x,y} \right)\sigma_{\text{abs}} \left( {T\left( {x,y} \right)} \right)\phi \left( {T\left( {x,y} \right)} \right)$$
(1)

where η is the detection efficiency, E laser is the laser energy, n tol is the toluene number density, σ abs is the absorption cross-section, and ϕ is the fluorescence quantum yield. Before yielding temperature information, the one-color fluorescence image must be corrected for laser energy, laser profile, absorption, toluene number density, as well as other detection nonuniformities [5].

In contrast, the two-color detection separates the fluorescence spectrum into two spectral bands referred to as the “red” and “blue” channel [7, 12, 23]. Separate LIF images are acquired for each spectral band, and the spectral ratio (i.e., S ratio = S RED/S BLUE) provides a temperature dependent LIF image which is independent of laser absorption, laser influence, and local mixture fraction inhomogeneities:

$$S_{\text{ratio}} = \frac{{S_{\text{RED}} \left( {x,y,T} \right)}}{{S_{\text{BLUE}} \left( {x,y,T} \right)}} = \frac{{\eta_{\text{RED}} E_{\text{laser}} \left( {x,y} \right)n_{\text{tol}} \left( {x,y} \right)\sigma_{\text{abs}} \left( {T\left( {x,y} \right)} \right)\phi_{\text{RED}} \left( {T\left( {x,y} \right)} \right)}}{{\eta_{\text{BLUE}} E_{\text{laser}} \left( {x,y} \right)n_{\text{tol}} \left( {x,y} \right)\sigma_{\text{abs}} \left( {T\left( {x,y} \right)} \right)\phi_{\text{BLUE}} \left( {T\left( {x,y} \right)} \right)}} = f\left( {T\left( {x,y} \right)} \right)$$
(2)

The one-color detection offers a better temperature sensitivity and precision uncertainty compared with the two-color detection. Over a typical temperature range during compression in IC engines (300–800 K), the quantum yield decreases by two and half orders of magnitude [17], while the spectral ratio typically changes less than a factor of 10 [7]. Although measurement uncertainty originates from intensified camera shot noise and laser energy fluctuations for both detection methods, the spectral ratio signal yields higher precision uncertainties due to lower signal-to-noise (SNR) levels and lower temperature sensitivities. Nonlinear pixel responses from intensified CMOS cameras have individual pixel intensity fluctuations [24], which will further increase noise levels, especially when dividing the blue and red channel images. The higher noise levels and associated increased measurement uncertainties can limit the detection of thermal gradients when employing the two-color detection strategy.

In comparison however, the main limitation of one-color detection is that the LIF signal cannot distinguish between local temperature inhomogeneities and local mixture fraction inhomogeneities. Thus, a spatially homogeneous mixture is required in order to avoid misinterpretation and systematic errors of the LIF temperature signal.

Although the advantages and limitations of each detection strategy are well known in principle, there is a lack of practical analysis and comparison of such techniques in complex environments such as IC engines. The inability to quantify local mixture homogeneity or clearly detect temperature gradients within high noise levels is often a limitation of LIF thermometry.

The purpose of this work is twofold: (1) Simultaneously apply the one-color and two-color detection strategies employed for high-speed toluene LIF thermometry to provide a quantitative comparison that identifies the advantages and limitations in the ability to quantitatively measure the local temperature field in an engine, and (2) Utilize both techniques to appropriately characterize the formation and transport of thermal stratification in an IC engine as an application example. To further assist the temperature imaging analysis, high-speed toluene LIF measurements are combined with high-speed particle image velocimetry (PIV) and Mie scattering imaging to provide information of local flow velocity and identify important physical processes that influence the formation of natural temperature stratification near solid boundaries inside the engine.

2 Experimental

2.1 Engine and operating parameters

High-speed toluene LIF thermometry and PIV measurements were performed in a 4-stroke, single-cylinder spark-ignition direct-injection (SIDI) optical engine [25]. The engine is equipped with a 4-valve pentroof cylinder head, side mounted injector, centrally mounted spark plug, quartz glass cylinder, and flat quartz glass piston. The spark plug was removed and replaced with a threaded plug, and the injector was inactive for the experiments.

Operating parameters and engine details are shown in Table 1. The engine operated under motored conditions at 1,000 RPM with dry, high-purity nitrogen used as intake gas to avoid quenching of the fluorescence signal by oxygen. The nitrogen was sent to the bubbling seeder to seed toluene vapor (2.75 % by volume) into the intake flow. The high levels of toluene vapor (Φ = 1.2 in-cylinder trapped mass if air was used instead of nitrogen) were chosen here to provide sufficient fluorescence signal when using low laser pulse energies associated with high repetition-rate laser systems. The volume of the bubbler seeder was 60 L and contained up to 30 L of liquid toluene. Considering the long residence time of the intake nitrogen and large volume of the bubbler seeder, it is assumed that this system provides toluene vapor equilibrium within the engine. This assumption is supported by an analysis of the laser attenuation, confirming the estimated toluene concentration. Silicone oil droplets, for PIV, were seeded into the intake flow by means of a separate droplet seeder (AGF-10.0, Palas). Both seeded mixtures were introduced into the intake flow separately one meter upstream the engine. The engine operated motored for 10 min before acquiring images to reach steady-state thermal conditions indicated by a stable exhaust gas temperature.

Table 1 Operating conditions and engine specifics
Full size table

2.2 Optical setup

The combined high-speed flow and temperature imaging diagnostics are the same as presented in [7], and a schematic of the setup is shown in Fig. 1. A frequency-quadrupled diode-pumped Nd:YAG 266 nm (Edgewave CX16II-E, 1.0 mJ/pulse) dual-cavity laser was used for the LIF measurements, while a frequency-doubled Nd:YVO4 532 nm (Edgewave IS4 II-DE, 4.0 mJ/pulse) dual-cavity laser was used for the PIV measurements. A Pellin–Broca prism was used to separate 266 nm light from 532 nm light of the Nd:YAG laser. The laser beams for the LIF and PIV were combined using a high-reflectivity (HR) 266 nm high-transmissivity (HT) 532 dichroic beam splitter. The laser beams were formed into light sheets (0.5 mm thickness), reflected off a 45° mirror in the engine crankcase, and passed through the quartz bottom piston to illuminate a vertical viewing plane within the central axis of the engine cylinder. The PIV laser used a pulse separation of 25 μs and the LIF laser was triggered 5 μs after the first PIV laser pulse.

Fig. 1
figure 1

Experimental setup for one- and two-color toluene LIF thermometry detection and simultaneous PIV measurements

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The schematic of the LIF and PIV detection systems are also shown in Fig. 1. The LIF detection system allowed for both the one-color and two-color detection strategies to simultaneously be applied. The fluorescence signal first passed through two 275 nm long-pass (LP) dielectric filters and a 350 nm short-pass (SP) dielectric filter before it was spectrally separated into two channels denoted as the “blue” (280–300 nm) and “red” (300–350 nm) channel using a dichroic beam splitter. The blue signal was reflected and passed through a 300 nm SP dielectric filter, while the red signal transmitted through the beam splitter. The filter transmission spectra from the chosen filter combinations are shown in [23]. Signals were collected and imaged with UV lenses (Halle, f = 150 mm, f # = 2.5) and two-stage intensifiers (LaVision HS-IRO, high-speed intensified relay optic) coupled to 12-bit CMOS cameras (LaVision HSS6). Gain settings were fixed for each intensifier to achieve a 1-to-1 quantum efficiency. On the opposite side of the engine, a CMOS camera (LaVision HSS5) was used to record Mie scattering images for PIV. The viewing plane consisted of a 25 × 30 mm2 region offset from the cylinder axis (exhaust side) near the cylinder head where thermal gradients are expected to occur due to the presence of colder wall surfaces (T cyl, head = 333 K).

An optical crank-angle encoder (AVL, 365C) was used to synchronize the lasers and cameras at 6 kHz to the engine at 1,000 RPM to obtain images every crank-angle degree (CAD). For a single experiment (i.e., recording sequence), LIF and double-frame Mie scattering images were acquired for four consecutive cycles (2,880 images). Experiments were repeated to obtain LIF and PIV images at every CAD for 72 cycles.

The power from the Nd:YAG laser (80 W, 532 nm, before conversion to 266 nm) used for toluene LIF proved to be problematic for some optics. After several minutes, the laser energy would damage the Pellin–Broca prism and began to inhibit the amount of transmitted UV light. Therefore, for each recording sequence, the height of the Pellin–Broca was adjusted to a new vertical position to prevent immense damage of the Pellin–Broca and allow maximum UV light into the engine. The adjustment of the Pellin–Broca height translated the laser sheet in the horizontal direction within the engine viewing plane. Therefore, for each recording sequence (4 cycles), a new laser profile and signal intensity would exist at a given x, y location and plays an important role during image post-processing.

2.3 Toluene LIF in a heated jet

Additional toluene LIF thermometry experiments were performed in a heated nitrogen-toluene coflow jet as described in [23]. These measurements addressed the role of important optical effects such as angle-dependent reflectivity of dielectric filters. For these experiments, the exact same optical setup including the engine quartz cylinder placed around the coflow jet was used and is further described in Appendix 1. The temperature of the jet spanned the range of the engine gas temperatures (295–573 K). A type K thermocouple was used to measure the temperatures along the horizontal and vertical central axis of the jet to obtain a temperature profile of the heated jet for comparison with LIF results.

2.4 Data processing

This work evaluates toluene LIF thermometry results derived from three different image processing methods. The experimental setup allowed for both one-color and two-color toluene LIF detection to simultaneously be applied. For the one-color detection, we utilized two separate image processing methods common in the literature. These methods are denoted as the “flat-field correction” (FFC) [3, 4, 6] and the “multi-step correction” (MSC) derived from [5]. This section summarizes the three image processing methods applied and further details of each method with illustrated examples are provided in Appendix 1.

The experimental setup utilizes two LIF detection systems (i.e., dual IRO-camera systems) for which image pre-processing is required to match characteristics of each system. Images acquired from each detection system are utilized for both the one-color and the two-color image processing. A commercial software (DaVis, LaVision) was used to build a transformation matrix based on images of a spatially defined target in the engine from both detection systems. This transformation matrix was applied to adjust the images from one detection system to the other in terms of translation, rotation, and scaling. This procedure ensured the robust superposition of the images for the red and blue channel images.

Each detection system is characterized to address pixel sensitivity, signal depletion from IROs, and spatial resolution. A linear camera model approach (including FFC from a uniform light source) is used to account for pixel sensitivity [24]. Transient response from high-speed intensifiers can lead to LIF signal depletion and was found to occur for the first 3,000 images for a constant LIF source [7]. Therefore, as a precaution the first 3,300 LIF images were removed from a 6,236 image sequence, leaving 2,936 usable LIF images for which 2,880 LIF images were synchronized with PIV images. It should be noted, however, that for the varying LIF signals as a function of crank-angle, depletion was not observed in a similar manner as for the constant LIF source. Individual cycle LIF traces for a given recording sequence collapse to a single representative curve, indicating that depletion is similar for all cycles at a fixed CAD and accounted for in the LIF-to-temperature calibration procedure described in Sect. 2.4.3.

The spatial resolution of each LIF detection system was different (due to different modulation transfer functions associated with each intensifier) and was determined with a 1951 USAF resolution target by assessing the contrast transfer function (CTF) for each channel. The resolution for the blue and red channels was 0.20 and 0.14 mm (CTF cutoff: 8 % as discussed in [26]), respectively, and includes a 3 × 3 pixel2 median filter applied for noise reduction. A 3 × 3 pixel2 binning, providing 0.08 mm/pixel, was used to provide similar resolutions for both detection systems.

2.4.1 Two-color toluene LIF processing

Once the images from each detection system were superimposed, the red channel image was divided by the blue channel image to yield a temperature dependent LIF ratio signal (\(S_{\text{ratio}} = S_{\text{RED}} /S_{\text{BLUE}}\) [7, 12, 23] ) which was independent of laser absorption, local mixture heterogeneities, and fluctuations in laser fluence [17]. LIF ratio images exhibited an angle-dependence for the fluorescence light reflected by the beam splitter (i.e., blue channel) and resulted in a linear decay of S ratio in the horizontal direction. The exact same linear decay of S ratio was present for LIF images acquired in the engine and for LIF images acquired in the heated toluene coflow jet (described in Sect. 2.3 and Appendix 1). The decay was corrected within the toluene jet by using a linear correction to match the horizontal temperature profile of the thermocouple. The linear decay of S ratio was found to be independent of temperature or CAD (see Appendix 1). In-cylinder LIF images were then corrected using the same linear correction found in the coflow jet experiment. Calibration of S ratio to temperature is presented in Sect. 2.4.3.

2.4.2 One-color toluene LIF processing

For the processing of the one-color detection strategies, the spectrally integrated fluorescence signal is obtained by adding the red and blue channel images (i.e., \(S_{\text{one - color}} = S_{\text{RED}} + S_{\text{BLUE}}\)). It is understood that the one-color detection could also be processed utilizing only one of the fluorescence channel images, but both were utilized to provide an improved signal quality over the range of temperatures and is more representative of the integrated LIF signal.

One-color detection requires several image corrections for toluene LIF thermometry. The UV laser pulse energy was measured with a photodiode (Fig. 1) and provided subsequent image normalization for the individual laser pulse energy. The toluene number density varies with crank-angle and requires an additional image correction [3, 5]. The images were normalized to a reference toluene number density at intake valve closing (IVC). Succeeding image processing steps are specific to the processing methods applied for one-color detection and are discussed in the following sub-sections.

2.4.2.1 Method 1: Flat-field correction (FFC)

The FFC method utilizes a multi-cycle mean LIF image normalization to correct for laser attenuation and detection nonuniformities [3, 4, 6]. It is recognized that the multi-cycle mean LIF image is nonuniform (see Appendix 1), and normalization removes any temperature structures of the mean temperature field (e.g., possible temperature boundary layers near solid surfaces) as long as the average attenuation along the laser beam path is not significantly varying from cycle to cycle. The mean temperature field is not of direct interest in this work however, and this method provides a clear representation of temperature variations relative to the mean [3, 4].

The damage and height adjustment of the Pellin–Broca prism limited the amount of images available to construct the multi-cycle mean LIF images. As previously mentioned the height of the Pellin–Broca prism was adjusted for each recording sequence (4 cycles) and resulted in a slight change of laser profile and LIF intensity. Thus, the multi-cycle mean LIF images were specific to a given recording sequence. The mean LIF image for a given CAD was constructed from 12 LIF images; images obtained at CAD (i), CAD (i − 1) and CAD (i + 1) for each of the 4 cycles of a given recording. While it is recognized that more than 12 images are typically needed to provide an accurate description of the average LIF image and would increase SNR of the flat-field image, the resulting mean LIF images provided a suitable flat-field correction for laser attenuation and detection nonuniformities. The convergence of the mean LIF images based on a limited number of sample images is analyzed in Appendix 2. It is shown that the percent difference in LIF intensity converges below 1 % for 12 sample LIF images and provides further confidence in its use for flat-field correction.

Each multi-cycle mean LIF image was normalized by its maximum intensity and allowed for the absolute value of the LIF signal to be retained in the individual LIF images after flat-field normalization. Example images describing the image processing procedure are presented in Appendix 1. Calibration of LIF signal to temperature is presented in Sect. 2.4.3.

2.4.2.2 Method 2: Multi-step correction (MSC)

The MSC method utilizes several processing steps to correct for laser attenuation and detection nonuniformities. This image processing method is based on the procedure presented by Dronniou and Dec [5], although some processing steps are applied differently in this work. Laser attenuation and nonuniformities are evaluated in the multi-cycle mean LIF image. As previously mentioned, ensemble-mean LIF images were constructed from 12 LIF images and were specific to each recording sequence. Laser attenuation occurs in the vertical direction and was corrected following the Lambert–Beer law. One of the critical assumptions of the Lambert–Beer correction is that the in-cylinder toluene concentration is uniform. Detection system and other laser sheet nonuniformities were corrected from a laser sheet normalization procedure, which differs slightly from the procedure presented in [5] and explained in detail within Appendix 1. An additional correction was applied to the resulting instantaneous LIF images to correct for vertical stripes [5] caused by beam steering and the aforementioned correction algorithms.

After the corrections were applied, the resulting instantaneous image exhibited vignetting near the piston surface and to a lesser extent, the cylinder head. Such vignetting effects were consistent for each image at a fixed CAD with similar laser pulse energy. Correction of vignetting is commonly performed with a normalization procedure (i.e., division mathematical operation) as performed in [5]. Such a normalization procedure could not be used here because reference images were not acquired for each piston position. To correct for the systematic error imposed by vignetting, the ensemble-mean temperature image (based on 72 cycles) was subtracted from the instantaneous temperature images. Although division is the appropriate operation to correct for vignetting, the subtraction method employed is still suitable here to correct for the systematic error imposed by vignetting because vignetting effects were consistent within the ensemble-mean image. This procedure is further described in Sect. 2.4.3 and Appendix 1. LIF and temperature information were not analyzed in such regions until vignetting effects were corrected.

2.4.3 LIF temperature calibration

For each processing method, the spatial average LIF signal at each CAD was extracted from a 5 × 5 mm2 region far from solid boundaries (6 mm from nearest boundary, see Appendix 1) and calibrated to the polytropic temperature. The polytropic temperature was calculated from the in-cylinder pressure trace (Fig. 2a), polytropic exponents (AVL, IndiCom) and measured intake conditions. In Fig. 2 and throughout this work, CAD 360 corresponds to top-dead-center (TDC) compression.

Fig. 2
figure 2

a In-cylinder pressure and polytropic temperature, b two-color detection LIF temperature calibration, c and d LIF temperature calibration for all 18 recordings (4 cycles each recording) for one-color FFC and MSC, respectively. Individual cycles showed excellent agreement to their respective calibration curves and exhibited a correlation coefficient value greater than 0.98

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The damage and height adjustment of the Pellin–Broca prism played an important role when calibrating LIF signal to temperature. The amount of light that passed through the prism decreased with time due to damaging of the prism from the high laser power. The prism height and the amount of time the laser light passed through the prism before measurements were taken differed for each experiment. Thus, each recording sequence (i.e., 4 cycles) exhibited local differences of the integrated LIF signal intensity for the same CAD and temperature. The two-color image processing was independent from deviations in the local laser profile and signal intensity, and the LIF ratio for all 72 cycles collapsed down to one calibration curve shown in Fig. 2b. The one-color image processing procedure, however, was very sensitive to local changes in laser profile and signal intensity and required a separate calibration curve for each recording sequence. The respective calibration curves for all 18 recordings for each one-color image processing method are shown in Fig. 2c (FFC) and Fig. 2d (MSC). The LIF signal from each individual cycle showed excellent agreement to their respective calibration curves and exhibited a correlation coefficient value (R 2) greater than 0.98.

Once the LIF signal was calibrated to polytropic temperature, the 72 cycle ensemble-average temperature image was calculated for each method. The ensemble-average temperature image was subtracted from the instantaneous temperature images to yield the relative temperature distribution which is evaluated extensively in this work. Image illustrations deriving the relative temperature image are shown in Appendix 1 for each image processing method.

2.4.4 Particle image velocimetry

Particle image velocimetry images were processed with a commercial software (LaVision DaVis 7.2). Mie scattering images were cross-correlated with decreasing window multi-pass iterations from 128 × 128 to 16 × 16 pixel2 with 75 % overlap. A 16 × 16 pixel2 interrogation window corresponds to a 1 × 1 mm2 region in the viewing plane. A 3 × 3 pixel2 Gaussian smoothing filter was applied to the vector field to remove noise at spatial scales near the resolution limit of the PIV measurements [27]. PIV images were aligned with LIF images using the spatially defined target in the engine. A dynamic mask was used to identify regions of the piston and cylinder head in the images.

3 Toluene LIF measurement uncertainties

Accuracy (bias error) and precision (random error) affect the ability to interpret the LIF temperature signal. The absolute accuracy is primarily associated with the accuracy of the polytropic temperature calibration approximation. For relative temperature evaluations, the accuracy in the absolute temperature is not required [3, 4]. However, this work also presents absolute temperature images derived from the two-color detection strategy and absolute temperature accuracy must be addressed. The polytropic temperature was calculated from the in-cylinder pressure trace and measured intake conditions. The gas temperature at IVC was assumed to be the same as the intake temperature (295 K). Additional intake charge heating from the cylinder head can increase charge temperatures [28], but was not accounted for. A reasonable temperature increase in 10 K at IVC would marginally affect the temperature by 3 % (i.e., 17 K) at TDC.

The one-color detection images will exhibit inaccuracies if the local LIF signal variations are additionally caused by local toluene mixture fraction inhomogeneities. Although toluene has been used as a fuel tracer to measure local mixture fraction for direct-injection operation [11, 29], the resulting LIF signal from the one-color detection still cannot distinguish between temperature and fuel concentration inhomogeneities. In principle, it should be possible to determine the local absolute temperature from the two-color detection and then calculate the local concentration from the Lambert–Beer law in the one-color LIF images. Given the low signal-to-noise signals of the two-color temperature images and differences in absolute temperature distribution between the one- and two-color images (see Appendix 1), this procedure is anticipated to introduce larger ambiguities (with large uncertainties) than meaningful results.

Precision uncertainty is primarily associated with random errors originating from intensifier shot noise and fluctuations in laser intensity. The precision of each LIF thermometry technique was assessed from the 5 × 5 mm2 rectangle used for calibration. A preliminary analysis assessed the precision based on single pixels [7] and increased in sampled size up to 5 × 5 mm2 (62 × 62 pixel2). In this work, precision uncertainty is reported from a 10 × 10 pixel2 (0.8 × 0.8 mm2) region. A region of this size was chosen as this scale was well representative of the local LIF structures observed within the viewing plane. Both ensemble-average LIF signal and relative temperature signals were extracted from the 10 × 10 pixel2 region for each LIF processing method. The percent LIF uncertainty was calculated from 72 cycles at each CAD and defined by the ratio of standard deviation to ensemble-average LIF signal. The corresponding temperature uncertainty was determined from the spatial deviation of relative temperature within the 10 × 10 pixel2 region.

The precision uncertainty for each technique is shown with respect to temperature in Fig. 3. Precision uncertainty is significantly lower for one-color detection than the two-color detection, but increases for each method with increasing temperature due to loss in LIF signal in both the red and blue channels [3, 4, 7, 12, 23]. Although toluene number density increases during compression, the decrease in fluorescence quantum yield is greater with increasing temperature [14] leading to lower toluene LIF signals during compression [3, 4, 7, 12]. For the 295–545 K temperature range, the temperature uncertainty (ε) for the one-color detection increases from ±2 to ±4 K, while ε (based on one standard deviation) increases from ±7 to ±12 K for the two-color detection. The larger precision uncertainty associated with the two-color detection primarily originates from lower SNR levels and lower sensitivities (SNRTwo-Color = 12, SNROne-Color = 28 at TDC). Precision uncertainty is shown to increase faster for temperature signal than LIF signal at higher temperatures for the two-color detection. The conversion from S ratio to temperature yields this nonlinear behavior in the temperature uncertainty, but is not present for the one-color detection.

Fig. 3
figure 3

a LIF precision uncertainty and b respective temperature precision uncertainty for toluene LIF detection strategies

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The reported one-color detection uncertainties are greater than in previous studies [3–5] due to significantly lower laser pulse energies of the high-speed laser system. The reported uncertainty for the two-color detection is lower than previous work of the authors [7] because temperature signal was extracted from a 10 × 10 pixel2 region rather than for single-pixel regions.

4 Results and discussion

The temperature and flow velocity analysis presented in this work is used to investigate the development of natural thermal stratification throughout an engine cycle. Relative temperature images from each detection and image processing method are compared to reveal their ability to detect local thermal stratification. Images are presented for an individual cycle which exhibits representative trends observed in all 72 motored cycles. Temperature details extracted from the images are analyzed in a statistical manner to verify trends for all cycles. PIV and Mie scattering images are used to understand the transport and potential sources of temperature stratification during an engine cycle.

4.1 Development of temperature stratification during compression and expansion stroke

Relative temperature images from each detection and processing method are presented in Fig. 4 at selected CADs during the compression and expansion stroke from an individual cycle. Although there is less relevance of natural temperature stratification during the expansion stroke, for this study, it is considered important because it provides information about the late development of temperature fields [5] and provides a better understanding between the one- and two-color detection strategies employed. The distribution of the relative temperature is shown in the relative temperature PDF displayed in the last column of Fig. 4. The two-color images reveal a fine-grain speckled pattern and results from the division of the red and blue channel images—both which contain unique nonlinear pixel responses and inherent shot noise from the IRO. The two-color measurements have a larger precision uncertainty and yield a broader relative temperature distribution shown in the histograms. The local velocity field (every 5th vector shown) is used to describe the transport of the gas and is overlaid onto the relative temperature field (FFC).

Fig. 4
figure 4

Relative temperature images for one- and two-color detection strategies for an individual cycle. The flow field (every 5th vector shown) from PIV is used to describe the transport of the gas and is overlaid onto the one-color FFC images. Temperature PDFs are shown in the right-most column. Temperature profiles are obtained along horizontal lines at locations A and B and shown in Fig. 5. Location A is 10.5 mm from the cylinder head, while location B is 0.5 mm above the piston surface or 0.5 mm above the bottom of the image when the piston is not in the viewing plane

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At CAD 300, relative temperature images show a homogeneous temperature distribution within ±8 K, and a large-scale clockwise tumble motion is present in the viewing plane. Although far less resolvable in the two-color image, colder temperatures are present near the piston at CAD 340, and the flow image shows a breakdown of the tumble motion with the flow being strongest near the piston moving right to left. Colder gases become more predominant along the piston surface at TDC and are transported along the piston surface by the flow. At higher gas temperatures (i.e., CAD 340 and 360), the two-color detection suffers from higher precision uncertainty and is not capable of clearly identifying the cold gas structures near the piston without the guidance of the one-color images. The relative temperature histograms are centered around zero and broaden during compression, particularly for the two-color images.

During expansion, temperature stratification increases and the relative temperature histograms broaden. At CAD 380, the two-color image remains hindered by the predominant speckled pattern, but colder gas regions are shown to extend from the piston surface. These colder gas structures are more apparent in the one-color images and are transported along the piston surface by the local flow velocity (described further in Fig. 8). The MSC image does not exhibit the colder gas region (−5 to −10 K) near the cylinder head at CAD 380. At CAD 390, temperature images reveal large discrepancies between the one- and two-color images. Besides the presence of cold gas regions, locally hot gases extend from the piston surface for both one-color strategies, while the two-color detection primarily shows mild regions of cold gas near the piston. At CAD 415, the two-color image reveals cold gases emerging from the right hand side of the viewing plane appearing to result from outgassing of colder gases from crevices volumes (e.g., cylinder head or piston ring top-land crevices) [5, 7]. The piston ring-pack is located 74 mm from the piston top to prevent the piston rings from riding over the quartz glass cylinder liner [25] and this leads to a large top-land crevice volume (~9.9 cm3, excluding thermal expansion of the aluminum piston). Although cold gases extend from the piston region in the one-color images, the cold gas emerging from the right side of the image is not as apparent as the two-color temperature image, and hot gases are shown to extend from the cylinder head primarily for the FFC method.

A more quantitative comparison of one- and two-color measurements is presented in Fig. 5. Relative temperature profiles are extracted and compared along horizontal lines at locations A and B shown in Fig. 4. Location A is 10.5 mm below the cylinder head surface, while location B is 0.5 mm above the piston surface or 0.5 mm above the bottom of the image when the piston is not in the field-of-view. Noise levels are greater for the two-color measurements which can be seen immediately in the temperature profiles. Noise levels are largest at CAD 360 when uncertainty is the largest. Despite limited precision in the two-color measurements, temperature profiles between all three methods show great agreement during compression, particularly near the piston surface (Fig. 5 g, h, i).

Fig. 5
figure 5

Relative temperature profiles along horizontal lines for location A and B shown in Fig. 4. Despite higher noise levels for two-color detection, good agreement is shown between each detection strategy during compression. Larger differences are shown during expansion and are suggested to originate from local mixture inhomogeneities (see Sect. 4.3), which bias one-color detection strategies

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During expansion, temperature profiles can show disagreement between the one- and two-color measurements and differences exceed the uncertainty bounds. Differences first become apparent near the piston surface, but also show significant differences near the cylinder head at CAD 415. At CAD 380, the cold gases extending from the piston surface can be up to 15 K colder for one-color measurements (Fig. 5j). At CAD 390, the MSC method exhibits a large temperature swing near the piston (−40 to +35 K) and can be drastically different than the other methods (Fig. 5k). The FFC method shows agreement with two-color detection measurements with exception of the hotter gases detected at x = 5–10 mm. Temperature profiles at CAD 415 reveal similar patterns between each method, but exhibit large differences (up to 20 K) on the right side of the image (Fig. 5f, l) where outgassing from crevice volumes is expected.

The trends exhibited between the one- and two-color measurements shown in the individual cycle are representative of the trends observed in all 72 motored cycles. This is further quantified by evaluating the difference of the temperature profiles between the one- and two-color measurements. The temperature difference between the two-color and respective one-color measurements (TDIFF,2,1, Eq. 3) is evaluated at each point (352 binned pixels) along the horizontal relative temperature profiles shown in Fig. 6.

Fig. 6
figure 6

PDFs of temperature differences (T DIFF,2,1) along temperature profiles shown in Fig. 5. Differences are shown between two-color and one-color measurements at each point (352 binned pixels) along the horizontal lines at location A and B (Fig. 4) for all 72 motored cycles

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$$T_{{{\text{DIFF}},2,1}} = {\text{RelTemp}}_{\text{Two - Color}} \left( x \right) - {\text{RelTemp}}_{\text{One - Color}} \left( x \right)$$
(3)

The distribution of T DIFF,2,1 at location A and B are shown in Fig. 6 for all 72 motored cycles. T DIFF,2,1 for the FFC method is shown in red, while T DIFF,2,1 for the MSC method is shown in blue. The distributions of T DIFF,2,1 for each one-color image processing method are similar at each CAD. During compression, TDIFF,2,1 spans the range of ±10 K (based on a 2σ value) and increases to ±17 K at TDC due to increased noise levels associated with the two-color detection. At CAD 380, T DIFF,2,1 continues to cover a large range (±20 K) and the distribution further broadens during expansion. At CAD 415, large differences exist between the one- and two-color measurements and can be larger than ±30 K.

Large differences between one- and two-color measurements are primarily due to high noise levels associated with the two-color measurements (primarily at CAD 360) as well as possible systematic errors in the one-color measurements during expansion. Discussion of such systematic errors due to local toluene mixture heterogeneities are observed and discussed in Sect. 4.3.

4.2 Local temperature evolution after TDC

The temporal evolution of the temperature and flow field after TDC is analyzed to investigate the transport of cold gases in the viewing plane and identify when one-color measurements begin to deviate from two-color measurements. Relative temperature images from each detection and processing method are shown in Fig. 7, and relative temperature profiles extracted along a horizontal line 0.5 mm above the piston surface are shown in the right column. The local velocity field (every fifth vector shown) is overlaid onto the relative temperature field (FFC) to describe the transport of the gas.

Fig. 7
figure 7

Temporal evolution of thermal stratification detected for one- and two-color images during early expansion. The velocity field (every fifth vector shown) describes the transport of the gas and is overlaid onto the one-color FFC images. Temperature profiles 0.5 mm above the piston surface are shown in the right column. Despite higher noise levels in the two-color measurements, excellent agreement is shown in the temperature profiles from CADs 365–369, but begin to show larger differences starting at CAD 371. The rectangle shown at CAD 365 highlights enlarged view shown in Fig. 8

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Temperature images reveal several regions of cold gases extending from the piston surface. Two-color images remain hindered by higher noise levels (fine-grained speckled pattern), but exhibit similar cold gas regions near the piston as the one-color images for CADs 365–369. One-color images, however, better resolve the transport of fine-scale temperature structures and are preferred when images are in general agreement with two-color images. The warmer temperatures in the upper left corner of the two-color images exhibit lower signal quality due to vignetting near the IRO boundary. Horizontal temperature profiles along the piston show excellent agreement between one- and two-color measurements for CADs 365–369. Starting at CAD 371, temperature profiles begin to show larger differences between the one- and two-color measurements and such differences increase throughout the image sequence. Differences between the one- and two-color images are first apparent near the piston surface, but are later shown near the right hand side of the image during outgassing of crevice volumes (e.g., CAD 390 and 415 in Fig. 4).

Figure 8 shows the relative temperature (derived from one-color FFC) and local flow velocity (every third vector shown) within an enlarged view (highlighted region shown at CAD 365 in Fig. 7) to describe the transport of the cold gases identified near the piston surface. Images are shown at selected CADs from 365 to 374. A single cold gas pocket at CAD 365 is slowly transported (right to left) across the piston surface by the local flow field. The cold gas pocket extends from the piston surface and begins to disperse within the surrounding warmer gases. At CAD 371, only a thin layer of cold gas exists along the piston surface, but is quickly accompanied by colder gases entering the right side of the viewing plane at CAD 373, which are likely colder gases outgassing from the nearby piston crevice. Although the transport of cold gas regions is adequately described in Fig. 8, the one-color FFC temperature images shown require homogeneous toluene mixtures to accurately interpret LIF temperature signals. Local mixture fraction inhomogeneities would bias the temperature images shown in the image sequence and might explain larger difference in local temperatures between the one- and two-color measurements starting at CAD 371 (shown in Fig. 7).

Fig. 8
figure 8

Enlarged view of the temperature transport near the piston surface during early expansion. Velocity field (every 3rd vector shown) is overlaid onto the one-color FFC relative temperature images. A single cold gas pocket is shown to convect and disperse across the piston surface. Additional cold gases enter the viewing plane at CAD 373 and are likely gases outgassing from the piston ring crevice. Note: temperature values associated with the one-color FFC images shown may be biased by local mixture heterogeneities when large temperature differences exist in relation to two-color images shown in Fig. 7

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4.3 Formation of local mixture fraction inhomogeneities and effects on toluene LIF thermometry

Possible mechanisms that would cause large differences between the one-color and two-color toluene LIF thermometry measurements in the engine are: (1) higher noise levels associated with two-color detection, (2) insufficient representation of multi-cycle mean for one-color image correction, or (3) local toluene mixture fraction inhomogeneities that bias the one-color detection method. Noise levels in the two-color images decrease during expansion and provide better precision of the detected thermal stratification. Convergence of the LIF signal was shown to decrease below 1 % difference for 12 LIF images (Appendix 2), for which a 1 % LIF difference would only yield a maximum local temperature difference less than 2 K (referred from Fig. 2). This section describes the formation of local toluene mixture inhomogeneities in the engine and the resulting systematic errors it causes in the one-color detection images.

As already mentioned, toluene vapor was premixed with nitrogen to deliver a homogeneous toluene mixture to the cylinder. LIF images during intake (not shown) did not show any evidence of local mixture inhomogeneities within the field-of-view. If the intake mixture is homogeneous during intake and turbulent in-cylinder mixing during compression would only further ensure a homogeneous toluene-nitrogen mixture, the question remains: How would local mixture inhomogeneities develop and cause systematic errors in one-color detection strategies? High-speed imaging throughout entire engine cycles provided the opportunity to investigate such phenomenon.

Mie scattering images reveal strong heterogeneous toluene mixtures during late expansion due to local regions of toluene condensation. Figure 9 shows a Mie scattering sequence of toluene condensation during expansion for the individual cycle presented in this work. At CAD 420, a small liquid droplet (highlighted by yellow circle) is first apparent near the cylinder head and is likely associated with the outgassing from exhaust valve crevices. Volumetric image information is required to further identify the exact origin of the condensation site. At CAD 430, a larger region of liquid toluene (bright intensity region) is shown below the cylinder head, while other liquid regions remain located near the cylinder head. Toluene condensation quickly progresses and liquid toluene regions completely saturate the Mie scattering camera from CAD 450 to CAD 570 (i.e., 1/5 of engine cycle). Liquid toluene exits the cylinder during the exhaust stroke and Mie scattering images reveal that the mixture primarily returns to a gas mixture during mid-exhaust stroke (~CAD 610, not shown).

Fig. 9
figure 9

Mie scattering image revealing toluene condensation during late expansion for the instantaneous cycle discussed in this work. Toluene liquid is first observed at CAD 420 near the cylinder head and quickly progresses during expansion, revealing significant in-cylinder local mixture fraction stratifications. Toluene condensation is observed for all 72 motored cycles and large liquid regions are commonly observed until CAD 610

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Local thermodynamic conditions are analyzed to better understand the condensation process during expansion. Figure 10 shows Mie scattering, absolute temperature, and velocity images at CAD 430 when individual liquid toluene regions are present in the gaseous mixture. The absolute temperature field (Fig. 11b, c) is derived from two-color toluene LIF detection. The larger region of liquid toluene is identified in the Mie scattering image by the red circle and is overlaid onto the temperature and velocity images. Temperature information within the circle should not be interpreted because of unknown fluorescence characteristics of liquid toluene at high temperatures and pressures. Figure 10 additionally shows the in-cylinder pressure trace for the individual cycle and a detailed view of the pressure during expansion. Pressures are highlighted for the images shown in this work.

Fig. 10
figure 10

a Mie scattering, b absolute temperature field derived from two-color toluene LIF detection, and c absolute temperature and velocity field (every 4th vector shown) at CAD 430 for the individual engine cycle. Red circle highlights region of liquid toluene during condensation. In-cylinder pressure trace is shown in d and e and pressures for the images shown in this work are highlighted

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Fig. 11
figure 11

Two-color toluene LIF detection strategy image procedure shown at CAD 367 for an instantaneous cycle. a red channel image, b blue channel image, c LIF ratio image, d LIF ratio signal decay along horizontal line in c, e corrected LIF ratio image. Rectangle shown in e represents 5 × 5 mm2 region where LIF signal is extracted and calibrated to polytropic temperature

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At CAD 430, the bulk gas temperature distribution approaches the toluene saturation temperature of 305 K for a toluene partial pressure of 0.055 bar [30]. These values are based on the 2 bar absolute pressure (Fig. 11d) and the 2.75 % toluene mole fraction introduced during intake. It is recognized that local toluene partial pressures, and thus saturation temperatures, will change if local toluene concentrations are heterogeneous. Although there are significantly colder gases on the right side of the image (~270 K), local toluene concentrations may be different or condensation may be present in the out-of-plane direction and is not detected in these planar images. Nonetheless, toluene condensation quickly progresses as pressure and temperature continue to decrease during expansion and liquid toluene is present within the entire viewing plane several CADs later.

In general, the heat loss of the gas-to-solid surfaces and the inevitable mass loss during compression (<2 % of total mass [25] ) create lower temperatures and pressures during late expansion, which promote condensation. The low intake temperature (295 K) and high toluene seeding densities (2.75 % by volume, global Φ = 1.2 if air is used instead of nitrogen) used in this work can lead to condensation during late expansion. Additional Mie scattering recordings were repeated with 338 K intake temperature, and the same toluene condensation behavior during expansion was observed (although at later CADs). Higher intake temperatures were not possible with the current intake heating system. The low laser energies (1 mJ/pulse) associated with the high-speed laser system required the high toluene seeding densities to achieve sufficient LIF signal intensities. Reducing the toluene concentration will reduce the likelihood of liquid condensation. Most LIF thermometry studies reported in the literature utilize lower amounts of tracer concentrations (e.g., 10 % tracer by volume blended into isooctane fuel injected into the intake system) [3–6, 10, 11]. It should be mentioned, however, that condensation of the fuel mixture can also occur under such operation. For the motored operation reported in this work, liquid condensation was also observed for experiments with port-fueled isooctane without toluene seeding (global air–fuel mixture of Φ = 0.2). Liquid condensation during late expansion was also observed for operation with non-dried air (relative humidity >25 %) without fuel or tracer seeding at the same operating conditions. A combination of higher intake temperatures and lower fuel concentrations as presented in [3, 5, 6] can prevent liquid condensation during expansion, but should be experimentally verified.

The liquid toluene present during expansion and exhaust is in contact with solid surfaces in the engine and individual droplets or a thin film could deposit on surfaces or within crevice volumes. If such droplets or films are present, the evaporation of such droplets during compression would cause both a local temperature and mixture stratification. Based on spray droplet evaporation calculations (KIVA-4 mpi, [31]), a toluene droplet with diameter 10 μm on the piston surface would take approximately 4.9 ms (i.e., 29 CADs) to fully evaporate with a constant surrounding gas temperature of 550 K (i.e., maximum temperature observed at TDC) and 5 m/s convection velocity over the droplet. Although evaporation of a single droplet with a diameter of 10 μm would not yield a detectable temperature or mixture fraction difference within measurement precision, this calculation demonstrates the ability of liquid toluene to remain on solid surfaces during the compression stroke. During expansion, the outgassing of colder crevice volume gases, which may contain heterogeneous toluene mixtures, will undoubtedly bias one-color temperature images and may explain the observed differences between one- and two-color measurements. For this work, local regions of higher toluene concentrations would result in higher LIF signals, which would be interpreted as lower temperatures (and vice versa) according to one-color calibration curves shown in Fig. 2.

It is difficult to resolve the local toluene mixture fraction without benchmarking the LIF signal for well-defined in-situ conditions (i.e., concentration, temperature, and pressure). Local toluene concentrations could, in principle, be calculated from the Lambert–Beer law and absolute temperature images, but local differences between one- and two-color absolute temperature images (e.g., vignetting, see Fig. 16) would likely introduce large uncertainties. Therefore, the development of mixture stratification is observed in the engine and is merely proposed as a potential cause of the large differences in relative temperature measurements between one- and two-color toluene LIF detection strategies presented in this work.

If liquid droplets or films do exist on solid surfaces or within crevices and evaporate during compression, the observed cold gases extending from the solid surfaces during compression and early expansion may not entirely result from gas-wall heat transfer as stated in [3–5], but could also result from evaporation of liquid toluene droplets on solid surfaces [29]. In this case, the natural temperature stratification observed could be imposed from the measurement technique itself. However, use of direct-injection of liquid fuels under fired operation would also produce the same droplet evaporation phenomenon near solid surfaces. Nonetheless, temperature stratification resulting from gas-wall heat transfer or droplet evaporation is deemed important to further understand heat transfer phenomena in IC engines.

Although operating conditions reported here are different than other toluene LIF thermometry investigations [3–5], specific engine geometries, heat transfer phenomena, mass loss, and operating conditions will result in different temperature fields and local mixture fraction inhomogeneities such as toluene condensation could still occur. A careful understanding of the development of potential mixture inhomogeneities should be considered for all LIF thermometry detection methods that are biased by local tracer concentrations. Additionally, temperature stratifications imposed from liquid droplet evaporation as well as gas-wall heat transfer should be carefully studied in complex environments to understand potential causes of observed temperature stratification in IC engines.

5 Conclusions

High-speed toluene LIF thermometry is combined with PIV measurements to investigate the development of natural temperature stratification during the compression and expansion stroke in an optical engine. One-color and two-color toluene LIF detection strategies were simultaneously applied to evaluate and compare each strategy’s ability to accurately resolve temperature stratification in harsh environments such as IC engines. Two image processing methods common to the literature were applied for the one-color toluene LIF detection. All imaging processing procedures are described in detail and image illustrations are provided in the appendix. Measurement uncertainties are greater for the two-color LIF measurements due to lower signal-to-noise levels in the spectral ratio. Precision uncertainties are largest at TDC where temperature is greatest (550 K) and is ±12 K for the two-color measurements and ±4 K for both one-color measurements employed.

Relative temperature images revealed a homogeneous temperature distribution during mid-compression. Near the end of compression, cold gases are identified near the piston and become more predominant during early expansion when cold gases extend from the piston surface. Cold gases are shown to be transported along the piston surface by the local flow field. Temperature stratification significantly increases later during expansion as entrained colder gases outgassing from crevice volumes enter the viewing plane.

One-color and two-color relative temperature images and profiles agree during compression and early expansion. However, two-color images are limited in their ability to detect thermal gradients near the end of compression due to high precision uncertainties at high temperatures. Local regions of cold gases in the two-color images are better identified with the guidance of the one-color images, which are better suited to identify temperature gradients when homogeneous mixture fields exist. During expansion, large temperature differences between one- and two-color measurements exist for all cycles and are suggested to be caused by local toluene mixture fraction inhomogeneities, which bias one-color measurements. Toluene condensation occurs during late expansion and the exhaust stroke and causes a heterogeneous toluene mixture fraction within the combustion chamber. Liquid is in contact with solid surfaces and crevices of the combustion chamber and can evaporate during compression or expansion causing both local temperature and mixture stratification. The high toluene seeding densities required for high-speed LIF imaging (i.e., low laser pulse energies) lead to condensation during late expansion. Although this is a ramification of the high-speed imaging technique, liquid condensation during late expansion was also observed for port-fueled isooctane operation (global Φ = 0.2) without admittance of toluene seeding at the same operating conditions. Therefore, condensation would not be avoided when lowering toluene concentrations (e.g., 10 % toluene by volume in isooctane injected mixture, global Φ = 0.4) as typically performed for LIF thermometry studies performed utilizing Hz repetition-rate systems with superior laser pulse energies [3–6, 10, 11].

This work demonstrates the advantage of high-speed imaging and use of multiple image diagnostics to reveal the development of natural temperature and mixture stratification in a motored IC engine. When liquid droplets are present within the engine system, this work suggests that natural temperature stratification commonly regarded from gas-wall heat transfer can also be influenced from liquid evaporation on solid surfaces. Although this phenomenon can be imposed by the diagnostic method chosen, droplet evaporation from solid surfaces or crevices is equally pertinent within all modern-day engine systems.