1 Introduction

The combustion process within an engine is greatly influenced by the in-cylinder flow-field. Spark-ignition (SI) engines are particularly sensitive to the intensity and scale of turbulent flow fluctuations, which have been shown to directly affect flame propagation speed and thereby the performance, efficiency, and emissions output of an engine [1,2,3,4,5,6,7]. It is necessary to continually improve the knowledgebase of these in-cylinder processes to meet the demands of ever-tightening regulations on pollutant formation and the increased expectations of consumers.

It is well known that there is a near-linear relationship between engine speed and burn rate in SI engines, which allows them to operate over a large speed range. Multiple studies utilising methods such as hot wire anemometry (HWA), laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) have shown that the reduction in time available for combustion at high engine speeds is compensated for by increased turbulence intensity, which in-turn increases the flame propagation speed of the mixture [1,2,3,4,5,6,7]. In order to further improve turbulence generation, various intake port geometries and flow shaping devices aimed at increasing tumble motion have been investigated, as large-scale tumble is known to decay into smaller turbulent scales during the compression stroke; thereby enhancing mixing and flame propagation [8,9,10,11,12,13].

According to established turbulent premixed combustion models, this enhancement in flame propagation speed is achieved through the transport of preheated material in the region of the flame front by small eddies at the mixing length-scale l m [6]. As the flame grows in size, larger eddies are able to interact with the flame front, resulting in a gradual rise in turbulent burning velocity. This implies that the majority of the turbulent scales present within SI engine flows are unable to interact with the early flame kernel, thus a global increase in turbulence intensity does not necessarily aid early flame development. Instead, successful flame kernel development is known to be dependent on minimising heat loss through the spark plug electrodes [14]. Numerous studies have shown that engine cycles in which the flame kernel is convected away from the spark plug electrodes exhibit significantly improved early flame development [15,16,17], especially for fuel lean mixtures [18, 19]. As this convection is performed by larger scale flow structures, it is thought that flame growth is initially dictated by bulk flow velocity rather than turbulence intensity. To draw a firm conclusion on this, however, more detailed flow/turbulence analysis is required.

Direct-injection (DI) adds further complexity to in-cylinder flow behaviour. The introduction of high-momentum fuel sprays, injected at pressures upwards of 10 MPa, can have a significant impact on both large-scale bulk motion and small-scale turbulent fluctuations [20,21,22,23,24,25]. For example, the late fuel injection events required for stratified charge operation have been reported to increase the velocity magnitudes in the near-spark region by a factor of three, resulting in a substantial displacement of the plasma channel [26]. Similar studies have found that the magnitude and direction of spray induced flow structures play a vital role in determining early flame heat release rate (HRR) and indicated mean effective pressure (IMEP), in both swirl dominated [27] and tumble dominated [28] flows. However, reliably obtaining these desired flow structures remains a non-trivial task, as cycle-to-cycle variation in large-scale pre-injection flow has a significant impact on flow-spray interactions [29, 30].

Spray induced flow is also reported to play a large role in homogenous charge engine operation, despite the use of significantly earlier injection timings. For example, a study performed in a hydrogen DI engine observed a complete reversal in the rotational direction of the tumble vortex [31], and theorised that injection-induced tumble break-down may lead to significant improvement in turbulence levels at the point of ignition. Splitting the injection into an intake stroke component and a compression stroke component can maximise the effect of this spray induced turbulence whilst still allowing ample mixture formation time [32]. This is highlighted by another study which observed that a short fuel injection event (400 μs duration) during the middle of the compression stroke resulted in an immediate 400% increase in turbulent kinetic energy (TKE) over non-fuel-injected operation, which quickly decayed to 200% within 16 °CA [33].

The potential advantages of multiple injection strategies extend beyond flow enhancement [34,35,36,37,38,39,40]. Simply splitting the injected mass into two or more closely spaced injections during the intake stroke has the potential to reduce wall wetting while still providing ample mixture formation time [35, 37,38,39]. Significant improvements in particulate emissions have been reported using this approach, with one study [35] reporting a 60% reduction for a double injection strategy and an 80% reduction for a triple injection strategy - operating at 1.1 MPa brake mean effective pressure (BMEP) in a boosted SIDI engine. The effects of charge cooling may also be altered — for instance, both volumetric efficiency and knock-limited spark-advance may be improved by combining intake stroke and compression stroke injections [34]. However, combustion performance is known to be very sensitive to injection strategy and timing [39, 41], likely due to a combination of varied in-cylinder flow and mixture quality conditions. For example, an early triple injection strategy was found to result in more spherical flames with minimal centroid displacement when compared to an equivalent single injection approach [39]. These triple injection flames also exhibited delayed combustion phasing and reduced IMEP, which could be the result of increased heat loss from the early flame kernel through the spark plug electrodes.

The current study builds on our previous work, where it was observed that the relationships between injection timing, flame propagation speed, combustion phasing, and IMEP are extremely complex [42]. Our aim is to evaluate the influence of in-cylinder flow and turbulence on these performance parameters by performing PIV at a sampling rate of 5 kHz for 5 selected fuel-injection timing combinations. In order to quantify turbulent flow parameters, a novel spatial filtering technique is applied to the instantaneous data, whereby the cut-off length of the filter is scaled by the mean flow speed at each crank angle location. This approach was developed in a parallel study [43], as a substitute for temporal filtering.

2 Experiments

2.1 Optical engine specifications and operating conditions

The experiments were carried out in an optically accessible single cylinder spark-ignition direct-injection (SIDI) engine with a side mounted injector and flat-topped piston [42, 44], depicted schematically in Fig. 1. Full engine specifications and operating conditions are listed in Table 1, noting that all timings are relative to the expansion stroke top dead centre.

Fig. 1
figure 1

Swirl plane PIV imaging configuration

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Table 1 Engine specifications and operating parameters
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The engine head is based on a production car double-overhead cam 16 valve inline-4 cylinder engine which has been modified to remove cylinders 2, 3 and 4. The cylinder has a geometric compression ratio of 10.5 and is of square configuration with a bore and stroke of 86 mm, resulting in a displacement volume of 500 cm3. Optical access is provided through a 49 mm diameter quartz window in the piston crown for imaging of the swirl plane, and through the top 35 mm of the quartz cylinder liner for imaging of the tumble plane. The remainder of the cylinder liner can be dropped down to allow for the cleaning of window surfaces between engine runs, ensuring that particulate matter and oil build up does not obstruct the region of interest.

In order to replicate a thermally stable warmed-up operating condition, 90°C water was constantly circulated through the cylinder head, liner, and engine block using a water heater/circulator (ThermalCare Aquatherm RA-series). The throttle was fixed in the wide-open position which resulted in an intake air pressure of 100 kPa absolute, and while not specifically controlled the intake air temperature was recorded consistently at 30 °C throughout the experiments. An AC motor and a large flywheel maintained a stable engine speed of 1200 RPM despite the inherently large oscillations associated with single cylinder engines.

The engine was controlled via a universal timing unit (Zenobalti ZB-9013P) which uses a rotary encoder (Autonics E40S8) on the crankshaft as its reference. Synchronisation of the high-speed laser and high-speed camera was achieved through the combination of a delay generator (Stanford DG-535) and two frequency dividers (Pulse Research Lab PRL-240A). Crank-angle resolved in-cylinder pressure traces were recorded via a pressure transducer integrated into the spark plug (Optrand C822J6-SP). The engine was fired 1 in every 10 cycles (i.e. 10 skip firing) in order to reduce thermal loading of the quartz windows. This firing sequence also leads to the complete expulsion of residual exhaust gases, which is likely to result in higher rates of reaction when compared to a continuous fire engine. However, as the engine load, speed and fuel mass are held constant, the effect of the absence of residual gases is expected to be consistent throughout the study.

A 1:1 ratio double-injection strategy was implemented for this study, with the exact timings of the injections selected as cases of interest based on our previous work conducted in the same optical engine [42] — ranging from two injections during the intake stroke to two injections during the compression stroke. Varying the split ratio and the number of injections was considered beyond the scope of this study, as the aim was to observe the effect of fuel injection on in-cylinder flow, rather than define a perfectly optimised operating condition.

Conventional 95 RON petrol fuel was supplied at a constant pressure of 15 MPa to a side mounted 6-hole injector (Continental DI XL2) placed between the intake valves as shown in Fig. 1. The injection duration was fixed at 1.15 ms per injection, resulting in a calculated equivalence ratio of 1.0. A Bosch-tube-type injection rate meter was used to measure the fuel mass per injection with backpressures from 0.1 to 1 MPa, simulating in-cylinder pressure at different points in the intake and compression stroke [44]. It was observed that the reduction in injected mass due to backpressure was very minimal, even at 1 MPa (corresponding to a very late injection of ∼30 °CA before top dead centre (bTDC)), and insignificant at the highest backpressure encountered in this study of < 0.1 MPa at 110 °CA bTDC. Therefore, the injection duration was held constant regardless of injection timing.

Ignition timing was fixed at 14 °CA bTDC, corresponding to the minimum advance for best torque (MBT) timing for the best performing cases; as improvements in IMEP through advancing the ignition timing for the slower flame development cases were found to be negligible. Fixing the ignition timing has the advantage of providing a level playing-field in terms of the effect of squish motion on tumble flow across each operating condition.

A non-injected (i.e. motored) condition was also analysed, in order to provide a baseline for the comparisons and investigate the level of flow enhancement provided by fuel-injection. This condition was also used to evaluate flow-field filtering methods in our previous work [43] — a brief explanation of which is provided in a later section.

2.2 Image acquisition

The intake flow was seeded with olive oil droplets from an atomiser (PIVTEC PIVpart 40), with a quoted nominal diameter of ∼1 μm — small enough to conform to 10 kHz flow fluctuations. The beam from a frequency doubled 532 nm dual oscillator Nd:YAG laser (Quantronix Hawk-Duo) was formed into a sheet using three cylindrical lenses — two controlling the breadth and one to gradually reduce the thickness of the sheet to roughly 1 mm at the region of interest. Image pairs were captured with a high-speed CMOS camera (VisionResearch Phantom v7.3) at a sampling frequency of 5 kHz (i.e. a camera frame rate of 10 kHz), corresponding to 1.44 °CA between pairs for an engine speed of 1200 RPM. The pulse separation (Δt) was set to 20 μs as this was found to provide a suitable dynamic range for all velocities encountered in this study, while maintaining a sufficiently high signal to noise ratio.

For the fuel-injected operating conditions, PIV images were captured for the horizontal (i.e. swirl) plane. Figure 1 depicts the orientation of the camera and laser for the swirl plane imaging, whereby the laser sheet was introduced horizontally through the top of the quartz window liner 5 mm below the fire deck, and the camera captured the images through the quartz piston crown via the 45-degree mirror in the extended piston. This imaging plane was selected as it provided flow-field information at the latest crank angle possible, given the optical access constraints of the engine employed for this study. Our previous work revealed that quantities obtained through swirl plane PIV imaging showed strong correlation with those obtained via the tumble plane, albeit with slightly lower magnitudes [43]. A Micro Nikkor 200 mm f/4 lens provided a 30.0 mm × 30.0 mm region of interest at a resolution of 468 × 468 pixels, corresponding to 64 μm per pixel. The aperture of the lens was stopped down to f/8 to increase the depth of field and improve image sharpness. The imaging settings are summarised in Table 2.

Table 2 PIV imaging parameters
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It should be noted that the images were only acquired for a brief period during the late stages of the compression stroke. This was due to injection events causing a saturation of the PIV signal, thereby cutting the sample into pre- and post-injection. This introduces a serious diagnostic limitation because the large fuel droplets following the injection are incapable of conforming to high frequency flow structures, which results in the velocities calculated from PIV analysis carrying a bias towards larger scales; i.e. the resulting flow field will represent the movement of the fuel droplets rather than the air. Figure 2 shows an example of the 110 °CA bTDC second injection case used in this study, where the image on the left shows a clear saturation of the signal during the injection event, and the central image taken at 80 °CA bTDC shows a significant presence of large fuel droplets. In this particular case, 40 °CA bTDC was chosen as the first frame, since the region of interest was reliably free of large fuel droplets by this point (right image of Fig. 2). The last image was acquired at 28 °CA bTDC, corresponding to the frame before the piston clipped the laser sheet. For each operating condition, images were acquired for 100 engine cycles.

Fig. 2
figure 2

Raw swirl plane PIV images after fuel-injection event. The injection occurs from right to left

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2.3 PIV analysis

Image pairs were processed with PIVlab, a Matlab-based open-source code [45, 46]. Contrast limited adaptive histogram equalization (CLAHE) with a window size of 20 pixels was performed as a pre-processing step on each image. This optimised the exposure of each region within the image, thereby improving the ability of the cross-correlation algorithm to detect valid vectors throughout the entire domain.

Critical PIV analysis settings are summarised in Table 3. Four passes of a FFT window deformation cross-correlation algorithm were performed with 50% overlap, and a Gaussian 3-point sub-pixel estimator was employed for peak finding. The first two passes were performed with an interrogation size of 48 × 48 pixels, and the last two with an interrogation size of 24 × 24 pixels — corresponding to 1.54 mm × 1.54 mm. This resulted in a vector spacing of 0.77 mm and a dynamic velocity range of 19.2 m/s according to the \(\frac {1}{4}\) window displacement rule [47]. Figure 3 shows the resulting instantaneous flow-fields of a selected non-injected cycle over the range of 190 to 40 °CA bTDC (or -190 to -40 °CA aTDC).

Table 3 PIV image processing parameters
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Fig. 3
figure 3

Instantaneous swirl plane flow-fields. Non-fuel-injected operation

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Erroneous vectors were detected with a standard deviation check and local median filter, then replaced with an interpolated vector if required [45]. A visual inspection of each flow field was also performed, and any remaining obvious outliers were removed and replaced. Note that the interrogation window sizes were selected based on obtaining a very high proportion of first-choice vectors, so the presence of erroneous vectors was less than 1% for almost all image pairs.

2.4 Flow-field post processing

A Reynolds decomposition was performed on the flow-fields in order to separate the mean and fluctuating components. The mean flow field was determined using a spatial low-pass filter. The following analysis was performed for both U and W velocity components on the selected swirl plane (see Fig. 1). For both filtering approaches, the Reynolds decomposition was performed as follows:

$$ U({\Theta},x,y,i)=\overline U({\Theta},x,y,i)+u_{hf}({\Theta},x,y,i) $$
(1)

Where U(Θ, x, y, i) is the instantaneous velocity, \(\overline U({\Theta },x,y,i)\) is the mean velocity according to the low-pass filter, and u h f (Θ, x, y, i) is the high frequency fluctuating velocity for crank angle Θ at point x, y in cycle i.

A low frequency fluctuating velocity component, which gives an insight into cycle-to-cycle variation, was also calculated:

$$ u_{lf}({\Theta},x,y,i)=\overline U({\Theta},x,y,i)-\overline U_{EA}({\Theta},x,y) $$
(2)

Where:

$$ \overline U_{EA}({\Theta},x,y) = \frac{1}{N} \sum\limits_{i = 1}^{N} U({\Theta},x,y,i) $$
(3)

Figure 4 shows the instantaneous, mean, and fluctuating flow fields resulting from a Reynolds decomposition using a spatial filter. The specifics of the filtering process are discussed in a later section.

Fig. 4
figure 4

Reynolds decomposition of an instantaneous flow-field (top left) into a mean flow-field (top right), and turbulent flow-field (bottom left). The turbulent field is shown again with a 50% larger vector scale to aid visual identification of vortices (bottom right). Adapted from [43]

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To derive further properties such as turbulent kinetic energy and turbulent integral length scale, it was necessary to first calculate the fluctuation intensities \(u^{\prime }_{hf}\) and \(u^{\prime }_{lf}\). This was defined as the root-mean-square (RMS) of the fluctuating velocity for crank angle Θ at point x, y across all cycles (similarly for u l f ):

$$ u^{\prime}_{hf}({\Theta},x,y)=\sqrt{\frac{1}{N} \sum\limits_{i = 1}^{N} u_{hf}({\Theta},x,y,i)^{2}} $$
(4)

Turbulent kinetic energy (TKE) was then calculated, ignoring the 3rd directional component:

$$ TKE({\Theta},x,y)=\frac{1}{2} (u^{{\prime}2}+w^{{\prime}2}) $$
(5)

TKE is averaged over each point in the spatial domain in order to provide a single value for each crank angle.

Spatially-averaged fluctuation intensities were also considered, as this approach results in independent turbulence quantification for each cycle — thereby providing insight into the cycle-to-cycle variation of TKE. This was calculated as follows:

$$ u^{\prime}_{hf}({\Theta},i)=\sqrt{\frac{1}{n\times m} \sum\limits_{x} \sum\limits_{y} u_{hf}({\Theta},x,y,i)^{2}} $$
(6)

Turbulent integral length scales L u and L w represent the weighted average of the highest energy containing turbulent flow structures. These were calculated by integrating the spatial correlation coefficient R x [48], which was calculated between the first point in each row and an adjacent point to the right, over all separation distances Δx. These values were then averaged over each row and each cycle for any given crank angle. Note that only the longitudinal integral length scale was considered in this study. The equations are as shown (similarly for L w ):

$$ L_{u}={\int}_{0}^{\infty} R_{xu}dx $$
(7)
$$ R_{xu}({\Theta},{\Delta} x, y)=\frac{u_{hf}(x_{0},y)\cdot u_{hf}(x_{0}+{\Delta} x,y)}{u^{\prime}_{hf}(x_{0},y)\cdot u^{\prime}_{hf}(x_{0}+{\Delta} x,y)} $$
(8)

In theory, the integration should be performed from 0 to infinity; however, due to the finite nature of the domain, the integration was instead performed up to the point where the correlation curve first crosses zero, with the remainder assumed to be negligible. Polynomial curve fitting was used on the correlation data, as this made it possible to accurately calculate the first positive root. It was found that the correlation coefficients from ensemble average (EA) based velocity fluctuations would not reliably decay to zero, therefore the integration was instead performed up to the point of the first local minimum.

3 Filtering Approach

Temporal filtering was deemed inappropriate for the fuel-injected cycles due to the small window of PIV image acquisition (i.e. 40 to 28 °CA bTDC), as the resulting sample length covered a shorter period of time than a full width of a widely used 300 Hz filter [49,50,51]. Instead, turbulent flow features must be identified through a spatial technique. Two common methods for spatially decomposing a flow-field include proper orthogonal decomposition (POD), and 2-D fast Fourier transform (2-D FFT) based filtering. These techniques operate in fundamentally different manners, yet share similar strengths and limitations. In particular, both techniques attempt to provide a distinction between large scale cycle-to-cycle variation and small scale turbulent fluctuations [49, 52,53,54]; however, the selection of cut-off modes (POD) [52] and cut-off lengths (spatial filtering) remain somewhat arbitrary due to the absence of spatial separation in internal combustion engine flows.

In the present study, spatial filtering was preferred to POD for two main reasons. Firstly, it is easier to draw comparisons between spatial filtering and the more common temporal filtering method; and secondly, the physical interpretation of POD output can be somewhat abstract, which may further complicate the analysis of results. As such, the mean flow \(\overline U\) was calculated by performing a 2-D FFT on each flow field to convert it into the spatial frequency domain, where a high-order low-pass Butterworth filter was applied. This approach was preferred over a top-hat filter as gradual filters reduce high-frequency ringing in the physical domain. Furthermore, the frequency bins in this study were broad due to the relatively small sample sizes (38 × 38 vectors), which would result in step-like behaviour if a top-hat filter were to be used. This was avoided with a gradual filter, as the amount of attenuation applied to each bin is infinitely adjustable with any change in cut-off length.

In accordance with Eq. 1, the high-frequency fluctuating velocity u h f was then calculated by subtracting the low-pass filtered mean flow \(\overline U\) from the instantaneous velocity U. This process is shown in Fig. 5 for the same frame displayed in Fig. 4, where the top left image represents the instantaneous field, the top right is the mean field according to an 8 mm cut-off length, and the bottom left is the resulting high-frequency turbulent field. Edge effects arising from the filter are clearly present in the turbulent field, where the magnitude of the velocity is often overestimated. To account for this the turbulent flow field was cropped by 4 data points along each edge, with the final result shown in the image on the bottom right (note the change in scale of the x and y axis).

Fig. 5
figure 5

Instantaneous U flow-field (top left), mean \(\overline U\) flow-field (top right), high-frequency fluctuation u h f flow-field (bottom left), cropped high-frequency fluctuation u h f flow-field to remove edge effects (bottom right). Adapted from [43]

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Common cut-off lengths in existing literature range from 6 to 15 mm [12, 13, 55, 56], with some researchers suggesting values as high as 20 mm [9]; however, defining a suitable cut-off length to separate mean and turbulent flow remains a highly arbitrary process. For instance, our previous study [43] showed that no single spatial filter is equivalent to a 300 Hz temporal filter over the entire domain, as the 300 Hz filter resulted in much higher TKE magnitudes throughout the intake stroke than the compression stroke. This behaviour can be explained if Taylor’s hypothesis is considered, whereby the spatial scale is equal to the product of the temporal scale and the mean flow speed [48, 57]. As such, it is reasonable to expect that for any change in mean flow speed, the relationship between a set spatial cut-off length and temporal cut-off frequency will change. A variable spatial filter was designed as a resolution to this phenomenon in our previous work — a brief description of which is provided below. For full details, please refer to the original text [43].

The variable filter consists of a fixed component and a scaling component, whereby the cut-off length grows with increasing mean flow speed. Tuning this was a trial and error process, which resulted in a final formula of:

$$ L_{C} = 5~mm\left( 1 + 0.4 ~\frac{s}{m} ~\overline{V}_{mag}(\theta)\right) $$
(9)

Where:

$$ \overline V_{mag}({\Theta})=\frac{1}{N}\sum\limits_{i = 1}^{N} \frac{1}{m\times n}\sum\limits_{x = 1}^{m} \sum\limits_{y = 1}^{n} \sqrt{U_{x,y,i,{\Theta}}^{2}+V_{x,y,i,{\Theta}}^{2}} $$
(10)

A comparison of the TKE derived from the scaled spatial filter and the 300 Hz temporal filter is shown for both the current swirl plane and a tumble plane (refer to [43]) bisecting the upper portion of the cylinder in Fig. 6, where a strong correlation between the two methods is observed. The exact formula used to match the two filtering methods is not expected to be robust for all applications; however, it is promising to note that it was consistent for the two imaging planes, despite significant differences in flow motion. Turbulent quantities for each operating condition in this study will be presented using both a fixed 8 mm cut-off and the scaled cut-off approach. In doing so, it may be possible to determine which method results in turbulent quantities that show stronger correlation with the behaviours observed in the in-cylinder pressure derived data.

Fig. 6
figure 6

TKE comparison of scaled cut-off length spatial filter with 300 Hz temporal filter (swirl plane and tumble plane). Adapted from [43]

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4 Results and Discussion

4.1 Effect of injection timing on combustion performance

Injection timing plays a significant role in determining combustion phasing and peak in-cylinder pressure. This is readily apparent in the top left image of Fig. 7, which shows the mean pressure trace for each operating condition. The 300 & 110 °CA bTDC and 140 & 110 °CA bTDC cases both show rapid heat release during the early stages of flame development, which should be associated with a high level of interaction between small-scale turbulence and the flame kernel. As expected, the cases with both injections during the intake stroke (namely 300 & 270 °CA bTDC and 300 & 210 °CA bTDC) have slower flame development, with the earliest second injection of 270 °CA bTDC resulting in the lowest peak pressure and most retarded combustion phasing. Surprisingly, the mean pressure trace of the 260 & 110 °CA bTDC case is close to that of the intake stroke injection cases, despite the late last injection. Note that this case exhibits the slowest early flame development, before accelerating at ∼5 °CA aTDC, suggesting that the reason behind the poor performance is linked to difficulties in flame kernel development rather than low turbulence intensity.

Fig. 7
figure 7

In-cylinder pressure traces. Mean cycles for each case (top left). All 300 & 270 °CA bTDC cases (top right). All 300 & 210 °CA bTDC cases (centre left). All 300 & 110 °CA bTDC cases (centre right). All 260 & 110 °CA bTDC cases (bottom left). All 140 & 110 °CA bTDC cases (bottom right). Mean traces are shown in orange

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To further investigate this behaviour, all 100 instantaneous cycles for each case are shown in the remaining images of Fig. 7. It is immediately evident that cycle-to-cycle variation is also strongly influenced by injection timing, as the 300 & 110 °CA bTDC and 140 & 110 °CA bTDC cases once again show the most promising performance. On initial inspection, it appears that the 300 & 210 °CA bTDC case exhibits larger variations than the 300 & 270 °CA bTDC case, although the tail is noticeably broader — suggesting that the cycles with delayed combustion phasing may still possess reasonably consistent indicated mean effective pressure (IMEP) as the in-cylinder pressure remains high throughout the later stages of the expansion stroke. In comparison, the slow burning cycles from the 300 & 270 °CA bTDC case do not appear to compensate for their poor early flame performance to the same degree, suggesting a higher variation in IMEP. The 260 & 110 °CA bTDC case clearly results in the highest level of variation, with some cycles presenting peak pressures of approximately 6.5 MPa and others being less than 4 MPa. These slow burning cycles have very late flame kernel development, with some even passing TDC before any noticeable heat release occurs.

To quantify heat release during different stages of the combustion process, the time taken (in crank angles, referenced from ignition timing) for the first 10% of mass fraction burned (i.e. CA10), and the time taken for the first 50% of mass fraction burned (i.e. CA50) are both shown in Fig. 8. These parameters were calculated from HRR traces derived from in-cylinder pressure data, according to methods proposed by Heywood [58]. In these box plots the median value for each case is shown as a horizontal line, the box limits represent the 25th and 75th percentiles, the whiskers encompass the remainder of data points, and outliers are noted as an orange plus symbol. As expected from interpreting the in-cylinder pressure traces, the 300 & 110 °CA bTDC and 140 & 110 °CA bTDC cases possess the fastest CA10 and CA50, with minimal spread. The trends observed in CA10 and CA50 are quite consistent, with the notable exception of the 300 & 270 °CA bTDC case which shows a more retarded CA50, indicating lower heat release rates during mid-stages of flame development.

Fig. 8
figure 8

CA10 (left) and CA50 (right) box plots for each operating condition, referenced from ignition timing

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The effect of these in-cylinder processes on the indicated output of the engine is shown in the IMEP box plots of Fig. 9. As suggested in our previous work using the same optical engine [42], it is thought that the combination of ample mixture formation time and high turbulence intensity results in the 300 & 110 °CA bTDC case exhibiting the highest IMEP. The points to the left have increased mixture preparation time yet lower suspected turbulence, and vice versa for the points to the right. In particular, the 140 & 110 °CA bTDC case has a noticeable decrease in IMEP, despite possessing very similar early heat release to the 300 & 110 °CA bTDC case, leading to the conclusion that the lack of mixture formation time results in lower combustion efficiency.

Fig. 9
figure 9

IMEP box plots for each operating condition

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Cycle-to-cycle variation is quantified as the coefficient of variance (CoV) of IMEP in Fig. 10. All 5 cases are within the common 3% limit used to define stable operation. As the box plots in Fig. 9 suggest, the 260 & 110 °CA bTDC case exhibits the greatest variation, followed by the 300 & 270 °CA bTDC case. Interestingly, comparing the combustion phasing data in Fig. 8 to the IMEP data in Figs. 9 and 10 reveals that the inconsistent early flame development behaviour observed for the 300 & 210 °CA bTDC case does not appear to have significant follow-on effects, as the spread in IMEP values is on par with the 300 & 110 °CA bTDC and 140 & 110 °CA bTDC cases. In contrast, the 300 & 270 °CA bTDC case shows the opposite behaviour, with a narrow spread in early flame development and a wide spread in IMEP. These results validate the earlier discussion based on the visual inspection of the individual pressure traces, where it was observed that the slow burning cycles of the 300 & 210 °CA bTDC case appeared to maintain higher pressures later into the expansion stroke.

Fig. 10
figure 10

CoV of IMEP for each operating condition

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4.2 Qualitative flow-field analysis

Fuel-spray induced flow momentum is substantial. Ensemble averaged flow-fields are presented in Fig. 11 and representative instantaneous flow-fields are presented in Fig. 12 at 28 °CA bTDC for each case, including the motored (i.e. non fuel-injected) condition. The first thing to note is that all injected cases increase the flow momentum noticeably over the motored condition, even when both injections take place early in the intake stroke (i.e. 300 & 270 °CA bTDC). There are significant differences in bulk flow structures from case-to-case, in terms of both magnitude and direction. Interestingly, relatively minor changes in injection timing appear to lead to larger flow-field changes than one might expect; for example, the disparities between the 300 & 270 °CA bTDC and 300 & 210 °CA bTDC cases, and between the 300 & 110 °CA bTDC and 260 & 110 °CA bTDC cases. In a similar trend to that seen in the in-cylinder pressure traces, the 260 & 110 °CA bTDC case once again behaves substantially different to the other 110 °CA bTDC second injection cases — as the bulk flow velocities appear to be much lower. A further observable characteristic is the reversal of bulk flow direction between the cases with an intake stroke second injection and those with a compression stroke second injection, which implies that certain injection timings are capable of reversing the tumble flow rotation, similar to the observations made in Ref. [31]. Drawing on this idea, it is possible that the low bulk flow velocity seen in the 260 & 110 °CA bTDC case may be a result of a cancellation effect, whereby the first injection assists the natural tumble flow structure only for the second injection to destroy it.

Fig. 11
figure 11

Ensemble average in-cylinder flow fields at 28 °CA bTDC. Motored case (top left). 300 & 270 °CA bTDC (top right). 300 & 210 °CA bTDC (centre left). 300 & 110 °CA bTDC (centre right). 260 & 110 °CA bTDC (bottom left). 140 & 110 °CA bTDC (bottom right)

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Fig. 12
figure 12

Instantaneous in-cylinder flow fields at 28 °CA bTDC. Motored case (top left). 300 & 270 °CA bTDC (top right). 300 & 210 °CA bTDC (centre left). 300 & 110 °CA bTDC (centre right). 260 & 110 °CA bTDC (bottom left). 140 & 110 °CA bTDC (bottom right)

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Ensemble averaged flow-fields are strongly influenced by cycle-to-cycle variation; for example, two individual cycles with high bulk velocities that are in opposite directions will result in a low magnitude ensemble averaged flow-field with little structure, yet two individual cycles with moderate bulk velocities in the same direction will result in an ensemble averaged flow-field with a similar magnitude and a relatively well-defined structure. Keeping this in mind, the strong directionality and very high magnitude of the ensemble averaged flow-field for the 300 & 210 °CA bTDC case suggests that cycle-to-cycle variation may be low for this particular case, in contrast to the 260 & 110 °CA bTDC case which exhibits little-to-no structure.

4.3 Cycle-averaged quantitative flow-field analysis

As described in the flow-field post processing section, cycle averaged analysis refers to RMS quantities being calculated at each x, y location over all cycles (see Eq. 4) — not to be confused with ensemble averaging based flow quantities. Before delving into turbulent properties, the mean flow speed of each case according to Eq. 10 must be considered. This is presented in Fig. 13, which shows a general trend similar to that observed in the raw flow-fields, although the relative differences are less drastic than the ensemble averaged flow-fields would suggest. The corresponding cut-off lengths used in the scaled filtering approach (according to Eq. 10) are also shown in Fig. 13. While the motored condition results in a cut-off of 7-8 mm, this grows to over 20 mm for the 140 & 110 °CA bTDC case as a consequence of the large differences in mean flow.

Fig. 13
figure 13

Mean flow speed for each operating condition (left); and corresponding scaled filter cut-off length (right)

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TKE profiles determined via the fixed 8 mm cut-off (left) and the scaled cut-off (right) are shown for each case in Fig. 14. Both filtering methods result in similar overall trends, with TKE remaining relatively constant across the domain for all conditions, bar the 140 & 110 °CA bTDC case which shows steady dissipation. Keeping in mind that the last data point here is 28 °CA bTDC and the ignition timing is 14 °CA bTDC, it is anticipated that the large gap between the TKE of the 140 & 110 °CA bTDC case and the other 110 °CA bTDC second injection cases will be further reduced before any flame-flow interactions occur. Noting the difference in y-axis values, the scaled filter produces noticeably higher TKE for all fuel-injected cases. More importantly, the scaled filter also changes the relative relationships between the operating conditions. For example, the 300 & 270 °CA bTDC case shows slightly higher TKE than the 300 & 210 °CA bTDC case in the 8 mm cut-off results, which is unexpected based on the in-cylinder pressure traces and CA10/CA50 box plots. This trend is reversed in the scaled cut-off results, owing to the much higher mean flow velocity of the 300 & 210 °CA bTDC case. Similarly, the TKE of the 260 & 110 °CA bTDC case is noticeably higher than that of the 300 & 110 °CA bTDC case in the 8 mm cut-off results, but the gap is narrowed substantially when the scaled cut-off approach is employed. As expected, the overall trend observed is that TKE increases with more retarded injection timing for both retarded first injection at fixed second injection and retarded second injection at fixed first injection with the retarded first/second injection showing the highest TKE.

Fig. 14
figure 14

TKE for each operating condition according to fixed cut-off (left), and scaled cut-off (right).

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Interestingly, the TKE values for the 300 & 110 °CA bTDC and 260 & 110 °CA bTDC cases do not explain the behaviour seen in the in-cylinder pressure derived data, even when considering the scaled cut-off filter results. Clearly, there are other factors influencing heat release rate — particularly during the early stages of flame development. One possible explanation is bulk flow structure. Bulk flow has been shown to be an important factor for flame kernel development[14, 16, 18, 19, 51, 59,60,61,62]. Moderate velocities in the region of the spark gap are desirable for reducing heat loss, as the stretching of the arc leads to the flame kernel developing further from the spark plug electrodes. If the bulk velocity is too low, early flame development is likely to suffer; yet if the bulk velocity is too high, the spark may be blown out (i.e. the arc will be stretched further than the spark energy can maintain). The operating conditions with the lowest mean flow speed (i.e. the 300 & 270 °CA bTDC and 260 & 110 °CA bTDC cases) also possess the latest CA10, suggesting that bulk flow in the vicinity of the spark gap is the dominant factor driving early flame development.

It follows that cycle-to-cycle variations in the mean flow-field are linked to cycle-to-cycle variations in flame development [14, 16, 18]. Low-frequency fluctuation intensity, based off differences between the cycle-resolved mean flow and the ensemble averaging according to Eq. 2, is plotted in Fig. 15. Here we see that the 260 & 110 °CA bTDC case possesses significant variation in its bulk flow behaviour, particularly when considering that its mean flow speed is low. In contrast, the 300 & 210 °CA bTDC case shows the lowest fluctuations out of all fuel-injected operating conditions. These observations, interpreted alongside Fig. 13, also reinforce the earlier discussion regarding the inability of ensemble averaged flow fields to represent a true average cycle due to how they are affected by cycle-to-cycle variation.

Fig. 15
figure 15

Low frequency fluctuation intensity for each operating condition according to fixed cut-off (left), and scaled cut-off (right)

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An alternative representation of low-frequency fluctuation intensity is provided in Fig. 16. Here, the fluctuation intensity of each case is normalised by its mean flow speed, resulting in a value which illustrates the ratio of variation in relation to the total flow. The figure shows values for only the last data point (i.e. 28 °CA bTDC), as this is most relevant to the flow field at ignition timing. Interestingly, the majority of the injected cases show lower variation than the motored condition, suggesting that well timed injection events have a steering effect on the flow which helps to guide bulk flow structures. As expected, the 260 & 110 °CA bTDC and 300 & 210 °CA bTDC cases present the highest and lowest variation respectively. Comparing this graph to the CoV of IMEP graph in Fig. 10 yields a very promising observation; there appears to be a clear correlation between cycle-to-cycle variation in bulk flow and cycle-to-cycle variation in indicated engine output. The slight kink in the trend, i.e. the 300 & 210 °CA bTDC case possessing similar CoV of IMEP to the 300 & 110 °CA bTDC and 140 & 110 °CA bTDC cases despite having much lower flow fluctuations, may be explained through interpreting the CA10/CA50 and TKE results. The significantly slower flame development of the 300 & 210 °CA bTDC case increases the exposure of the early flame to the high velocity bulk flow, which in-turn can cause undesirable effects such as excessive stretching of the flame front, or heightened contact with the wall.

Fig. 16
figure 16

Mean flow speed normalised low frequency fluctuation intensity for each operating condition according to fixed cut-off (left), and scaled cut-off (right)

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4.4 Spatially-averaged quantitative flow-field analysis

A further source of variation in flame development may arise from inconsistencies in total flow energy and turbulence from cycle-to-cycle. By calculating RMS quantities in the spatial domain, it is possible to obtain flow-field information for each individual cycle. Figure 17 shows box plots for the total kinetic energy (KE) spread of each case at 28 °CA bTDC. The trend observed in the median values is to be expected, based off the mean flow speeds shown in Fig. 13.

Fig. 17
figure 17

Total KE box plots for each operating condition

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Surprisingly, the case with the second largest spread of values is the 300 & 210 °CA bTDC case, despite exhibiting the least low-frequency flow fluctuation intensity. This apparent inconsistency is easily explained — the fluctuation metric is directional, whereas total kinetic energy is not; implying that this injection strategy results in consistent flow structures (i.e. it is highly directional as seen in Figs. 11 and 12), yet the strength of the flow varies significantly. In contrast, the 260 & 110 °CA bTDC case has a much smaller spread; implying that the strength of the flow is consistent, while the structure is not.

Early flame development may be more influenced by variation in TKE rather than total KE, as only very small turbulent eddies may interact with the flame kernel. However, the box plots in Fig. 18 suggest that the 300 & 110 °CA bTDC and 260 & 110 °CA bTDC cases possess near-identical spreads in TKE values from cycle-to-cycle, which does not explain the CA10 data in Fig. 8. Note that the turbulent fluctuating velocities derived through the filtering approaches used in this study describe larger structures which are more representative of the middle-to-late stages of flame development. It is possible that a stronger correlation between variation in turbulence and early flame development may be observed if very small cut-off lengths are applied to higher resolution flow-field data.

Fig. 18
figure 18

TKE box plots for each operating condition according to fixed cut-off (left), and scaled cut-off (right)

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It must be mentioned that mixture quality may be a further contributing factor to the poor early flame development inherent to the 260 & 110 °CA bTDC operating condition. One possibility is that the 40 °CA bTDC retardation in first injection timing moves the point of fuel impingement from the piston top to the cylinder liner, which may be undesirable for a number of reasons. Firstly, a portion of the liquid fuel may be lost via escaping past the compression rings as the piston travels up during the compression stroke. Additionally, the slowly vaporising liquid fuel will result in relatively rich mixtures in the surrounding regions, which for piston-top impingement is more towards the centre of the combustion chamber, rather than at the edge as in the case of liner impingement. Another possibility is that injecting fuel close to peak intake valve lift may result in wetting the rear of the valves. Ideally, an optical measurement (e.g. fuel fluorescence or Rayleigh scattering) could be conducted to reveal more information about the spatial distribution of fuel throughout the cylinder.

4.5 Integral length scales

Integral length scales were calculated for each case based off the high-frequency fluctuating velocities, rather than the traditional ensemble averaging based approach. The reasoning for this is addressed in our previous study [43], where it was found that fluctuation intensity in ensemble averaged data was more representative of cycle-to-cycle variation rather than true turbulence. In Fig. 19, the integral length scale of each case is presented for both the 8 mm and scaled cut-off filters, with the values being averaged over the entire crank angle domain (i.e. 40 to 28 °CA bTDC). The results suggest that the effect of fuel injection on integral length is minimal, with each case presenting only a slight increase over the motored condition when the fixed cut-off approach is used. The size of the filter applied to the dataset has a much larger effect, which is to be expected as a longer cut-off length results in larger flow structures being considered turbulence, which in turn increases the correlation co-efficient for larger separation distances. As such, the mostly arbitrary nature of defining cut-off lengths somewhat limits the quantitative value of these results, and once again points out the difficulties involved in separating mean flow from turbulent flow.

Fig. 19
figure 19

Integral length scales for each operating condition according to fixed cut-off (left), and scaled cut-off (right)

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5 Conclusions

Flow-field analysis was performed for 5 fuel-injected operating conditions in an optical engine motored at 1200 RPM with 100 kPa intake pressure. The aim of the study was to determine the effect of fuel-injection timing on bulk flow and turbulence, and to draw comparisons between these results and the combustion performance results obtained from in-cylinder pressure data. PIV images were acquired on a horizontal (swirl) plane 5 mm below the fire deck from 40 to 28 °CA bTDC, limited by the presence of fuel droplets and the piston blocking the field of view, respectively. The flow fields were decomposed into mean and fluctuating components via two spatial filtering approaches — one using a fixed 8 mm cut-off length, and the other using a mean flow speed scaled cut-off length. The scaled method was designed in order to match the TKE profile of a 300 Hz filter, and the specifics of the process can be found in our previous work [43].

The operating conditions investigated in this study were selected based on a timing sweep [30] which revealed complex relationships between fuel-injection, combustion phasing, and IMEP. Each condition utilised a 1:1 split ratio double-injection strategy, providing a stoichiometric global air-fuel ratio. Timings ranged from two injections in the intake stroke to two injections in the compression stroke, resulting in a variety of in-cylinder environments from well-mixed to highly turbulent. The major findings of this study are summarised as follows:

  • Relatively minor changes in injection timing can have a large influence on the magnitude and cycle-to-cycle variation of in-cylinder pressure traces. For example, a retardation of just 40 °CA in first injection timing between the 300 & 110 °CA bTDC and 260 & 110 °CA bTDC cases resulted in a decrease of approximately 1.5 MPa in mean peak pressure, mostly driven by substantially higher variation in early flame development. This behaviour was then reversed when retarding the first injection to 140 °CA bTDC, which resulted in very similar peak pressure and early flame development as the 300 °CA bTDC first injection case.

  • Injection timings which resulted in the least consistent early flame development (determined via CA10) also exhibited the highest CoV of IMEP, namely the 260 & 110 °CA bTDC and 300 & 270 °CA bTDC cases.

  • The non-monotonic behaviour observed in the pressure derived data was also present in the in-cylinder flow fields — i.e. relatively minor changes in injection timing resulted in large differences in flow structures and magnitudes. Once again, the 260 & 110 °CA bTDC case was the biggest outlier, showing very little bulk flow velocity despite its late second injection.

  • The direction and strength of tumble flow was heavily influenced by injection timing. The 300 & 210 °CA bTDC case substantially enhanced the natural tumble flow motion, whereas the 300 & 110 °CA bTDC and 140 & 110 °CA bTDC cases exhibited a noticeable reversal of the tumble flow direction. This behaviour could explain the low bulk velocity of the 260 & 110 °CA bTDC case, as the second injection may be interferring with the flow established by the first injection.

  • As expected, retarded injection timings resulted in increased TKE. The majority of cases showed mostly consistent TKE over the observed crank angle domain, except for the 140 & 110 °CA bTDC which was still undergoing significant decay.

  • The relative change in relationships between the TKE of each case suggests that the scaled filter shows better correlation with the in-cylinder pressure results, particularly in regard to the 300 & 270 °CA bTDC and 300 & 210 °CA bTDC cases, and the 300 & 110 °CA bTDC and 260 & 110 °CA bTDC cases.

  • Cycle-to-cycle variation in bulk flow behaviour was quantified as a low-frequency fluctuation intensity. When normalised by the mean flow speed, these fluctuations showed strong correlation with the CoV of IMEP for each case.

  • Variation in TKE from cycle-to-cycle did not show the same trends, suggesting that early flame development is far more dependent on bulk flow behaviour than turbulence — likely linked to the flame kernel experiencing heat-loss through the spark plug electrodes. Higher resolution imaging to capture the smaller-scale flow features in the vicinity of the spark plug may be required to draw a firmer conclusion.

  • Fuel-injection did not result in significant modulation of integral length scales when the fixed 8 mm cut-off filter was applied; rather, the integral length scales were heavily dependent on the cut-off length. Accurately determining the integral length scales associated with engine flows remains a non-trivial task.