1. Introduction

Infrared laser absorption spectroscopy is a widely used technique for quantitative, nonintrusive line-of-sight (LOS) measurement of gas quantities, such as temperature, species mole fractions and pressure [1]. For combustion diagnostics, typically near-infrared (NIR) and mid-infrared (MIR) sensing based on the absorption of light at specific wavelengths is used, which correspond to the rotational-vibrational transitions of the respective molecules. As the relative intensity of these transitions is related to the molecular populations in various quantum states that can be modeled, the gas quantities can be inferred from the measured absorption spectra [1,2].

In combustion applications, inferring temperature and species mole fraction traces of multiple reaction educts, products and combustion intermediates is essential to achieve a comprehensive understanding of reaction kinetics, the related combustion efficiency and pollutant formation. Thus, broadband sensors are favorable that cover the spectral range of various rotational-vibrational bands and thereby allowing for the simultaneous detection of multiple species with ideally a single instrument [3]. Moreover, considering a wide range of temperatures (e.g., 300 K to above 2000 K), resolving tens or even more absorption features, which contain thousands of absorption lines of a rotational-vibrational spectrum, leads to a higher temperature accuracy and sensitivity as each spectral line or feature has a unique scaling of its magnitude with temperature [2].

Depending on the observed absorption transition strengths, the absorber densities and the absorption path length, increasing the path length (e.g., by multi-pass approaches) can be favorable in order to achieve a higher signal-to-noise ratio (SNR) and thereby increasing the accuracy and sensitivity for the measured gas quantities. In case of high-speed measurements in turbulent flames and internal combustion (IC) engines, the reaction rates may also require at least few tens of microseconds resolution in order to resolve ignition delay times based on the temperature and species mole fraction profiles. These applications also demand a robust optical setup as the dynamic and harsh conditions are likely to cause severe beam steering due to density gradients or mixture inhomogeneities caused by temperature or pressure fields inside the combustion chamber [4].

Furthermore, in case of limited space and/or harsh environmental conditions or vibrations, a decoupling of the instruments from the studied system might be necessary, which can be accomplished by fiber coupling. Fiber based approaches can be installed very close to the desired measurement section and further reduce the open optical path length. Thus, measurement errors such as bias due to absorption in the LOS outside the test section (e.g., by air humidity) and signal fluctuations caused by relative movements between laser and sensor can be minimized. Hence there are several aspects to be considered in combustion applications.

Starting with fiber coupling, typically, in absorption spectroscopy, such as tunable diode laser absorption spectroscopy (TDLAS), the laser light is either guided by a multi-mode fiber (MMF) or single-mode fiber (SMF) and collimated into the measurement section. The beam is then either directly coupled to the detector, e.g., [5,6], or is coupled into a MMF that guides the light to the detector, e.g., [7,8]. It is well known that a MMF induces several modal effects, such as mode-coupling (energy is transferred from, e.g., the Gaussian mode to higher order modes due to imperfections within the fiber) and modal dispersion (different group velocities of the modes) [9,10]. The resulting modal noise, however, limits the achievable SNR [11]. So far, using an SMF also on the detector side, which would eliminate all MMF induced noise, has been theoretically considered for broadband AS in combustion applications [4,12], but only little research work has been published in this regard, e.g. [13,14]. Furthermore, to the best of the authors’ knowledge, the physical peculiarities of SMF coupling over MMF coupling have not been addressed for combustion applications, but must be considered in particular for beam steering environments.

With regard to the choice of the laser absorption technique, many different approaches have been applied to combustion research, such as TDLAS and wavelength modulation spectroscopy (WMS), cavity ringdown spectroscopy (CRDS) or cavity-enhanced absorption spectroscopy (CEAS), Fourier-domain mode-locked laser absorption spectroscopy, frequency comb spectroscopy and supercontinuum laser absorption spectroscopy (SCLAS) [1,2,15–19]. Narrowband approaches, such as TDLAS, provide limited capabilities if the absorption feature linewidths exceed the measured spectral range due to high-pressure broadening. For this reason, these approaches are often limited to pressures below 5 bar to 10 bar and therefore used within, e.g., shock tube studies, but are less suitable for IC engine or rapid compression (expansion) machine (RCM/RCEM) measurements. Broadband approaches have been demonstrated based on wavelength-agile absorption spectroscopy [20,21], SCLAS [18,22,23] and recently by dual-frequency comb spectroscopy [2]. Thus, using a single broadband light source and spectrometer, RCEM temperature, pressure and H₂O mole fraction measurements could be demonstrated at pressures exceeding 65 bar [22].

For a detection of multiple species based on broadband sources, the order of magnitude of the species concentrations to be measured must be considered and a suitable spectral range for the detection must be chosen. These considerations are necessary due to the largely differing spectral absorptivity coefficients, which mainly depend on the vibrational transition and the molecule species (which may differ by several decades and may also spectrally overlap). In general, a detection in the MIR spectral range is advantageous due to the spectral separation of the rotational-vibrational transitions of different molecules and the higher line strengths. However, depending on the laser and sensor type, the accessible spectral range is often limited. For the present study, the spectral subrange from 1350 nm to 1700 nm of the InGaAs-based spectrometer-camera is well suited for combustion measurements. Combustion educts and products, such as H₂O, CH₄ and CO₂, but also intermediate species (C₂H₂, C₂H₄, CO, OH) have distinct absorption features in this spectral range. However, for the NIR based approach, the detection sensitivity and SNR is challenging due to the weaker absorption strengths of, e.g., CO₂ and CO.

Therefore, increasing the absorption path length is a straightforward and efficient method to enhance the measured absorption, thereby increasing the SNR and sensitivity. Typical path length increasing approaches are CRDS or off-axis CEAS [1], but also multi-pass cells (MPCs), such as the White cell (WMPC) [24] or the Herriott cell (HMPC) [25–27]. With CRDS and CEAS, the light is coupled into the cavity through highly reflective (typically dielectric) mirrors. They are often used for shock tube (ST) studies [28] with absorption path gains of more than 80 (e.g., [29]) and have further been applied in RCM measurements by Nasir et al. [16,30] with a gain factor of 133 (averaged). As a drawback of CRDS or CEAS, the gain factor can be altered during the measurement and most of the laser power is lost when the light is coupled through the reflective mirror surface. Moreover, in order to maximize the potential path length gain, the cavity mirrors are mounted in direct contact with the absorbing gas of the reactive flow and are not separated by optical windows [31]. Thus, maintaining clean mirrors is critical for a high measurement sensitivity and can be difficult to achieve in combustion applications, e.g., in IC engines or RCM/RCEM facilities with direct fuel injection and/or soot formation. Furthermore, using replaceable cavity mirrors inside an ST or RCM/RCEM can limit the maximum system pressure, if the mirror axis needs to be adjustable.

For this reason, external multi-pass approaches, which are separated from the reacting gas by windows, can be beneficial. External fabry-perot cavity enhanced measurements in an ST were reported by Krasnoperov et al. [32]. Although coated windows were used, the cavity coupling and window reflection losses limited the gain to 12.4 ± 1. Compared to internal cavity approaches, the lower gain factor and its high uncertainty make the use of classical MPC an obvious choice. For cells of the WMPC and HMPC types, the light is either directly coupled in and out laterally (WMPC) or through an aperture hole in the mirror surface (HMPC). Thus there are no coupling losses and window fouling is less problematic. Typically, HMPCs are used for trace gas detection. In this regard, concentration measurements of carbon monoxide with detection limits up to the ppt (parts per trillion) level have recently been reported based on light-induced thermoelastic spectroscopy (LITES) in an HMPC with 34 passes at 10.1 m path length [33,34]. With regard to the application to combustion processes, the achievable optical path lengths are generally limited by the size of the measurement volume and potential perturbations (e.g., vibration and beam steering). WMPC-based TDLAS multispecies measurements within an IC engine exhaust manifold with a gain factor of about 16 at 97 cm path length at fired engine operation have been reported [7,35], so have HMPC-based measurements within an IC engine exhaust duct with a gain factor of about 50 and about 4.3 m path length [36]. The authors state that the approaches are stable (e.g., in case of engine vibrations or pressure changes), but these measurements were conducted at comparatively low pressures and are less suited for RCM/RCEM experiments: Here, window sizes are limited due to safety issues for improved pressure stability, especially at “engine-knock” conditions. Furthermore, the optically accessible distance between the piston- and cylinder head can be well below 10 mm at the end of compression. As the coupling beam spots need to be well separated from the reflecting spots on the mirrors (especially with beam steering), the number of passes – or the achievable gain factor – is thereby limited by the beam spot size and the available and optically accessible mirror surface, thus limiting the maximum number of passes achievable. For this reason, a planar multi-pass beam pattern with a sufficient distance to the piston and cylinder head and limited size is desirable. In this context, with regard to RCMs, Tanaka et al. have recently published 7-pass HMPC absorption measurements of formaldehyde and iso-octane at a compression pressure of 7.7 bar (non-fiber-coupled) [37]. There, cylindrical mirrors were used for the HMPC [38], however, the authors give no detailed information on the optical alignment, beam pattern and temporal/beam steering stability.

In the present study, we demonstrate SMF-coupled SCLAS with an external planar 9-pass Herriott type multi-pass cell for auto-ignition and combustion measurements in an RCEM. A key aspect of this work is the external HMPC, which allows for re-coupling into an SMF at a constant gain factor in an environment with significant beam steering. A ray tracing analysis of the HMPC-setup and flame luminosity images of the combustion experiments give deep insights into the SCLAS signal perturbations by the flame front.

For the RCEM measurements, methane is of particular interest: CH₄ or CNG (compressed natural gas), respectively, have the capability of a distinct CO₂-reduction compared to diesel fuel. So far, RCM/RCEM broadband absorption measurements for methane have been realized, e.g., within combustion measurements using the ν₃ absorption band based on a spark plug probe with comparatively broad spectral filters (about 100 nm FWHM, pressure up to 40 bar) at a temporal resolution of 110 µs [39]. Furthermore, dual frequency comb spectroscopy was utilized based on CH₄-absorption measurements in the 2ν₃ band at a high spectral resolution of about 0.15 cm⁻¹, but at a limited temporal resolution of 704 µs (spectral bandwidth 45 nm, pressures up to 21 bar) and without combustion [2].

Within this work, we first present auto-ignition and combustion measurements with temperature, H₂O, CH₄ and CO₂ courses at up to 25 µs temporal resolution and a spectral resolution of 1.43 cm⁻¹ (FWHM) for n-heptane/methane-air (“dual-fuel”) mixtures at various air-fuel ratios (AFR). As methane does not show auto-ignition under typical diesel-engine conditions, an additional more “reactive” fuel must be added to improve ignitability. Here, n-heptane as a typical diesel-fuel surrogate is used. Additionally, as a typical operation condition of diesel-engines, measurements for n-heptane/EGR-air (exhaust gas recirculation) are performed based on an air dilution with a CO₂-N₂ mixture.

The paper is organized as follows: Section 2.1 provides a detailed description of the optical setup for the RECM experiments, including the HMPC and the SCLAS- and flame luminosity imaging setup. In Section 2.2, the physical peculiarities of SMF-coupling over MMF-coupling of the spatial coherent SC laser light to the spectrometer are briefly addressed. Subsequently, a design guideline for the planar HMPC is given in Section 2.3. There, axial and vertical beam-steering are discussed on the basis of a ray tracing analysis. In Section 2.4 the RCEM experiment settings for homogeneous mixture auto-ignition and combustion measurement conditions are described. A brief description of the spectral model is given in Section 3, followed by the data analysis method based on HITEMP [40] line parameters in Section 4. In Section 5.1, firstly the beam steering effects on the SCLAS signal are discussed and compared to high-speed flame luminosity images and the ray tracing analysis. Additionally, the achieved single-peak SNR-values are summarized. Subsequently, the SCLAS results for n-heptane/methane-air measurements for various AFR are presented in Section 5.2. For these measurements, a brief comparison between the results based on line parameters from HITEMP and HITRAN [41] is given in Section 5.3. Furthermore, SCLAS temperature measurement uncertainty and mole fraction precisions are quantified. The results for n-heptane/EGR-air mixtures for repeated measurements at constant EGR-concentration are presented in Section 5.4.

2. Experimental setup and design of the Herriott-MPC

2.1 Experimental setup for the RCEM measurements

The combustion measurements were conducted in an RCEM. In contrast to classical RCMs, in the RCEM there is no motion locking at maximum compression (top dead center, TDC) and thereby the expansion immediately follows after the compression, similar to IC engines. The combustion chamber and boost pressures are separately measured with a piezoelectric pressure sensor (Kistler, type 6045A) and a 6 bar pressure transducer (class 1 accuracy), respectively. The 6 bar sensor is also used for preparing the gas mixtures (Biogon C20/air and CH₄/air) based on the partial pressures inside the combustion chamber. In addition, the piston position is measured with a high-speed magnetic incremental encoder (RLS, LM10, 20 µm accuracy class) mounted to the piston shaft. Heating cartridges inside the cylinder head and piston and an external fluid temperature control system allow for tempering of the combustion chamber. The temperature is thereby controlled by PT1000 resistance thermometers mounted inside the cylinder head and the piston. The in-cylinder temperature distribution at bottom dead center (prior to compression) was measured at several positions with thermocouples. A 84 mm diameter, full metal piston was used, which features a flat 5 mm deep piston bowl (74 mm diameter). Optical access is accomplished by 3 flat windows in the heated cylinder wall.

The optical setup consists of an SC laser (NKT Photonics, SuperK Extreme EXR-15), the RCEM (Testem GmbH, KM-13) equipped with the in-house designed external Herriott multi-pass cell and the optimized Czerny-Turner spectrometer (Fig. 1).

 

Fig. 1. Optical setup of the SCLAS experimental setup, including the cross section through the RCEM cylinder head with the planar Herriott-MPC setup. Components: longpass filter (LPF), fiber end (FE), achromatic fiber port (AFP), Herriott mirror (HM), window (W), fuel-injector (INJ), pressure transducer (PT), reflective parabolic collimator (RPC), fiber core (FC), high-speed imaging camera (HS-cam).

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Similar to our previous measurements [22,23], the EXR-15 SCL with a spectral power of up to 4.5 mW/nm (averaged) at 40 MHz repetition rate is used. After a longpass filter (850 nm cut on wavelength) the NIR SC light is guided by an SMF (NKT Photonics) to an achromatic fiber port (Thorlabs, PAF2-A4C). The light is coupled through the center aperture of the first HMPC mirror (d = 25.4 mm, FL = 100 mm, protected gold coating) at a divergence half angle θ_c of approximately 0.45° (NA ≈ 0.008) through the 24 mm thick flat cylinder windows (Corning 7979 IR Grade, 20 mm by 40 mm optical access). Reflected by the second HMPC mirror, the SC beam passes the combustion chamber 9 times, before it exits the cell through the center aperture. Considering the RCEM window surface distance of 85 mm and the beam incidence angles, this results in a total path length of 767 ± 3 mm, which corresponds to a gain factor of 9.02. The spacing between the mirror surfaces is about 177 mm for the 9-pass approach. For the presented measurements, a constant distance of 4.5 mm towards the cylinder head was used, which results in a distance of 5.5 mm to the piston crown top surface and 10.5 mm to the piston bowl surface at TDC for the presented compression ratios. After a second longpass filter (1300 nm cut on wavelength) the beam is focused behind the SMF core (Thorlabs, P1-SMF28E-FC-10) by a 90° fiber collimator (Thorlabs, RC04FC-P01), featuring an off-axis parabolic (OAP) mirror. The coiled 10 m long SMF ensures a high attenuation of the propagating modes in the fiber cladding. A 50:50 fiber coupler (Thorlabs TW1550R5F1) is used to connect two different CTS (only the broadband CTS is used within this study). There, the fiber cores (8.2 µm diameter) are used as entrance slits. During the measurements, all open optical paths outside the RCEM combustion chamber were flushed with nitrogen in order to suppress ambient absorption.

The CTS is based on the high-speed NIR spectrometer presented by Werblinski et al. [23]. An identical CMOS line-scan camera (Sensors Unlimited, GL2048L, InGaAs-array, 2048 pixel, 12 bit) was used for detection, however, all optical components were exchanged to enable an enhanced spectral range for multispecies measurements with high spectral resolution and a widely consistent instrument function over the spectral range. Furthermore, a robust, compact and mobile setup with high mechanical stiffness for transportation and the application of the SMF core as entrance slit were desired.

The CTS has a crossed layout for space reduction according to Fig. 1, with the entrance slit defined by the fiber core (Corning, SMF-28, 8.2 µm diameter, MFD 10.4 µm at 1550 nm, NA = 0.14). In order to minimize aberrations (spherical, coma and astigmatism), the first spherical mirror was exchanged by a 45° OAP mirror (d = 50.8 mm, reflected FL = 203.2 mm) and aligned with a shearing interferometer for a high quality collimated beam. Potential stray light is blocked by an optical iris. The light is diffracted by a reflective diffraction grating (300 lines/mm, 1200 nm blaze) and focused on the line-scan camera sensor by a spherical mirror (d = 50.8 mm, FL = 200 mm). In order to enhance the stiffness and shock resistance, all optomechanical components are attached to a 20 mm aluminum breadboard with 1-inch steel posts and steel mounts. For the OAP mirror and the camera, custom made mounts were designed, including a dowel pin rotation lock for the OAP mirror alignment. The breadboard is further mounted into a gear protector case and decoupled by rubber shock absorbers. The modifications result in a spectral range of 1374 nm to 1669 nm (5991 cm⁻¹ to 7278 cm⁻¹, 295 nm spectral bandwidth, tunable) at 0.144 nm per pixel. Thus, the measured spectrum ranges from the H₂O ν₁ + ν₃ P-branch to the CH₄ 2ν₃ Q-branch. The exact instrument function was determined with two tunable laser sources (Agilent, 81600B, 160 TLS module; HP, 8168F) for 18 equally distributed wavelengths ranging from 1475 nm to 1641 nm. For these measurements, the corresponding wavelengths were measured by a wavemeter (Burleigh WA-1100, accuracy ±1.5 pm at 1550 nm). For the instrument function, we calculated an average full width at half maximum (FWHM) of 0.345 nm (2.4 pixels) ± 0.01 nm. The spectral power at the SMF entrance core of the spectrometer was 1.0 µW/nm (+/−20%) for full saturation (camera settings: 3/4 gain at 17 µs exposure time, 1550 nm). This is in accordance with the expected value calculated from the camera manufacturer data (typ. 0.75 µW/nm), taking into account further losses such as the grating efficiency.

Alternating with the SCLAS HMPC setup (Fig. 1), an UV filtered intensified high-speed imaging camera (bandpass filter: Schott UG 11, objective: Nikon UV-Nikkor 105 mm f/4.5, intensifier: LaVision IRO-X S20, camera: Phantom V2012) was used to track the flame propagation via the recorded flame luminosity images. To this end, the HMPC optics rail was removed and the imaging system was attached from the side, with the optical axis perpendicularly to the cylinder axis according to Fig. 1.

2.2 Fiber coupling of broadband coherent sources

A key aspect within this work is the recoupling of the SCL-light for a fiber based connection of the CTS. In this regard, the choice of a suitable fiber type is of paramount importance, so relevant differences between MMFs and SMFs must be carefully considered. Coupling a coherent Gaussian beam into a MMF typically results in a speckle pattern at the fiber output caused by mode coupling, which depends on the coupling conditions, the core diameter and wavelength, but also the orientation and movement of the fiber. This movement of speckles in space and time can induce modal noise, e.g., if the photodiode attached to the fiber end has no uniform quantum efficiency over its active area [11]. This effect is less problematic, if the whole fiber core is imaged or butt-coupled to the active area of the photodiode as it is typically the case in a TDLAS approach or a temporal dispersion of the spectrum of an SCL. However, for MMF-coupling of coherent broadband light (such as an SCL) into a spatial dispersion spectrometer (such as a CTS) with a dimension of the entrance slit well below the fiber core diameter, this phenomenon induces severe spectral modulations: The entrance slit spatially filters the speckle pattern at the MMF end. This results in spectral intensity-modulations that are inconsistent over time, which superimpose the actual absorption signal and make it difficult to infer solely the gas-absorbance.

In an SMF, only the (close to) Gaussian mode (one of the two linear polarized LP₀₁ modes) can propagate through the fiber and a Gaussian-like, speckle-free distribution of the light exists at the fiber core end. Thus, no modal noise is induced by the fiber. Moreover, the small fiber core diameter and mode field diameter (about 10 µm for NIR) allow for the direct use as an entrance slit of the spectrometer. Furthermore, optical aberrations within the spectrometer are reduced as the slit or core position, coupling angle and numerical aperture are reproducible.

For an SMF, highest coupling efficiencies are achieved if the field distributions of the Gaussian beam and the fundamental fiber mode match [42]. With regard to the presented planar HMPC layout, it has been shown that such a layout preserves the complex q-parameter of the Gaussian beam [43]. Thus, for an unperturbed beam, high SMF-coupling efficiencies are achievable. In comparison to an MMF, efficient coupling is rather unlikely to achieve in combustion environments due to the rather small area of the fiber core and beam steering, which alters the Gaussian field distribution. Thus, a slightly divergent beam is launched into the combustion chamber and the beam waist is focused behind the spectrometer fiber core entrance surface, as also recommended by Kranendonk et al. for MMF-coupling in beam steering environments [4]. From this overfilled launch, the coupled energy to the fiber cladding is attenuated over a 10 m long coiled fiber. As a drawback, the field distributions of the beam and the fundamental fiber mode only poorly match, resulting in poor coupling efficiencies, which must be compensated by the SCL brightness and the CTS efficiency. We estimate the average coupling efficiency for the divergent beam to the SMF of the spectrometer to be 0.1% at 50% camera saturation. This calculation is based on the measured camera sensitivity and the spectral power output of the SCL, further losses (e.g., at the RCEM windows) are excluded.

It is worth mentioning, that an SMF effectively filters out biasing incoherent light sources [42]. These include, for example, stray light, thermal radiation or spontaneous emission. Furthermore, given the small core diameter, coupling of undesired reflections from the optical windows is very unlikely compared to an MMF.

2.3 Ray tracing analysis of the external Herriott-MPC

Whereas in many applications of an HMPC the cell is not intersected by coupling windows that refract the laser beam and typically no beam steering gradients within the cell are present, these issues must be carefully addressed for the present approach.

To this end, the HMPC cell was designed and modified in a ray tracing software (Zemax OpticStudio, non-sequential mode). Possible beam path configurations and stray light caused by partial reflections on the glass/gas-interfaces were analyzed. Beam steering was addressed by two separate gradient index (GRIN) volumes that induce 1-dimensional refractive index gradients ∇n within the combustion chamber, which represent the occurring main refractive index gradients for the conducted measurements. Of course, this simplified approach is not able to fully represent the complex refractive index field within the chamber, but provides valuable insight for the design and into the limitations of the approach. In order to enhance the coupling probability within the beam steering environment, a higher beam divergence angle is established. This leads to a larger beam diameter within the MPC, which is less sensitive against small disturbances, but also increases the beam spot diameters on the MPC mirrors and furthermore the focal spot diameter for recoupling to the SMF attached to the spectrometer.

In the first beam steering case, a refractive index gradient in direction of the lower temperature surface of the cylinder head is considered as the surface is closely spaced to the HMPC beam pattern. In the second case, the refractive index gradient points perpendicularly to the flame front in direction of the unburned gas mixture with lower temperature. The basic layout for the beam steering analysis is shown in Fig. 2.

 

Fig. 2. Basic geometric setup of the planar HMPC for the first 2 passes with a refractive index gradient pointing towards the cylinder head (RCEM windows are excluded).

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The beam is coupled from the left through the aperture of the first HMPC mirror. The laser beam diameter Ø_c, the beam divergence half angle θ_c, the coupling angle β_c,yz in the yz-plane and the distance between the mirrors define the beam spot size and position at the second HMPC mirror. Neglecting the GRIN, the beam is aligned along the ${\vec{v}_0}$ vector. Considering a 1-dimensional, cylindrical GRIN field (∇n) perpendicular to the cylinder head, the beam is continuously refracted while it propagates through the field. Thus, the incident beam hits the second mirror at a horizontal offset d_i,xz. Dependent on the beam incidence angle and the local normal vector towards the mirror surface ${\vec{v}_\textrm{n}}$, which changes with the focal length (FL), the beam is reflected in direction of the gradient field, where it is steered again. The beam spots must be spatially separated from the cell mirror apertures in order to prevent an early decoupling. Thus, the maximum potential path length gain of the planar HMPC is limited by the mirror distance, the coupling and divergence angle, the laser beam diameter/waist and the mirror and aperture size. With fixed mirror focal lengths, the number of passes increase with increasing mirror distance, which is limited to double the FL. For the optical components used, a maximum number of 15 passes is practically achievable, if the beam divergence angle is maintained. All experiments were conducted with a 9-pass alignment, for which the corresponding ray tracing analysis is shown in Fig. 3.

 

Fig. 3. Planar 9-pass beam pattern through the RCEM cylinder windows with beam steering cases. (a) Unperturbed beam propagation (similar to experimental setup, without combustion); perturbed beam propagation with the refractive index gradient towards the cylinder head (b) and the refractive index perpendicular to virtual flame front (c); coherent irradiance at the collecting fiber surface for the unperturbed beam (d) and the horizontal perturbed beam (e).

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In Fig. 3(a), the planar HMPC layout without the presence of a GRIN field is shown. For a better visualization, a smaller value for θ_c was chosen than within the experimental setup. For the two beam steering cases (Fig. 3(b,c)), an exemplarily refractive index gradient of ∇n = 2·10⁻⁴/mm is defined. The order of magnitude for ∇n is realistic when considering the present combustion gas conditions [44,45].

Figure 3(b) shows the beam steering case towards the cylinder head (horizontal). The steered beam is stabilized due to the spherical mirror surface, which refocuses the beam (dependent on the incident angle) inside the HMPC and partially compensates for the steering effect. Thus, the HMPC alignment is no longer within a plane, but broadened in x-direction dependent on  ∇n. With increasing values of ∇n, the horizontal offsets d_i,xz also increase, and values for ∇n should not exceed 4·10⁻⁴/mm for sufficient fiber coupling. For higher values, the beam either is blocked by the RCEM metal cylinder wall, which surrounds the windows, or exits the MPC at the mirror edges. During the measurements, beam steering in x-direction was also detected by an additional camera through the cylinder top window, in particular within the expansion phase. There, horizontal fluctuations of the beam spots on the mirror surface occurred, what we attribute to the piston induced flow field.

In Fig. 3(c), an example for the vertical beam steering case with a local GRIN perpendicular to a virtual flame front, represented by the rectangular cuboid, is shown. The vertical gradient leads to severe changes of the beam path as it interferes with the beam path locally and enhances the angular differences between the incident beams and the local mirror normal vectors ${\vec{v}_\textrm{n}}$ (yz-plane). Beam steering results in larger vertical offsets of the beam spots and the beam is likely to exit the MPC early trough one of the mirror apertures (as depicted in the image with only 7 passes) or at the mirror edges. Thus, the image represents only one of several different propagations that can be expected. For sufficient fiber coupling (vertical case), ∇n should not exceed 5·10⁻⁵/mm, however, this is only a rough estimate considering the simplified model.

The incident coherent irradiance E_e,c on the collecting fiber end surface is shown for the unperturbed beam in Fig. 3(d) (irradiance perpendicular to the fiber surface, values not to scale) and for the beam steering case towards the cylinder head in Fig. 3(e). There, the 90° fiber collimator and the experimental conditions (Ø_c = 0.76 mm, θ_c ≈ 0.45°) were considered. While only a small fraction of the coherent irradiation is in the fiber core area, the E_e,c values at the core are only reduced by about 40% by the GRIN. This implies that the detected transmission signal is less prone to beam steering in x-direction due to the divergent beam launch. In case of beam steering in y-direction, the beam is likely to exit the HMPC early through one of the HMPC mirror holes.

With regard to alternations of the number of absorption passes due to a beam exiting early (or late), which would lead to lower (or higher) mole fractions or pressures determined according to Eq. (1) - as a constant path length is used -, the coupling efficiency is several orders of magnitude lower because of the physical peculiarities of the SMF-approach. Small changes of the angle of incidence on the fiber core result in a poor match between the field distributions of the incident beam and the fundamental fiber mode (note that this is partially compensated by the divergent beam). This behavior is confirmed within our SCLAS and flame luminosity measurements: Dependent on the flame front area that propagates in direction of the depicted GRIN (Fig. 3(c)) through the combustion chamber, the SCLAS signal is either temporally attenuated or completely lost. Generally, the mole fractions are expected to follow continuous traces. The laser beam is coupled efficiently only in the design case with 9 beam passes, discontinuous jumps for the evaluated mole fractions would occur in case of, e.g., 7 or 11 passes. For the SMF-approach, increased path lengths are probably solely caused, if the beam pattern is broadened by steering in x-direction or slight steering in y-direction. For the presented beam steering case in x-direction, the effective path length increases by less than 0.2%. However, for MMF-approaches or free space coupling to the spectrometer, an early/late exit could lead to much lower (or higher) values for the inferred species mole fractions and pressures due to the higher coupling efficiencies for beams with altered effective absorption path lengths.

From the ray tracing analysis, we found alignments for $5 + 4m$ passes to be significantly more stable against horizontal beam steering than for $3 + 4m$ passes. Here, m is any integer with $0 \le m \le 3$. For the first alignment case, the exiting beam almost preserves the coupling angle of the launching beam. For the latter case, the beam is likely to miss the exit hole and to be trapped inside the HMPC. This could also be verified by laboratory experiments with 9 pass and 11 pass alignments, respectively, where the 9-pass setup yielded significantly lower fractions of underexposed frames.

2.4 Experiment settings and measurement conditions

The SCLAS spectra were recorded at 40 kHz frame rate with an overall measurement time of 2.5 s (100,000 frames). The start of each SCLAS measurement was triggered at 50 mm piston stroke. For the flame luminosity images, a frame rate of 80 kHz was utilized with overall measurement times between 20 ms and 150 ms. Auto-ignition experiments with homogeneous fuel lean mixtures of n-heptane and methane (dual-fuel) at different AFR and, furthermore, fuel-rich mixtures of n-heptane with EGR were conducted. The term “dual-fuel” describes a homogeneous mixture of n-heptane and methane and air provided before compression, rather than the classic dual-fuel combustion process where the ignition-fuel is injected just before the piston reaches TDC. A cylinder head temperature of 393 K was adjusted in order to guarantee full vaporization of n-heptane, which could wet the cylinder wall during fuel injection. With the current maximal piston temperature of 373 K, this results in a temperature stratification in the cylinder, but improved evaporation and mixture formation.

The air-fuel mixture is created within the combustion chamber as following: Initially, the RCEM combustion chamber is filled with air, which is heated by the conditioned piston and cylinder head at ambient pressure (1011-1012 mbar). Multiple n-heptane (EMPLURA, purity ≥ 99.0%) injections at 2.5 Hz (1000 bar rail pressure, Continental research injector, 3 nozzles) are performed about 90 seconds before the actual RCEM shot. After injection the RCEM driving gas pressure is adjusted, followed by feeding methane (CH₄, 99.5% purity) as secondary fuel or Biogon C20 (mixture of 20% ± 2% CO₂ with N₂) as artificial exhaust gas into the combustion chamber, until the partial pressure reaches the desired level. Then, in order to measure H₂O absorption within the compression phase, humidified air is fed into the combustion volume, until the partial pressure equals a total boost pressure of 2 bar (note: the initial H₂O mole fraction thereby is significantly lower for the EGR experiments). The RCEM piston is thereafter slowly hydraulically pushed in direction of the cylinder head, followed by the actual fast compression when the piston position exceeds about 22 mm of the 150 mm piston stroke. After each experiment, the combustion chamber is flushed multiple times with dehumidified air. The compression ratios (CR) and species mole fractions X_i prior (index 0) and after (index 1) the combustion are summarized in Table 1.

Table 1. Overview of adjusted CR and species mole fractions during dual fuel and EGR experiments in the RCEM.

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We calculate the mole fraction for the reaction products based on the global reaction equations, assuming a full consumption of the initial O₂ mole fraction. Thus, intermediate species that could change the combustion gas composition (e.g., CO) are not considered. The injected n-heptane mass is known from an injection rate analysis (Moehwald HDA-500, injection quantity and rate measuring unit). For all dual fuel measurements, an n-heptane mass of 30.4 mg was injected, spread over 4 split injections. Thereby, the AFR is solely adjusted by the CH₄ mole fraction in the combustion volume. The CR was adjusted in order to approximately synchronize the ignition timing of the individual dual-fuel measurements. For all EGR measurements, an n-heptane mass of 85.9 mg was injected, spread over 12 injections. Although little window fouling due to combustion residues was visible after about 5 to 10 cycles, the SCLAS signal level required cleaning only after about 50 consecutive cycles.

We expect higher uncertainties of about ± 5% (relative) for X_CH4 due to the low partial pressure and the limited set-point resolution within the RCEM software. The X_CO2 error is further estimated at below ± 3% (relative) based on the set-point resolution and the Biogon C20 production tolerances. The error for the injected fuel mass is calculated to be ± 2% based on the injection rate analysis and fluctuations of the rail pressure. The air humidification was performed for each measurement by pipetting a constant mass of distilled water to a pipe fitting filled with a porous foam that is attached to the RCEM compressed air supply. Thus, no uncertainties can be provided. The CR is calculated based on the RCEM position sensor and combustion chamber geometry up to the two check valves for gas feeding. We calculate a CR uncertainty below ± 4%, which results in corresponding uncertainties in the adiabatic compression temperature.

3. Spectral model

Here, a brief description of the underlying absorption model is provided, see also Ref. [23]. Within the model, we calculate the broadband absorbance spectra from the HITEMP [40] line list parameters with a line by line code. In Eq. (1) the underlying Beer-Lambert law and the related absorbance model function are shown.

Here, α_ν is the absorbance at wavenumber ν, S_j (T) is the temperature T dependent line strength of the transition j, ϕ_ν,j is the line shape function of transition j at wavenumber ν, P is the static pressure, χ is the gas composition vector, X_i is the mole fraction of the absorbing species i and L is the path length through the absorbing gas. A Voigt line shape function considering the Doppler and pressure (collisional) broadened line shape with broadening coefficients from the spectral databases is used and the temperature dependence of the transition line strength is calculated according to [23]. The NLLSQ algorithm determines all variables simultaneously. Thus, pressure, temperature and all species mole fractions are iteratively inferred, which removes the barrier for the number of optimized variables of lookup table approaches. For the multi-species gas mixtures studied, we calculate the collisional broadening (Lorentzian) FWHM for each species according to

Here, ν_C is the collisional FWHM, γ_self and γ_air are the self-broadening and air-broadening coefficients from the HITEMP database, respectively, n_self and n_air are the temperature-dependence exponents for the broadening coefficients and T₀ is the reference temperature (296 K). Thus, molecular collisions with other species are calculated as collisions with air molecules. This simplification of the gas composition vector χ is performed as the broadening coefficients for other collisional partners (e.g., CH₄ with H₂O, γ_CH4-H2O) are not provided by the spectral databases in the broad spectral range. Furthermore, as HITEMP only provides the air temperature dependence exponents n_air, we use single average values for n_self within the power-law for all transitions of one species. From Refs. [1,46,47] we estimate the average n_self (H₂O,CO₂) = 0.5 and the average n_self (CH₄) = 0.84 according to [48]. Furthermore, both the air-pressure shift and the temperature dependence of the pressure shift are incorporated in the absorption model according to, e.g., Ref. [1]:

Here, v_S is the line shift, δ_air is the air pressure-induced line shift parameter from HITEMP and η is the temperature dependence exponent for the pressure shift. According to Refs. [1,49] we assume an average η(H₂O,CH₄) = 1 and further assume η(CO₂) = 1 although no proper suggestions for the corresponding spectral bands could be found. A comparison of the HITRAN and HITEMP database with regard to the improvement of the spectral line shape predictions based on temperature scaling coefficients for the air pressure shift and self-broadening coefficients for H₂O (6800 cm⁻¹ to 7200 cm⁻¹) can be found in [46].

Furthermore, it must be considered that several assumptions are made within Eq. (1). These include a uniform distribution of the gas properties along the LOS. This only applies to a limited extent because of, e.g., temperature inhomogeneities before and after the flame front, gas mixing caused by the piston induced flow field, temperature gradients towards the walls/windows and/or thereby inhomogeneous species mole fractions due to incomplete combustion caused by quenching effects. For the partial pressures or species mole fractions, we additionally assume an ideal gas behavior of the gas mixture. It must also be taken into account that, although the HITEMP database provides line parameters for higher rotational quantum numbers, which are needed to model elevated temperatures, the averaged broadening and shift parameters from this database and the average temperature dependence exponents for the pressure shift are likely to cause larger residuals and erroneous bias to the parameter courses for lower temperatures when compared to HITRAN. Line mixing effects and the limited accuracy of the spectral databases for high pressure conditions are also likely to bias the measurement results.

4. Data processing

A nonlinear least squares (NLLSQ) curve fitting algorithm based on the Matlab “lsqnonlin”-solver is used to compute the best fit between the modeled and the measured absorbance spectra according to Eq. (1). We calculate the measured absorbance from the transmission spectrum I (with absorbing gases) and the background spectrum I₀, which is averaged from 1000 consecutive spectra measured prior to the combustion experiments with dehumidified air. The transmission spectra I and I₀ are calculated by subtracting the average pixel dark noise values from the recorded camera intensity spectra. Data processing is performed on the first derivative of absorbance with respect to wavelength. This simple but robust approach, presented for broadband multiparameter spectroscopy in a HCCI engine by Kranendonk et al. [50], significantly reduces low-frequency noise and spectral offsets (e.g., by window fouling or beam steering) within the absorbance spectra.

In Fig. 4 an absorbance spectrum (Fig. 4(a)) with the according best spectral fit based on the derivative (Fig. 4(b)) is shown for one of the dual-fuel experiments. The data analysis is performed on the entire spectral range shown (1374 nm to 1669 nm). Consequently, the spectral lines of the species H₂O, CH₄, CO₂ and furthermore CO, C₂H₂ and H₂O₂ were calculated in a temperature interval between 300 K and 2500 K. Lines with a minimum line strength of at least 10⁻²³ cm⁻¹∕(molecule·cm⁻²) to 10⁻²⁷ cm⁻¹∕(molecule·cm⁻²) (dependent on the species absorbance contribution) are considered. This results in about 21,800 line profiles (about 12,000 for H₂O, 1800 for CO₂, 2800 for CH₄) that are modeled within the line by line code at a resolution of 0.05 nm (6000 wavelength steps) and are then summarized and interpolated to the measured wavelength positions. We constrain the pressure by a ± 1% boundary interval based on the RCEM pressure transducer data, mole fractions are bounded between 0 and 1 and the temperature between 250 K and 3000 K, respectively. For each evaluated spectrum, this results in an average of 48 s solving time for the 6 species mole fractions, the temperature and pressure on a Xeon E3-1240 v3 CPU.

 

Fig. 4. Example for the NLLSQ curve fitting spectra evaluation based on the first derivative of absorbance with respect to wavelength. (a) Measured absorbance spectrum (single frame, t = −2 ms, AFR = 1.54 (dual-fuel)) and best fit for the considered spectral range; (b) differentiated absorbance spectrum and best fit; (c) remaining residuals; (d) left section from (b), H₂O absorption; (e) right section from (b), CH₄ absorption.

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Larger residuals remain from the measured absorbance data due to etaloning effects (probably caused by the line scan camera detector glass at ν_FSR ≈ 100 GHz) according to Fig. 4(c). As I₀ and I are measured at different times, a slight shift of the etaloning phase (e.g. by temperature effects) results in a high-frequency absorbance pattern, which is further pronounced with differentiation. Although residuals remain larger, we account the robust spectral fit to the fact that the interference frequencies are higher than those of the absorption peaks, thus enveloping the absorption profiles and consequently average out due to the large spectral range. In contrast to Refs. [22,23,50], no spectral smoothing is performed, although the differentiation increases noise by a factor of approx. √2. Smoothing leads (in our case) to a slightly biased result when applied to the modeled and measured spectra, although both share the same resolution and wavelength positions. This bias is on the one hand caused by the limited pixel/nm-resolution as pixel noise can lead to a differing smoothed shape of single absorption peaks. On the other hand, we assume that this is caused by the remaining absorbance residuals due to HITEMP line parameter errors. In Fig. 4(d,e), zoomed sections of the spectrum with mainly H₂O (ν₁ + ν₃, P-branch) and CH₄ (2ν₃, R-branch and Q-branch), respectively, are shown.

5. Results and discussion

The results section first focuses on the signal stability of the HMPC approach with regard to beam steering effects within the RCEM experiments. In the second part, we demonstrate the inferred parameter courses for temperature, X_H2O and X_CH4 as well as X_CO2.

5.1 Flame-induced beam steering

In Fig. 5 flame luminosity images of an example dataset of fuel-rich n-heptane/EGR ignition and combustion are shown.

 

Fig. 5. Single shot flame luminosity images of a RCEM cycle at 80 kHz frame rate for the experiments with EGR (AFR = 0.76). 1^st and 2^nd stage ignitions occur as downwards propagating flame areas through the RCEM cylinder wall windows. Intensity values are logarithmized. HMPC marks the studied volume of the cylinder.

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For all presented measurements, both the 1^st and 2^nd ignition flame areas propagate from the “top” downwards through the window region. We attribute this to the temperature stratification in the RCEM as the piston head (here on the right side) has a higher temperature than the piston (left side). Thus, prior to the start of the compression, the mixture has a higher temperature close to the cylinder head in the top right corner of the images due to natural convection, which is also observed with thermocouple measurements.

For the EGR experiments, a delay time between the 1^st and 2^nd flame front of 375 µs to 425 µs can be observed in the HMPC region. This is confirmed by the evaluated SCLAS data in Fig. 8 (see Section 5.4) and the corresponding transmission signal intensity (not shown here), which is altered due to the occurring beam steering. For the dual-fuel experiments, significantly higher delay times of about 2.5 ms are observed, which we attribute to the low n-heptane concentration leading to a lower reactivity. There, the area of the 1^st ignition flame front is significantly larger than for the EGR measurements (not shown here). Dependent on the temperature/density gradients that are induced by the propagating flame front within the 1^st and 2^nd stage ignition, we expect the beam to be mainly altered according to Fig. 3(c). Thus, the SCLAS signal is likely to drop significantly.

This can be observed in the SCLAS transmission signals, exemplarily shown for a dual-fuel experiment in Fig. 6. In Fig. 6(a), the transmission spectrum (camera intensity) is depicted at −2 ms with H₂O and CH₄ absorption present. In Fig. 6(b), the corresponding time series of the measured spectra around the TDC region is provided. When the 1^st flame front interferes with the HMPC beam pattern, there is a broadband signal drop of about 60%. In case of the EGR experiments, no transmission signal is detected for about 100 µs to 175 µs. We attribute this to the vertical beam steering case in Fig. 3(c). For the EGR-experiments, the smaller 1^st ignition flame and the larger temperature increase (≈180 K, Fig. 8; see Section 5.4) cause higher beam steering than the larger 1^st ignition flame of the fuel-lean dual-fuel mixture with a lower temperature increase (≈70 K, Fig. 7). With the 2^nd flame front, which induces a much larger temperature gradient, the SCLAS signal is temporally lost completely for both dual-fuel and EGR-experiments for 125 µs to 225 µs. After the main (2^nd) ignition, the flame luminosity images indicate a relatively homogeneous reaction. Thus, we suspect the occurring signal drop and fluctuations to be mainly caused by the flow field in the LOS region: For the “weak knocking” conditions (AFR = 1.23) occurring here, a flow and density field is immediately induced by the oscillating pressure wave, whereas without knocking, the flow field induced by the piston movement is likely to propagate later in the LOS region. The resulting signal drop temporally lead to poor SNR, before the signal stabilizes about 10 ms after TDC. Nevertheless, parameter traces can be inferred around TDC at 40 kHz from the SCLAS data, as shown in the following sections. There, frames with more than 15 saturated pixels and otherwise frames with more than 5 weakly exposed pixels (dark-noise-corrected intensity below 8 counts, typically at strong absorption peaks) are excluded through threshold filtering. Thus, for the presented data (−19 ms to 60 ms), 97.3% of the recorded dual fuel frames and 97.7% of the EGR frames were accepted and shown in the following parameter traces.

 

Fig. 6. Measured SCLAS transmission (dual-fuel, AFR = 1.54). (a) Transmission spectrum over wavelength/wavenumber (single frame at −2 ms, raw data); (b) related time series of the transmission spectra around TDC with 1^st and 2^nd stage ignition and the early combustion phase (40 kHz frame rate, 0 ms corresponds to TDC).

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Fig. 7. Parameter courses for individual heptane-methane (auto-ignition) RCEM experiments for different AFR (0 ms corresponds to TDC). (a) Pressure from the pressure transducer; (b) normalized cylinder volume based on the piston position sensor; (c) temperatures calculated from the broadband absorbance spectra and adiabatic calculation; (d) relative deviations for temperature (AFR = 1.54 and CH₄ w/o C₇H₁₆); (e) H₂O mole fraction; (f) CH₄ mole fraction; (g) CO₂ mole fraction; (h) relative deviations from the mean mole fraction (AFR = 1.54, CO₂ not shown). All spectra were recorded at 40 kHz frame rate, the effective evaluated frame rate varies between 2 kHz and 40 kHz.

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With start of compression, SNR values for the adiabatic reference measurement (without combustion) for H₂O and CH₄ start at 71 and 52, respectively. At TDC, values of 97 (H₂O) and 72 (CH₄) are achieved, lowest SNR values accepted by the signal threshold filter are at about 3 to 4. CO₂-SNR values do not exceed a value of 4 over the whole cycle (at 1570 nm). SNR values are calculated based on the largest species absorption peak height (in counts) and the average camera noise standard deviation of 3.06 counts. The overall system noise based parameter uncertainties (including shot noise, camera noise, laser relative intensity noise) can be well assessed based on the parameter precisions for the start of compression up to about TDC. There, measurement errors caused by the temperature stratification and piston induced convection can be neglected in a first approximation. Precisions are listed in Table 2 and additional values are provided and discussed in Sections 5.2 and 5.4, respectively.

5.2 N-heptane-methane (dual-fuel) fuel-lean experiments

In Fig. 7 the results for three different AFR-values and an adiabatic reference measurement for CH₄ in humidified air without n-heptane (and thus without ignition) are shown. Mean values for the (relative) difference plots in Fig. 7(d,h) are based on a 10 (for temperature) or 20 (for X_i) sample points window length moving average filter. This filter is only used to calculate the local (local in time) precisions and to visualize the local relative deviations from the mean courses. Frame averaging was partially performed for the early compression stroke and late expansion stroke, which results in a lower temporal resolution according to Fig. 7(a). Thereby, the presented evaluated frame rate varies between 2 kHz (500 µs temporal resolution, averaged frames) up to 40 kHz (25 µs temporal resolution, single frame) for the ignition and combustion phases. For all experiments, 0 ms corresponds to TDC (top dead center).

In Fig. 7(a) the measured pressure traces from the pressure transducer are shown. There the adiabatic reference experiment w/o C₇H₁₆ reaches a pressure maximum of about 32 bar, while the combustion experiments reach 45 bar, 49 bar and 81 bar, respectively. The compression ratios were adjusted in order to synchronize the ignition timings according to Table 1. For the lowest calculated AFR = 1.23, slight knocking with pressure oscillations of about 10 bar can be observed after the main ignition, starting at 2 ms. Note that the larger pressure leads to a higher acceleration of the piston for the lowest AFR, which is shown by the normalized combustion chamber volume traces in Fig. 7(b). Within the diagram, apart from the main compression, a second damped compression can be observed at about 25 ms to 50 ms, caused by the floating piston.

In Fig. 7(c) the evaluated SCLAS temperature traces are shown. The temperature traces are arranged in order of the corresponding AFR-values, with a maximum inferred temperature for the fuel-richest operation point with over 1800 K, 1520 K at AFR = 1.54 and the lowest peak temperature of 1430 K at AFR = 1.67. For AFR = 1.23, the largest temperature gradients for both main ignition and expansion are observed. We attribute the former to the higher reactivity and a faster fuel consumption. Furthermore, the combustion is more complete compared to the fuel-leaner operation points, thus the temperature reduction caused by the gas expansion and heat transfer to the walls is more noticeable. For AFR = 1.23, the expansion temperature drop is further enhanced by the higher piston acceleration, thus the volume increases faster here. For fuel-lean combustion, the unsteady temperature rise occurring prior to the pressure rise of the second damped compression (at about 40 ms), implies a further ongoing combustion. This was also observed in the flame luminosity images, with a homogeneous signal rise around 25 ms to 50 ms. With regard to the beam steering stability, the transmission spectra of the 1^st stage ignition flame front could be captured for all experiments (see zoomed section), whereas the 2^nd stage flame front is only partially accessible for fuel-leaner operation.

In terms of measurement precision, mean standard deviations (STD, σ) for the inferred parameters (x) were calculated for different time periods t for both single and repeat measurements according to Table 2. The values for $\overline {{\sigma _x}(t )} $ are calculated as the mean values of the respective parameter standard deviations in the time period t for a single measurement. $\overline {{\sigma _x}(t )} $ is a combination of the fluctuations due to turbulent processes in the cylinder (i.e., turbulent flow fields and/or inhomogeneous combustion), engine knock as well as measurement uncertainty (e.g. in case of low SNR values and noise). Additionally, for the EGR-experiments, the measurement precision $\sigma ({\overline {x(t )} } )$ is calculated as the STD of the mean parameter values $\overline {x(t )} $ in the time period t of three consecutive measurements. $\sigma ({\overline {x(t )} } )$ is a combination of the variability of the RCEM and cyclic fluctuations. All σ-values are based on an (N - 1) normalization. For AFR = 1.54, we determined an average STD for temperature $\overline {{\sigma _T}(t )} $ at 40 kHz evaluated frame rate (f_eval) of about 5.1 K at around TDC and 12.8 K after the 2^nd ignition (t = 2.7 ms to 4.3 ms), which almost doubles to 24.2 K in the expansion phase (t = 4.5 ms to 5.5 ms).

Table 2. Standard deviations for the quantities of interest for two operating points at three example points in time (TDC, at 1^st ignition, at 50 ms after TDC).

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In order to compare the inferred temperature with a calculated temperature, an adiabatic core compression model was used based on the known cylinder volume and a temperature dependent heat capacity ratio (NIST data) for an air-H₂O-CH₄ mixture. In Fig. 7(c), calculated temperature curves are shown for CH₄ (w/o C₇H₁₆) for two different start temperatures (T₀ = 383 K and T₀ = 393 K), where the higher temperature represents the wall temperature of the cylinder head (close to the LOS) and the lower temperature refers to the average in-cylinder start temperature. Note that the compression ratios vary according to Table 1 and the lower heat capacity ratio of additional n-heptane would result in lower adiabatic temperatures.

In this context, Fig. 7(d) shows the absolute temperature difference of the reference measurement (w/o C₇H₁₆) and the adiabatic reference T₀ = 393 K (right y-axis). The measured temperature matches the adiabatic reference up to 10 bar (which is reached at t = −8 ms), followed by an overestimation of about 10 K in the late compression phase. With the pressure increasing above 20 bar to 25 bar (at about −3 ms), the temperature falls below the T₀ = 393 K reference, but matches the T₀ = 383 K reference. We assume that this shift is mainly caused by temperature stratification in the cylinder: the mixture with lower temperature present in the piston region is pushed in direction of the LOS region at higher temperature. With proceeding expansion, the temperature decreases due to heat transfer from the gas to the walls. Furthermore, it becomes apparent how the temperature stratification, heat losses to the cylinder wall and the flow field dominate the relative deviations in the expansion stroke. On the left y-axis (ΔT/T_mean), the relative differences of the inferred temperatures from the mean temperature course T_mean for AFR = 1.54 is highlighted, which is generally below 2%. It can be seen that both the system pressure (and thereby the absorber density) and the frame averaging affect the relative temperature deviation (and thereby $\overline {{\sigma _T}(t )} $).

The species mole fraction courses for H₂O and CH₄ are shown in Fig. 7(e,f), respectively. As within the temperature courses, the 1^st stage ignition with partial fuel consumption can also be fully resolved for H₂O and CH₄. During the 1^st ignition, X_H2O increases by 0.01, whereby X_CH4 decreases about 20%. However, there is a significant pressure (and temperature) dependence for the measured CH₄ profiles. Especially during compression, the CH₄ mole fraction rises significantly, which is not plausible. This effect is less apparent for the H₂O curves. We trace this back to the averaged, but thereby inaccurate broadening and pressure shift parameters within the HITEMP database (see Section 5.3). Furthermore, potential errors from the pressure transducer could result in an unwanted bias of the mole fraction results, due to the strong correlation between mole fraction and pressure within the pressure broadening (see, e.g. [23]) and the narrow pressure boundary constraints within the presented data evaluation. Further it must be mentioned that, while the induced n-heptane mass is well known, we infer X_CH4-values from the SCLAS measurements, which are 12% below the RCEM partial pressure settings on average according to Table 1. In addition, the maximum X_H2O-values after combustion are 20% below the expected mole fractions based on a global reaction equation. We suspect that both lower CH₄ mole fractions and an incomplete/ongoing combustion are present. The latter is also confirmed by the X_CH4 and temperature courses and the flame luminosity images.

With regard to the CO₂ courses (Fig. 7(g)), the average X_CO2 is significantly overestimated in the compression phase and prior to combustion, which continues after the combustion phase (see Table 1). After combustion, the AFR-dependent differences for the produced CO₂ mole fractions are first distinguishable at about t = 400 ms (not shown), with temperatures below 750 K. We attribute the large CO₂ measurement uncertainties to various effects, namely the low CO₂ absorbance resulting in poor SNR values and the remaining residuals because of the interference with H₂O absorption lines, which can lead to a measurement bias due to the line parameter uncertainties and line mixing. Furthermore, for the CO₂ 3ν₃ band and the main absorption feature at about 1430 nm, Cole et al. [51] found differences between the measured spectrum and the HITRAN 2016 simulation exceeding 20%. There, measurements were performed in a uniform high-pressure high-temperature gas cell at p = 19.8 bar and T = 730 K. From measurements in our laboratory, we can confirm increasing residuals from pure Biogon C20 measurements with pressures up to 80 bar (T = 300 K) and significant differences in our calibration to the HITEMP database (unpublished work-in-progress). Based on the standard deviations for CO₂, the remaining interference patterns and the CO₂ line list errors, we note that sampling rates greater than 10 kHz are not reasonable with the present data analysis.

In Fig. 7(h), additionally the calculated relative species mole fraction differences from the moving average X_i,mean are presented for AFR = 1.54, which highlight the frame averaging effects and changing SNR values with start of combustion. The relative difference values for X_H2O and X_CH4 are in general below 4% up to TDC and increase to about 60% with the main ignition for CH₄ due to poor SNR and spectral overlapping of CH₄ and H₂O.

5.3 Choice of the spectral database

The average line parameters of the HITEMP database and the underlying uncertainties result in uncertainties and bias to the evaluated temperatures and mole fractions. In order to give a rough estimate of these effects, the measurement data of the n-heptane-methane experiments was additionally evaluated based on the HITRAN 2016 database. At start of compression, the evaluated temperatures are equal (within the STD). With increasing pressure, the HITRAN temperature falls below the HITEMP temperature. At TDC, this results in a temperature difference of 65 K, which we attribute to the missing high temperature lines in HITRAN. HITRAN-based CH₄ and H₂O mole fractions are less dependent on pressure. Thus, these courses are less increasing within the compression phase. We attribute this to the more accurate line broadening parameters. Furthermore, HITRAN-values for CO₂ are about 50% lower after combustion compared to HITEMP and thus more accurate, considering the incomplete combustion. Neglecting the temperature dependence exponent of the pressure shift (η) within the presented evaluation, the species mole fraction courses start to decrease with pressures exceeding about 20 bar. This is caused by the resulting larger spectral shift between the measured and modeled absorbance peaks. Thus, the measurement uncertainty is essentially determined by the quality of the underlying database. Further discussion on accuracy of broadband AS measurements due to different line lists can be found in Refs. [46,52].

5.4 N-heptane-EGR fuel-rich experiments

With regard to the CO₂ evaluation performance at higher mole fractions, EGR measurements based on a mixture of Biogon C20 with dehumidified air and n-heptane were performed according to Table 1. Parameter courses for three consecutive repeated measurements with an AFR of 0.76 are shown in Fig. 8.

 

Fig. 8. Parameter courses for three consecutive, individual n-heptane/EGR auto-ignition experiments (TDC at 0 ms). (a) Temperatures calculated from the broadband absorbance spectra and adiabatic calculation; (b) H₂O mole fraction; (c) CO₂ mole fraction with moving average based on three experiments. All spectra were recorded at 40 kHz frame rate, the effective evaluated frame rate varies between 2 kHz and 40 kHz.

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The effective evaluated frame rate varies similarly according to the dual-fuel measurements (Fig. 8(a)), and the adiabatic reference temperature is calculated for an air-H₂O-Biogon C20 mixture (similarly to the dual-fuel calculation). From the temperature courses in Fig. 8(a) and the X_H2O courses in Fig. 8(b), the advantage of the high temporal resolution becomes evident. Although the delay between the end of the 1^st stage ignition and the start of the 2^nd stage ignition is much shorter than for the dual-fuel measurements (due to the higher n-heptane mole fraction, which results in an increased reactivity), it can be resolved within 6 to 8 frames (150 µs to 200 µs). This is in accordance with the flame luminosity images in Fig. 5. The time delay between the first and second stage can also be observed within the corresponding pressure transducer data (not shown here). The temporal variation of the 1^st stage ignitions is within ± 100 µs for the three consecutive measurements.

With regard to the adiabatic reference calculation, the measured temperatures are larger (starting with 10 K up to 20 K in the mid compression phase). Around TDC, the temperatures match the adiabatic reference (see zoomed diagram section), however, we expect the temperature to be below the adiabatic reference similar to the dual-fuel measurements due to the lower temperature gas mixture close to the RCEM piston. We cannot trace these differences back to a specific source of error, but we suspect that these are caused by differences and errors within the transition line strengths of H₂O, CH₄ and CO₂ and furthermore by the implemented average temperature dependent shift coefficients. Further errors could arise from the broadband spectrometer, the complex gas composition field and other effects, e.g., line mixing.

With regard to the completeness of combustion, considering the initial X_H2O-values (humidified air), the measured H₂O mole fraction is 6% below the calculated value based on a global reaction equation. This could be caused by incomplete combustion, which is obvious in our experiments, and/or the production of carbon monoxide, which reduces the available amount of oxygen for H₂O and CO₂ production.

The average values for the CO₂ mole fractions (Fig. 8(c)) are overestimated by about 50% in the compression phase and even higher after combustion, what we mainly attribute to the discussed database uncertainties in Sections 5.2 and 5.3. With regard to the STD of the CO₂ mole fractions, we obtain higher values in the compression phase compared to the dual-fuel experiments despite higher SNR values. We trace this back to the 0% mole fraction limit, which constrains the mole fraction distribution.

Standard deviations of the temperature measurements are significantly larger than for the dual-fuel measurements in the compression phase, which we trace back to the 70% lower initial H₂O mole fraction (and thus reduced SNR) and the missing CH₄ absorbance. Thus, we achieve $\overline {{\sigma _T}(t )} $ = 17.2 K at TDC, which reduces by over 60% with the first ignition according to Table 2. The reproducible compression ratios (see Table 1) result in a repeat measurement precision for temperature $(\sigma ({\overline {T(t )} } ))$ of 3.5 K at TDC based on the mean temperature values of the 3 individual experiments. With the main ignition, the temperature exceeds 1550 K for all three measurements and $\sigma ({\overline {T(t )} } )$ = 11.4 K is achieved after the 2^nd ignition (t = 1.5 ms to 3 ms). For the mole fractions, this amounts to $\sigma ({\overline {{X_{\textrm{H}2\textrm{O}}}(t )} } )$ = 0.038% and $\sigma ({\overline {{X_{\textrm{CO}2}}(t )} } )$ = 0.36% (around TDC) and $\sigma ({\overline {{X_{\textrm{H}2\textrm{O}}}(t )} } )$ = 0.12% and $\sigma ({\overline {{X_{\textrm{CO}2}}(t )} } )$ = 0.44% (t around 55 ms).

6. Conclusions

A first Herriott-cell based multi-pass setup for fully SMF-coupled broadband laser absorption spectroscopy measurements in environments with distinct occurrence of beam steering, such as an RCEM, has been presented. The planar HMPC 9-pass layout has been described in detail for an external installation around the windows of our RCEM. Effects of axial and vertical beam steering on the beam propagation path were discussed based on a ray-tracing analysis. Within RCEM combustion experiments for premixed dual-fuel (heptane-methane) and heptane-EGR auto-ignition, the compact experimental SCLAS measurement setup has been demonstrated, which consists of the SCL, the HMPC, a CTS and the connecting SM-fibers. There, the ray-tracing analysis has been compared to both the recorded SCLAS spectra and flame luminosity images. The results have shown that the HMPC approach is well suited for environments with limited optical access and significant beam steering unless strong refractive index gradients propagate vertically through the HMPC beam pattern in form of flame fronts. Thus, for the presented time interval of the RCEM measurements, more than 97% of the recorded spectra could be evaluated with reasonable SNR values, even in the presence of beginning engine knock. Temperature and multi-species mole fractions were simultaneously inferred from the recorded NIR spectra based on the HITEMP database at up to 25 µs temporal resolution for the dual-fuel (H₂O, CH₄ and CO₂) and n-heptane-EGR (H₂O and CO₂) measurements. Temperatures and pressures exceeded 1800 K and 80 bar, respectively. Within all measurements, the two stage ignition of n-heptane could be resolved in the temperature, H₂O and CH₄ mole fraction courses. A comparison with experiments in [22] revealed that with the novel approach, standard deviations for temperature could be reduced by 90% at similar measurement and evaluation conditions. The measured CO₂ mole fractions mainly suffer from errors within the spectral databases and a limited SNR. Furthermore, H₂O and CH₄ mole fractions suffer from a pressure dependent bias. Thus, we consider any development of advanced spectral models and improvements to the spectral databases for high-temperature and high-pressure applications a valuable contribution to the scientific community. Parameter standard deviations and precisions are provided for different periods prior, during and after combustion. Temperature-STD-values below 5 K could be achieved. We see further potential for reducing standard deviations, especially during and after combustion, by more advanced absorbance evaluation strategies, as the utilized derivative approach is not immune against broadband spectral fluctuations caused by beam steering or etaloning effects. Further research work is intended to infer combustion (intermediate) species (e.g., CO, C₂H₂, C₂H₄) that are within the measured spectral range.