Study on the Influence Mechanism of Spoiler on Flow and Combustion Process in Rotary Engine Cylinder

Internal combustion engines serve as a reliable power source across various industries. Today, cost-effective and dependable small engines are prevalent in motorcycles, all-terrain vehicles, boats, and small aircraft [1,2]. Despite their widespread use, small engines exhibit lower efficiency than larger piston engines. For instance, a specific small-displacement four-stroke reciprocating engine achieves a peak efficiency of only 12–15% [3–5]. In contrast, in a traditional four-stroke engine, where the piston momentarily halts four times per cycle to adjust its direction of movement, a rotary engine maintains continuous unidirectional rotational motion, resulting in enhanced stability and reduced vibrations [6–8]. Additionally, the rotary engine boasts high power density, simple design, compact size, and lightweight construction [9–11], positioning it as a formidable competitor to reciprocating piston engines in applications such as extended-range vehicles and small drones [12–14].

However, the rotary engine faces challenges in achieving the fuel efficiency of reciprocating engines due to its narrow and flat combustion chamber shape, high surface area, and low compression ratio [15,16], thereby limiting its application across various fields [17,18]. To enhance fuel economy and optimize rotary engine performance, researchers worldwide have undertaken numerous studies on engine structure [19–22]. Kuo et al. [23] investigated the impact of rotary profile on engine compression flow via numerical analysis, revealing that increasing the shape coefficient K can enhance compression efficiency and mixture formation. Tartakovsky et al. [24] focused on optimizing the rotary combustion chamber structure, starting from the in-cylinder flow field, resulting in improved engine performance. Similarly, Jeng et al. [25] emphasized fuel-air mixing as the starting point, enhancing engine performance by optimizing the rotary combustion chamber structure. Additionally, Wei et al. [26–28] observed that the position of the rotary combustion chamber influences flame propagation, thus optimizing engine performance by adjusting its position.

Furthermore, scholars have recognized the potential of spoilers within the rotary combustion chamber to enhance engine performance [29–31]. Shi et al. [32] investigated the impact of spoiler positioning on rotary engine combustion, demonstrating that closer proximity to the spark plug increases turbulence velocity and dissipation rate in the spark region, which accelerates mixture combustion and enhances combustion characteristics and emission performance. Furthering this line of research, Shi et al. [33] also developed a novel turbulence-induced blade configuration for a hydrogen-enriched rotary engine, revealing that strategic placement within the rotor chamber significantly boosts turbulence, accelerates combustion, and greatly improves thermal efficiency and emissions performance. Complementing these findings, Kordi and Esfahanian [34] conducted a detailed exploration of the axial vane rotary engine using a quasi-dimensional modeling technique, showing that spoiler variations in the cam blade profiles critically impact dynamic behaviors, thereby affecting the engine's time between overhaul.

However, existing studies on spoilers primarily focus on their structural parameters' impact on engine performance, without elucidating the mechanism by which spoilers affect flow and combustion processes within the cylinder [27,35–40]. Therefore, by analyzing the motion patterns of the rotary, this study discovers that volume inconsistencies arise between two cylinder areas separated by the spoiler, influenced by rotary movement. If the material exchange between these areas is not promptly completed, pressure differences arise, forcing the gas to flow from higher-pressure areas to lower-pressure areas. To distinguish this flow phenomenon from the forced flow caused by the spoiler, it is termed “pressure differential flow,” resulting from local pressure variations in the cylinder induced by the combustion chamber, cylinder body, and spoiler structure. To investigate the impact of pressure differential flow on in-cylinder flow and combustion processes, this article develops a mathematical model for in-cylinder flow and a three-dimensional simulation model of the engine. Studies on the structural parameter of spoiler height were conducted, calculating the minimum height required to produce pressure differential flow and verifying it through three-dimensional simulation models. The study analyzes spoiler heights' effects on in-cylinder flow patterns, elucidating the impact of pressure differential flow on ignition delay, maximum cylinder pressure, ignition timing, and combustion stability. This article uncovers a unique phenomenon of high-speed local gas flow within rotary engines and studies its causes and effects on in-cylinder flow and combustion characteristics, providing a theoretical basis and guidance for further optimization of rotary engine spoilers.

In contrast to conventional engines that convert piston reciprocating motion into crankshaft rotation, the rotary engine's eccentric rotation results in different volumes of the combustion chamber due to varying angles within the cylinder body [41]. Figure 1 illustrates the rotary area, rotating clockwise. In the diagram, region A represents the area formed by the rotary, cylinder, and spoiler in the rotation direction, while region B denotes the area formed in the opposite rotation direction. The space between the spoiler and the rotary cylinder serves as the flow area connecting areas A and B.

When assessing the volume of different cylinder areas, the cylinder's flow process is initially simplified as follows:

1. The width of the spoiler is disregarded, and the extension line of the rotary's center to the spoiler's center is taken as the virtual boundary between combustion chambers A and B.

2. The gas within the cylinder is treated as an ideal gas, with constant temperature during rotary selection.

3. The effects of the spoilers on the gas are neglected.

4. The effects on the translation distance are excluded, and both cylinder and rotary profiles are considered theoretical.

5. The impact of leakage on cylinder quality is disregarded.

6. Chemical reactions do not occur among the substances within the cylinder.

Figure 2 presents a schematic illustrating the geometric relationship between various areas of the combustion chamber, rotary, and cylinder block at a rotation angle α. In the figure, O represents the rotation center, $O′$ denotes the rotary center, $O′A2$ and $OA1$ are parallel to the x-axis, $B1$ indicates the intersection of the rotary's rotation direction and the cylinder body, $B3$ represents the intersection of the rotary in the opposite direction of rotation and the cylinder body, $B4$ signifies the spoiler center, $B2$ depicts the intersection of the extension line of the rotary center $O′$ and the spoiler center $B4$ with the cylinder body, and C marks the intersection of $O′B1$ and $OB2$⁠, $∠A1OO′=3∠A2O′B3=α$⁠.

By integrating Eqs. (1)–(26), we can determine the volume $FA$ of area A and the volume $FB$ of area B.

If the average flow velocity at the junction of areas A and B at time t falls below $vΔt$⁠, exchange of material between these two areas may not occur within the required timeframe. When Eqs. (15)–(20) are integrated, it becomes evident that this discrepancy will cause the average pressure $PAt+Δt$ in area A and the average pressure $PBt+Δt$ in area B at time $t+Δt$ to no longer be equal, thereby resulting in a pressure difference across different areas of the combustion chamber. As a consequence of this pressure differential, the average velocity at the junction of areas A and B will exceed the theoretical average velocity, subsequently influencing the flow and combustion process within the cylinder. This article discusses the local pressure disparity within the cylinder, arising from the combustion chamber, cylinder body, and spoiler structure, along with ensuring high-speed gas flow within the cylinder, termed pressure differential flow.

To validate the pressure difference flow phenomenon discussed in Sec. 2, this study employs the renormalization group K–ε model to simulate airflow dynamics within the cylinder [42–44]. Combustion computations were conducted using the primary reference fuel framework mechanism, comprising 41 components and 124 chemical reactions, coupled with the software for analysis of gas-phase chemistry and aerosol formation in the environment (SAGE) detailed chemical kinetic model [45,46]. A three-dimensional simulation model of a rotary engine was developed to investigate in-cylinder flow and combustion processes at various spoiler heights [47]. This study employs a single-cylinder gasoline rotary engine for investigation and validation, with structural parameters detailed in Table 1. The corresponding solid model is illustrated in Fig. 3.

To mitigate the impact of grid count on calculation outcomes and ensure accuracy, it is essential to conduct a grid independence analysis on the simulation model beforehand, selecting an optimal grid count to minimize computation time. This study assesses alterations in in-cylinder pressure across four varying grid counts, maintaining consistent boundary conditions throughout [48]. Details of the boundary condition settings for the rotary engine are outlined in Table 2. Figure 4 depicts the pressure change curves at different mesh counts. Using adaptive mesh refinement based on a 2-mm grid size, the cylinder pressure variation curve aligns closely with the curve at a 1-mm mesh count, indicating stable computational results. Based on the analysis above, the study opts for a 2-mm adaptive mesh division considering computational efficiency, accuracy, and timing [49]. In this article, the rotary engine is modeled with approximately 200,000 hexahedral cells during the simulation process, as shown in Fig. 5.

This section delves into the influence of spoiler height, positioned at the rotary's center, on pressure differential flow, as well as its effect on the cylinder flow and the combustion processes. The maximum spoiler height, measured from the bottom edge of the combustion chamber to the rotary profile, stands at 4.19 mm. Simulations were conducted for nine spoilers of varying heights, namely 100% maximum height (4.19 mm), 95% maximum height (3.97 mm), 90% maximum height (3.77 mm), 85% maximum height (3.56 mm), 80% maximum height (3.35 mm), 75% maximum height (3.14 mm), 70% maximum height (2.93 mm), 65% maximum height (2.72 mm), and 60% maximum height (2.51 mm). Figure 6 illustrates cross-sections of the rotary solid model at 100% maximum height, 80% maximum height, and 60% maximum height, with h representing the spoiler height.

As the spoilers of the nine rotary types mentioned above are all situated at the rotary's center, volume changes across different areas remain consistent. Figures 7(a) and 7(b) display the comparison between volume change curves derived from Eqs. (1)–(13) and the actual volumes computed by the simulation model for various regions. Figure 7(c) illustrates a comparative diagram between the theoretical flow area computed using Eq. (14) and the actual flow area at 100% maximum height. Table 3 presents the discrepancy between theoretical calculations and actual results. It is evident from the table that the volume calculated using the flow area method exhibits minimal error compared with the actual volume. The volume calculation exhibits an average error of 1.20% in area A and 0.96% in area B. Additionally, the average error in flow area calculation is 7.42%, providing reliable data for in-cylinder flow analysis and computation.

Figure 8(a) depicts the volume change rates of various regions as computed from theoretical volume adjustments. Observing both Figs. 7 and 8(a), it becomes apparent that within the range of −40°CA to 20°CA, region A initially experiences a decline in volume followed by an increase, whereas region B demonstrates a swift decrease in volume. This varying trend in regional capacity change will result in inconsistent gas densities across the two regions, thereby generating pressure differences between them and ultimately inducing pressure differential flow among different regions. Unequal alterations in regional volume serve as the foundation for pressure differential flow. Figure 8(b) illustrates a curve representing the variation in rotary flow area at different spoiler heights, plotted against the crankshaft angle and calculated using Eq. (14). From the figure, it is evident that with the rotary's fundamental structural parameters, rotation speed, and combustion chamber shape held constant, the spoiler height directly influences the flow area between various regions, consequently resulting in different pressure differential flows. As the spoiler height increases, the flow area between different regions decreases, leading to a more pronounced generation of pressure differential flow.

Conversely, the lower the spoiler structure, the weaker the effect, potentially resulting in insufficient generation of pressure differential flow. For rotary at the same spoiler positions, flow area trends remain consistent across various spoiler heights. This trend entails a gradual decrease from −40 °CA to 5 °CA, followed by a rapid increase after 5 °CA. Moreover, at the same angles, the flow area decreases with the increasing spoiler height. This variation in flow area constitutes the primary factor influencing pressure difference flow. An excessively large flow area between different regions may expedite a material exchange, resulting in either no or minimal pressure difference due to negligible air density disparities, thereby weakening pressure differential flow. Conversely, a smaller flow area impedes material exchange between different regions, leading to higher-pressure differences attributable to air density variations, thereby enhancing pressure differential flow. Figure 9 depicts a schematic of the flow area at 5°CA and 15°CA, marked with arrows, showing a rapid increase in the flow area post 5°CA due to the spark plug chamber's influence.

Equation (20) was employed to compute the critical average flow velocity $vΔt$ of the rotary with various spoiler heights, and the outcomes are depicted in Fig. 10. Notably, under identical spoiler positions, the critical average flow velocity of rotary with different spoiler heights follows a consistent trend, steadily rising with increasing spoiler height at equivalent angles. Furthermore, the critical flow velocity of rotary with varying spoiler heights exhibits a similar trend of change, gradually increasing from −40 °CA to 5 °CA. Subsequently, post 5 °CA, the flow area increases due to the influence of the spark plug chamber before decreasing. Additionally, at the same angles, the flow area decreases with increasing spoiler height, as illustrated in the figure. The critical velocity serves as a prerequisite for initiating pressure differential flow. As seen from Eq. (20), the critical velocity and the theoretical maximum flow velocity at the regional boundary collectively determine the occurrence and magnitude of pressure differential flow between different regions. When the disparity between the critical velocity and the theoretical maximum velocity at the regional boundary is negative, it signifies that material exchange can occur effectively, resulting in no pressure variance between different regions and thus no pressure differential flow. When the disparity is positive, it indicates that material exchange is influenced by pressure differential among various regions, as exchange cannot be completed promptly. Moreover, a greater disparity suggests a slower-than-anticipated material exchange, resulting in an increased pressure difference between regions. Consequently, this amplifies the strength of pressure differential flow across different areas.

Figure 11 illustrates the pressure difference between areas A and B at various spoiler heights, as calculated by the three-dimensional simulation model. Positive values denote greater pressure in area A than in area B, resulting in the airflow from A to B, while negative values indicate the reverse. The black solid line represents the pressure difference without a spoiler structure. Figure 12 depicts the maximum speed at the area A and area B junction for different spoiler heights, with the black solid line denoting speeds without a spoiler. The figure indicates that influenced by the flow area, critical velocity, and theoretical maximum flow velocity at the regional interface, both the pressure difference and flow velocity increase as spoiler height increases at the same angle. A spoiler height less than 75% of the maximum height has a minimal effect on pressure, with its pressure variation area similar to that without the spoiler. The figure also reveals that the trend of the maximum speed curve of the spoiler heights ranging from 100% to 80% of the maximum height is consistent. However, for the spoiler heights between 75% and 60% of the maximum height, the pressure difference is smaller, leading to a reduced pressure difference flow. As a result, the trend in this range is similar to that of the structure without spoiler. This indicates that when the spoiler height exceeds 75% of the maximum height, the cylinder's flow is primarily influenced by the pressure difference between different areas and the forced flow generated by the spoiler. Conversely, when the spoiler height is less than 75% of the maximum height, the cylinder's flow is mainly driven by the forced flow created by the spoiler itself.

Figure 13 presents pressure cloud diagrams for structures with spoilers at 100%, 80%, and 75% of the maximum height spoiler, as well as a structure without a spoiler, at −10 °CA, 0 °CA, and 10 °CA. The figure clearly shows a pressure difference between various areas. When the spoiler height exceeds 75% of the maximum height, the regional pressure difference caused by the spoiler is more pronounced. Conversely, when the spoiler height is below 75% of the maximum height, the regional pressure difference is less significant. Compared with the structure without spoilers, structures with spoilers exhibit lower pressure at the time of ignition (−10 °CA to −5 °CA) and in the ignition area (area A), with the pressure in the ignition area decreasing as the spoiler height increases.

Figure 14 displays velocity cloud diagrams of the structures with spoilers at 100%, 80%, and 75% of the maximum height, as well as for a structure without a spoiler, at −10 °CA, 0 °CA, and 10 °CA. The figure shows that the flow velocity in the cylinder increases with higher spoiler height. When the spoiler height is more than 75% of the maximum height, the pressure difference flow is more pronounced, and the flow field distribution is more uniform. In this case, the cylinder experiences both pressure difference flow and forced flow caused by the spoiler. When the spoiler height is less than 75% of the maximum height, the pressure difference flow is weaker, and the flow field distribution resembles that of a structure without a spoiler. Here, the forced flow in the cylinder is primarily due to the spoiler. The high-speed area in the figure indicates that the pressure difference flow mainly occurs between the spoiler and cylinder body, following the cylinder body's rotation, with the high-speed area peaking at 10 °CA. The pressure difference flow also influences the position and intensity of the vortex within the cylinder. As the spoiler height increases, the vortex intensity in the spark plug chamber decreases. At the crankshaft angle of 10 °CA, the spark plug chamber of the structure with a spoiler at 100% maximum height shows almost no vortex motion. This occurs because the junction between the spark plug chamber and the cylinder is nearly enveloped by the high-speed airflow moving in the rotation direction, creating a closed area that restricts gas flow. As the spoiler height increases, the vortex in the cylinder gradually shifts from the cylinder body to the junction area between the spoiler and the combustion chamber. Structures with higher spoiler heights have less orderly in-cylinder flow in the early stage of combustion (after 10 °CA) than those with lower spoiler heights.

Figure 15 illustrates the flame morphology for structures at 100%, 80%, and 75% of the maximum height, as well as a structure without a spoiler, at −10 °CA, 0 °CA, and 10 °CA. The figure shows that when the spoiler height exceeds 75% of the maximum height, the pressure difference flow results in a higher flame propagation speed in the early stage of combustion. However, the propagation speed is inconsistent in all directions, potentially not only enhancing fuel combustion and increasing explosion pressure but also leading to poor combustion stability. When the spoiler height is 75% of the maximum height, the pressure difference flow is weak, resulting in a more uniform flow field that resembles the distribution of the structures without spoilers.

Figure 16 illustrates a comparison between the cylinder pressure, cylinder temperature, and heat release rate curves for structures with spoilers at 100%, 80%, and 75% of the maximum height spoiler, as well as for a structure without a spoiler. The figure reveals that the cylinder pressure and temperature curves for the spoiler structures at 100% and 80% of the maximum height follow a similar trend. Conversely, the curves for the spoiler at 75% of the maximum height and the structure without a spoiler exhibit a consistent trend. This aligns with the earlier analysis regarding the impact of spoiler height on cylinder flow. The heat release rate curve shows significant fluctuations for structures with taller spoilers, indicating poor combustion stability attributed to early-stage flow field effects.

Figures 17 and 18 depict the curves illustrating the maximum cylinder pressure and the angle of the maximum cylinder pressure relative to the top dead center, respectively, as the spoiler height varies. In the figure, the black solid line parallel to the X-axis represents the value without a spoiler structure. The ignition time, defined as the moment when 0.5% of the fuel's heat is released, and the ignition delay, defined as the duration between ignition and when 10% of the fuel's heat is released, are analyzed in Figs. 19 and 20, respectively. In the figure, the black solid line parallel to the X-axis represents the value without a spoiler structure.

It can be observed that the maximum cylinder pressure rises with increasing spoiler height, surpassing that of the structure without a spoiler. This trend is attributed to increased flow velocity within the cylinder, mitigating vortex formation and thus enhancing flame propagation speed and combustion acceleration. As the spoiler height increases, ignition time is delayed, primarily due to lower pressure and higher flow velocity in the ignition area of structures with taller spoilers, inhibiting initial fire core formation. Conversely, the ignition delay angle decreases with increasing spoiler height, as taller spoilers induce greater flow velocity, accelerating flame propagation. Consequently, the angle of the maximum cylinder pressure relative to the top dead center decreases with increasing spoiler height, becoming smaller than that of structures without spoilers when spoiler height exceeds 76% of the maximum height.

Structures with different spoiler heights are categorized into two groups based on cylinder flow characteristics: low spoiler height (between 60% and 75% of the maximum height), where the dominant flow in the cylinder is the forced flow induced by the spoiler, and high spoiler height (between 75% and 100% of the maximum height), where both pressure difference flow and forced flow from the spoiler coexist in the cylinder. The change rates of various performance indicators with spoiler height were calculated and are presented in Table 4.

The table reveals that different in-cylinder flow forms resulting from the spoiler have different effects on the performance indicators. Compared with low spoiler height, the change rate of performance at the ignition time for high spoiler height increases from 0.1366 °CA/% to 0.1696 °CA/%, marking a 24.1% increase. The change rate of ignition delay decreases from −0.1805 °CA/% to −0.2202 °CA/%, a decrease of 21.9%, indicating that pressure difference flow has both a negative impact on delaying ignition timing and a positive effect on accelerating combustion speed in the cylinder.

Considering the cylinder flow analysis, the lower pressure and higher flow velocity in area A at the ignition delay moment lead to delayed ignition, while the higher flow velocity and complex flow field distribution postformation of the fire core accelerate the flame propagation and shorten the ignition delay. Moreover, higher spoiler heights significantly increase the rate of maximum cylinder pressure increase, from 0.0085 MPa/% at low spoiler height to 0.0379 MPa/% at high spoiler height, marking a 345.8% increase. This is primarily due to higher flow velocity and more complex flow field distribution in the cylinder, accelerating flame propagation and fuel combustion. However, the impact of different spoiler heights on the change rate of the angle of maximum cylinder pressure from the top dead center is relatively minor, decreasing by only 9.1% from −0.1239 °CA/% at low spoiler height to −0.1351 °CA/% at high spoiler height.

This article has investigated the impact mechanism of the rotary engine spoiler on the flow and combustion process within the cylinder. It theoretically examines the pressure difference flow, which arises from local pressure differences in the cylinder caused by the combustion chamber, cylinder body, and spoiler structure, resulting in localized high-speed gas flow within the cylinder. A corresponding mathematical model is established. Various factors influencing the generation and development of differential pressure flow are theoretically analyzed, and the effects of spoiler height on differential pressure flow, in-cylinder flow, and the combustion process are studied. The study leads to the following conclusions:

1. In rotary engines, the spoiler divides the cylinder space into two regions, influenced by the rotary's movement patterns. If the material exchange between these regions is not completed promptly, it results in a pressure difference, forcing the gas to flow from high-pressure to low-pressure areas. The spoiler height directly determines the flow area between these regions. At the same angle, the flow area decreases with increasing spoiler height. A larger flow area between regions allows rapid material exchange, leading to small or no pressure differences due to minimal air density variations, thus weakening the pressure differential flow. Conversely, a smaller flow area hinders material exchange, causing a higher-pressure difference due to air density variations, thus enhancing the pressure differential flow. The critical speed, necessary to maintain equal pressure differences between regions, along with the theoretical maximum flowrate at the junction, determines whether pressure differential flow occurs and its intensity. If the difference between the critical speed and the theoretical maximum flowrate is negative, material exchange can be completed without creating a pressure difference, eliminating pressure differential flow. If positive, the delayed material exchange due to the pressure difference slows down more than expected, increasing the pressure difference and intensifying the pressure differential flow. Influenced by the flow area, the critical average flow speed at the same angle increases with the spoiler height.

2. The flow patterns in the cylinder influenced by the spoiler are primarily divided into forced flow directly caused by the spoiler and pressure differential flow induced by local pressure differences within the cylinder. When the spoiler height exceeds 75% of the maximum height, the cylinder flow is primarily influenced by both the pressure difference flow between different areas and the forced flow created by the spoiler. However, when the spoiler height is less than 75% of the maximum height, the flow is mainly driven by the forced flow from the spoiler. Additionally, pressure difference flow primarily occurs in the region between the spoiler and the cylinder body, with high-speed flow area developing along the cylinder body's rotation direction and peaking at 10 °CA. The vortex intensity in the spark plug chamber decreases as the spoiler height increases, with almost no vortex motion at 10 °CA for the 100% maximum height structure. As the spoiler height increases, the in-cylinder vortex shifts from the cylinder body to the junction area of the spoiler and the combustion chamber. Structures with higher spoiler heights exhibit poorer in-cylinder flow orderliness, consistent flame propagation speed, and stable combustion in the early combustion stage compared with those with lower spoiler heights.

3. Increasing the spoiler height leads to higher maximum cylinder pressure and ignition time, while the angle of the maximum cylinder pressure from the top dead center of the crankshaft and the ignition delay decrease. The pressure difference flow delays the ignition moment but accelerates combustion speed, significantly increasing the rate of the maximum cylinder pressure rise. However, it has minimal effect on the rate of change of the angle between the maximum cylinder pressure and the top dead center.

We thank LetPub for its linguistic assistance during the preparation of this manuscript.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.