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1 

 

 

 

Article 

Effect of piston bowl geometry on combustion, 

performance, and emission characteristics of a 

dual-fuel engine 
Abdullah Al Rifat, Md. Mizanur Rahman, Md. Arafat Rahman* 

Department of Mechanical Engineering, Chittagong University of Engineering and Technology, Chittagong-4349, 

Bangladesh 

A R T I C L E   I N F O 
 

Article history: 
Received 05 August 2025  
Received in revised form 
14 September 2025 
Accepted 30 September 2025 
 
Keywords: 
Piston bowl, Dual-fuel, Engine, Energy share, 
Combustion and emission 
 
*Corresponding author 
Email address:  
arafat@cuet.ac.bd 
   
DOI: 10.55670/fpll.fuen.5.1.1 

A B S T R A C T 
 

The piston bowl shape plays a crucial role in turbulence, swirl, and subsequent 
fuel-air mixing, which in turn affect combustion, emissions, and performance 
attributes. A cylinder stepped and modified re-entrant combustion chamber 
was investigated through Ansys Forte 2023 R1 CFD software to analyze 
combustion, emission, and performance characteristics in a diesel-methane 
dual-fuel engine. Numerical investigation is performed under 0.44 MPa load, 
50% methane energy contribution, 7° start of injection bTDC, and with a 120° 
spray angle. Methane is injected into the inlet manifold to be premixed with air. 
The maximum thermal efficiency was found to be 34.11%, and a specific fuel 
consumption of 270.44 g/kW-h was indicated by the modified re-entrant bowl 
shape. The combustion duration for a modified re-entrant is 6.73% and 14.38% 
higher than that of a cylinder and stepped bowl. Higher combustion efficiency, 
combustion duration, and total apparent heat release demonstrate sustained 
combustion in the modified re-entrant bowl. Strong early premixed combustion 
in a cylinder-shaped bowl gives the highest percentage of NOx. The stepped 
bowl has fuel-rich zones near the center after 19° CA, with lower temperatures 
near the center, giving higher amounts of UHC and VOC emissions. The amount 
of O and OH radical formation in the modified re-entrant bowl was lower, and 
delayed oxidation resulted in a higher amount of CO emission. The modified re-
entrant bowl offered the best combustion, performance, and emission 
attributes among the bowl shapes. 
 

 
1. Introduction  

Internal combustion engines (ICE) persist as a significant 
part of the energy cycle. The global impact of vehicle 
emissions on the environment is increasing. ICEs must meet 
high-performance and minimal-emission regulations, which 
complicates engine design [1]. Engine manufacturers have 
expanded their research on reducing exhaust emissions in 
response to growing awareness of air pollution and 
increasingly restrictive emission regulations. In addition, 
several studies are conducted on the parameters that 
influence the performance of engines and combustion [2]. The 
efficiency, combustion characteristics, and emissions of a 
compression ignition engine are influenced by various 
factors, including fuel standards, operating conditions, and 
engine structural design [3]. A more rapid and efficient blend 
of air and fuel is the most significant requirement for lowering 
exhaust emissions, boosting engine performance, and 
enhancing combustion characteristics [4]. The piston bowl, or 
upper section of the piston, creates the combustion chamber 

alongside the cylinder bowl. The design of the piston bowl 
alters the turbulent nature of the flow and the consistency of 
the air-fuel mixture [1]. Improving the geometry of the 
combustion space, adjusting injection parameters, and 
optimizing air movement characteristics can enhance the 
mixing ability of diesel fuel with air. For optimal geometry, the 
ratio of air to fuel should be adjusted, and for better 
evaporation, there ought to be greater circulation of air in the 
cylinder in the form of swirl, squish, and turbulence [2]. The 
effect of piston bowl shape on engine flow, turbulence, mixing, 
and burning has been widely studied in the literature [5–11]. 
Advances in fuel-air mixing across the cylinder have an 
opportunity to significantly improve combustion and thereby 
increase engine performance [12]. The gas flow inside the 
cylinder is primarily influenced by swirl alongside turbulent 
kinetic energy, which in turn affects flame propagation [13]. 
Over the last decade, researchers have shown a strong 
interest in diesel engine combustion chamber design, which 
offers various approaches for enhancing airflow within the 

 

 

Future Energy 

Open Access Journal 

https://doi.org/10.55670/fpll.fuen.5.1.1 

 

 

 

 

 

 

February 2026| Volume 05 | Issue 01 | Pages 01-09 

Journal homepage: https://fupubco.com/fuen 

 
ISSN 2832-0328 

mailto:arafat@cuet.ac.bd
https://doi.org/10.55670/fpll.fuen.5.1.1
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AA. Rifat et al. /Future Energy                                                                                                February 2026| Volume 05 | Issue 01| Pages 01-09 

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engine's cylinders. Optimal bowl shape increases air/fuel 
mixture creation while reducing rich regions [14]. Both 
nitrogen oxide (NOx) emissions and local temperature rise 
can be reduced by eliminating rich mixing regions [15]. The 
impact of combustion chamber shape on the performance of 
the engine, flow field, and air-fuel interaction is extremely 
complex. The ICEs intricate structure has hampered 
experimental studies into the shape of the piston bowl. The 
investigation will be costly and time-consuming. As a result, 
numerical modeling has become a helpful tool for evaluating 
and improving engine control systems due to its greater 
versatility and lower cost when compared to experimental 
approaches [16]. 

Kakaee et al. [17] studied numerically three piston bowl 
shapes, namely stock, bathtub, and cylindrical, in a diesel 
engine at medium load. Reported that the bathtub shape 
turned out to have the best performance and emission values. 
The bowl profile did not significantly affect the combustion of 
the reactivity-controlled compression ignition (RCCI) engine 
at low engine speeds, but it had a substantial impact at higher 
engine speeds. The bowl profile had a considerable effect on 
NOx, but a negligible effect on unburned hydrocarbons (UHC) 
and carbon monoxide (CO). Singh et al. [18] studied various 
combustion chamber shapes, finding that the required 
tumble, swirl, squish, and turbulence attributes in the 
chamber can be enhanced, resulting in lower emissions and 
improved performance. The re-entrant piston bowl is best for 
generating turbulent kinetic energy and swirl during the 
compression stroke. Hariharan et al. [19] studied with re-
entrant bowl and shallow bowl geometry. Under identical 
conditions, there was a slight variation in the combustion 
aspect between these two geometries; however, the shallow 
bowl design performed somewhat better in terms of thermal 
efficiency. 

Saito et al. [20] evaluated traditional and re-entrant 
bowls in a diesel engine to evaluate performance, emissions, 
and combustion characteristics. Consequently, the ignition 
delay is minimized because the re-entrant configuration is 
hotter than the opposite wall where the fuel strikes. 
Furthermore, as the number of air motions in the cylinder 
increased, turbulence also increased, and combustion 
attributes improved. Gülcan and Ciniviz [10] studied the 
effects of toroidal and toroidal re-entrant chamber geometry 
on a methane diesel engine. The testing results revealed that 
the toroidal re-entrant combustion chamber (TRCC) design 
eliminates the long ignition delay caused by methane addition 
and provides more stable combustion under all torque 
settings. In summary, the TRCC geometry has been 
demonstrated to be a practical approach for achieving 
improved combustion and reduced emission levels in dual 
fuel mode under torque conditions ranging from 3 to 9 Nm. 
Yaliwal et al. [21] found that the re-entrant design 
combustion chamber performed best at an injection pressure 
of 23 MPa and a nozzle opening of 0.25 mm, with 4 holes. 
Dempsey et al. [22] demonstrated that at a low load, the 
shallow cylinder has much higher combustion efficiency than 
the re-entrant bowl piston due to lower heat transfer losses 
and greater combustion efficiency. Using the typical re-
entrant piston bowl design, these fuel combinations achieve 
minimal NOx and particulate matter (PM) emissions while 
reaching a maximum gross required efficiency of 48%. Over 
the whole load and speed range, the redesigned piston 
produced minimal NOx and PM emissions, with a peak gross 
stated efficiency of around 51%. Bapu et al. investigated the 
Modified Hemispherical Combustion Chamber (MHCC) and 
traditional Hemispherical Combustion Chamber (HCC) 

designs in a diesel engine using ANSYS Fluent software. 
According to the results, mixing was improved when flow 
motions at different places of the piston were studied instead 
of the HCC [23]. Pham et al. [24] studied the impact of piston 
bowl shape on combustion and emissions in a heavy-duty 
marine diesel engine. Three different piston bowl 
configurations were numerically investigated. The study 
found that ω-type and re-entrant piston chambers increased 
cylinder power and decreased specific fuel consumption 
compared to U-type chambers. ω-type and re-entrant piston 
heads have lower peak temperatures than U-type piston 
crowns, resulting in decreased NOx emissions. Piston bowl 
design was also discovered to have no influence on soot and 
carbon dioxide (CO2). The application of re-entrant piston 
chambers is strongly suggested for improving engine 
efficiency and fuel economy while lowering nitrogen 
monoxide (NO) emissions. 

Mobasheri and Peng [25] employed computational fluid 
dynamics (CFD) modeling to investigate the impact of a 
reentrant chamber on mixture preparation, combustion, and 
engine performance. When determining the influence of the 
combustion chamber, thirteen alternative designs were 
analyzed and categorized into four key aspects: bowl depth, 
breadth, bottom surface, and lip area. The findings indicated 
that the shape of the combustion chamber has a substantial 
impact on the combustion process. It was demonstrated that 
by modifying the shape of the bowl, the level of emission 
pollutants could be lowered while other engine performance 
metrics remained constant. The purpose of this research is to 
assess the performance, combustion, and emission 
characteristics of a dual-fuel diesel engine with different 
piston bowl shapes via ANSYS Forte 2023 R1 CFD numerical 
software. While piston bowl design has a substantial impact 
on air-fuel mixing, ignition delay, and combustion parameters 
in diesel engines, it draws little attention in studies of 
methane-diesel dual-fuel combustion. This study conducts a 
complete CFD-based analysis of various bowl shapes to 
determine their effects on in-cylinder pressure, thermal 
efficiency, and emissions. The findings demonstrate the 
piston bowl effect as a viable strategy for enhancing 
performance and lowering emissions in dual-fueled engines. 

2. Computational methodology 

2.1 Governing equation 
The gas-phase working fluids are modeled using a 

mixture of several gas species in CFD. The continuity equation 
for a whole gas-phase fluid can be obtained by combining the 
equations for all species. Their composition changes while the 
engine is running due to molecular diffusion, flow convection, 
turbulence transport, contact with fuel sprays, and 
combustion. Governing equations are essentially dictated by 
the perfect gas law during the gas phase, Newtonian fluid 
dynamics, Fick's law governing mass diffusion, and Fourier's 
law governing thermal diffusion. The species conservation 
equation [26] is stated in Eq (1). Here, n=1, 2, … N, subscript 
n is the species index, N is the total species number, �̃� is the 

density, �̅� is the velocity, 𝑦𝑛 =
𝜌𝑛

𝜌
 is the mass fraction of 

species n; and �̃�𝑛
𝑐  𝑎𝑛𝑑 �̃�𝑛

𝑠  are chemical reactions and spray 
evaporation terms, respectively. The term, 𝜙 is the effect of 
the ensemble's mean convection factor [27] stated in Eq (2). 

𝛿�̃�𝑛

𝛿𝑡
+ 𝛻. (�̃�𝑛�̅�) = 𝛻. [�̃�𝐷𝛻�̃�𝑛] + 𝛻. 𝜙 + �̃�𝑛

𝑐 + �̃� 𝑛
𝑠          (1) 

𝜙 = �̃�𝑛�̅� − 𝜌�̇�𝑣̅̅ ̅̅ ̅             (2) 



AA. Rifat et al. /Future Energy                                                                                                February 2026| Volume 05 | Issue 01| Pages 01-09 

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The continuity equation of the gas phase fluid is stated in Eq 
(3) [27,28]. 

 

𝛿�̃�

𝛿𝑡
+ ∇. (�̃��̅�) = �̃�𝑠            (3) 

Equation (4) is the momentum equation used in Ansys Forte, 
which accounts for convection, pilot fuel spray, viscous stress, 
pressure force, gravity force, and turbulence transport effect 
[26]. Where, �̅�, �̅�𝑠, �̃� and �̅� are the pressure, momentum gain 
rate for spray per unit volume, stress due to the effects of 
ensemble-averaging the nonlinear convection, and body 
force, respectively. The viscous shear stress, �̃�, is stated in Eq. 
(5) where, 𝐼 and 𝜐 accounts for the identity tensor and 
kinematic viscosity, respectively. 

𝛿�̃��̅�

𝛿𝑡
+ ∇. (�̃��̅��̅�) = −∇�̅� + ∇. �̃� − ∇. Γ̃ + �̅�𝑠 + �̃��̅�         (4) 

�̃� = �̃�𝜐 [∇�̅� + (𝛻�̅�)𝑇 −
2

3
(𝛻�̅�)𝐼]           (5) 

From 1st law of thermodynamics, a change in internal energy 
needs to be equalized by pressure work and heat transfer. Eq 
(6) is the internal energy transport mathematical equation 
[27,28]. Where,  �̃�, 𝜀̂, �̅�𝑟 , �̅� and H ̃ are the specific internal 
energy, dissipation rate, radiation heat loss, heat flux vector 
and effect of convection parameter filtering, respectively. The 
�̅�𝑐 and �̅�𝑆 are the source effects due to chemical heat release 
parameters and spray interactions, respectively. 

𝛿�̃��̃�

𝛿𝑡
+ ∇. (�̃��̅��̃�) = − �̅� ∇. �̅� − ∇. �̅� − ∇. �̃� + �̃�𝜖̂ + �̃�𝑐 + �̃�𝑆 − �̃�𝑟  

            (6) 

The flow turbulence model is for solving the Reynolds-
averaged Navier-Stokes (RANS) equations. The focus of RANS 
is to simulate the ensemble-mean flow. The ensemble is an 
average that enables the understanding of incidents 
depending on the repeatability of multi-component flow 
streams. The Reynolds stress tensor, �̃�, and the turbulent 
kinematic viscosity, 𝜐𝑇, are shown in Eqs (7) and (8), 
respectively [27], where, 𝐶𝜇 is the model constant that varies 

with various turbulence models.  The turbulent kinetic 

energy, 𝑘�̃�  , is represented in Eq (9) [29]. 

�̃� = −�̃�𝜐𝑇 [∇�̅� + (𝛻�̅�)𝑇 −
2

3
(𝛻. �̅�)𝐼] +

2

3
�̃�𝑘�̃�𝐼         (7) 

𝜐𝑇 = 𝐶𝜇
𝑘�̃�

2

�̂�
            (8) 

𝑘�̃� =
1

2�̃�
𝑡𝑟𝑎𝑐𝑒 (Γ̃) =

1

2
�̅�. �̅�̅̅ ̅̅̅           (9) 

The turbulence flux parameter in the species transport 
numerical model [29] is represented in Eq. (10). Equations 
(11) and (12) refer to the turbulence flow factor, �̃�,  [27], and 
the Reynolds stress, �̃�, respectively [28]. Where DT and �̅�𝑡𝑐 are 
the turbulence diffusivity and  turbulence thermal 
conductivity, respectively. 

𝜙 = �̃�𝐷𝑇∇�̅�𝑡𝑐           (10) 

�̃� = −𝑘∇�̅� − �̃�𝐷𝑇 ∑ ℎ̃𝑛∇�̅�𝑛𝑛          (11) 

�̃�𝑟 = �̃�(𝑣𝑣̅̅ ̅ − �̅��̅�)          (12) 

2.2 Bowl geometry and mesh 
Three different piston bowl geometries, namely cylinder, 

stepped, and modified re-entrant, shown in Figure 1(a)-(c), 
respectively, are analyzed at 110° spray angle. To account for 
the symmetry of the combustion chamber, the bowl of eight 
injectors is divided into one-eighth sections. For injectors that 

are uniformly spaced, factors like injection pressure, 
temperature, air-fuel mixing, and combustion events are 
considered to be similar across each hole in the injector and 
the corresponding spray [27]. In this study, the sector angle is 
set to 45°, having periodic boundary conditions applied at the 
periodic faces. 

 
Figure 1. Piston bowl shape, (a) cylinder, (b) stepped, and (c) 
modified re-entrant 

The peak cylinder pressure (PCP) values for the cylinder-
shaped bowl model range from 7.78 MPa to 8.31 MPa, as 
illustrated in Figure 2(a). Mesh count 20600 has a PCP of 8.31 
MPa and is used as the final mesh for modeling a cylindrical 
bowl. The PCP in a stepped bowl occurs at 15660 and 18375 
mesh counts; these two PCP are close enough, and the highest 
is shown in Figure 2(b). The final mesh number for the 
stepped bowl is 18375. For the modified re-entrant bowl, 
mesh number 18120 is used for the final mesh. Hydrocarbon 
(HC) and CO pollutants firstly increased and then decreased 
over different methane energy share (MES), and a maximum 
reduction of NOx by 35% at a 50% MES level [30]. CO 
decreased when the MES was increased from 0 to 50%. CO 
emissions increase significantly as the MES reaches 75%. 
Methane absorbs a considerable portion of the oxygen inside 
the intake manifold, minimizing CO oxidation. At 75% MES, 
the diesel amount is extremely low to ensure complete 
combustion of methane, and it cannot burn on its own 
because of its greater auto-ignition temperature. Incomplete 
combustion causes higher CO emissions [31]. This study uses 
50% MES to examine combustion, performance, and 
emissions. The engine operating conditions for the bowl 
shapes are given in Table 1. 

Table 1. Engine parameters 

Type of engine Single cylinder, 4-
stroke 

Piston diameter 139.7 mm 

Piston stroke 152.4 mm 

Squish 5.6 mm 

Connecting rod dimension 304.8 mm 

Crevice width 1.67 mm 

Crevice height 37.2621 mm 

Geometric compression ratio 11.1957 

Total nozzle count 8 

Nozzle orifice diameter 0.1961 mm 

Speed 1200 rpm 

Start of diesel injection −7° aTDC 

Spray angle 110° 

Inflow droplet temperature 384 K 

Discharge co-efficient 0.7 



AA. Rifat et al. /Future Energy                                                                                                February 2026| Volume 05 | Issue 01| Pages 01-09 

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Table 2 demonstrates the initial and boundary 
conditions utilized in this simulation. These values are useful 
in scenarios involving three different piston bowl shapes. The 
piston, head, and liner all have a wall model, which allows for 
more accurate capture of the influence of the wall boundary 
layer. 

2.3 Chemistry and sub-models 
To set out the chemical reaction process for dual fuel 

combustion, a Chemkin file was developed by combining the 
diesel and methane Chemkin mechanism data with the 
CHEMKIN 2023 R1. The n-heptane [32] describes how diesel 
fuel burns in a conventional diesel engine. The GRI-Mech 3.0 
[33] is a popular chemical kinetics instrument for modeling 
methane combustion. The total number of species and 
reactions was below the individual sums of the two processes. 
The explanation is that both processes contain the same 
species and reactions. This merged Chemkin file is added to 
the chemical set in the chemistry model. Table 2 lists some of 
the other CFD sub-models required for this study.  

2.4 Model validation 
The numerical findings of PCP for diesel combustion are 

then compared with in-cylinder pressure by Musculus's 
reported data [34], demonstrating appropriate consistency as 
shown in Figure 3.  The PCP fluctuations of approximately 
2.45% were discovered when compared to the current study. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2. Initial and boundary conditions 

 

 

 

 

 

Parameters Correspondent data 

Intake valve closing 165° bTDC 

Exhaust valve opening 125° aTDC 

Intake pressure 2.33 bar 

Intake mixture temperature 384 K 

Primary swirl ratio 0.5 

Primary swirl shape factor 3.11 

Turbulent kinetic energy 10,000 cm2/sec2 

Wall temperature of piston 400 K 

Head temperature of piston 375 K 

Liner temperature of piston 365 K 

 

Figure 2. Optimum mesh: (a) Cylinder, (b) Stepped, and (c) Modified re-entrant 

 



AA. Rifat et al. /Future Energy                                                                                                February 2026| Volume 05 | Issue 01| Pages 01-09 

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Figure 3. Validation for cylinder pressure with Musculus  

3. Results and discussion 

3.1 Bowl shape effect on combustion 
The PCP of the modified re-entrant bowl is 0.28% and 

0.7% higher than the cylinder and stepped bowl, respectively. 
The highest PCP of modified re-entrants suggests an early 
start of combustion. The area under the cylinder pressure 
(CP) and crank angle (CA) demonstrates the net release of 
heat during combustion. Figure 4 represents CP variation for 
three different bowl shapes. The modified re-entrant bowl 
promotes more complete burning compared with the cylinder 
and stepped bowl. The uniform pressure variation of the 
modified re-entrant suggests turbulence increased in the 
combustion chamber, which enhances mixing of the premixed 
charge and diesel. The peak cylinder temperature (PCT) of the 
modified re-entrant shape is 1.24% and 0.46% higher than 
that of the cylinder and stepped bowl, respectively. Figure 5 
represents cylinder temperature variation over crank angle. 
The modified re-entrant bowl leads to more efficient heat 
transfer inside the combustion chamber. Improved mixing 
and turbulence can lead to higher PCT. The peak apparent 
heat release rate (AHRR) is 0.075% and 9.53% higher in 
cylinder shape than in the modified re-entrant shape and 
steeped, respectively. The peak AHRR in the cylinder and the 
modified re-entrant shape are almost the same. AHRR for the 
three bowl shapes is shown in Figure 6 at various CA. From -
5° CA to -1.75° CA, AHRR increases and then decreases at the 
same rate; and at this range, values are close enough for both 
the modified re-entrant and cylinder shapes. After -1.75° to 3° 
CA, the AHRR curve for the cylinder shape is above the 
modified re-entrant. After 3° CA, the AHRR curve of the 
modified re-entrant curve surpasses the cylinder bowl.  

 
Figure 4. In-cylinder pressure variation for three different piston 
bowl shapes 

This phenomenon exhibits weaker swirl, less turbulence, 
and early burning of the premixed phase, resulting in weaker 
diffusion-controlled combustion. The modified re-entrant 
bowl enhances air-fuel mixing, allowing more of the methane-
air mixture to participate in sustained combustion after the 
premixed phase. The total apparent heat release (AHR) for the 
modified re-entrant is 8.07% and 2.74% higher than the 
cylinder and stepped bowl, respectively, as shown in Figure 
7(d). The longest duration for combustion is for the modified 
re-entrant shown in Figure 7(b) and is for a maximum heat 
release of 2046.18 J. During the premixed phase, the 
combustion fuel burns rapidly. Main diffusion phase 
combustion, which follows the premixed phase, is related to 
combustion duration with heat release rate (HRR) [35]. 
Combustion efficiency (CE) of the modified re-entrant is 
2.12% and 7.41% higher than that of the cylinder and stepped 
chamber, respectively, as shown in Figure 7(a). The 10% to 
90% heat release duration for the modified re-entrant is 
6.73% and 14.38% higher than that for the cylinder and 
stepped bowl, respectively, as shown in Figure 7(b). Lower 
combustion duration (CD) signifies a short diffusion stage of 
combustion and improved premixed phase combustion [36]. 
A longer duration of heat release and the highest CE indicate 
sufficient time to oxidize fuel, more sustained combustion, 
and an increase in total heat release. For the stepped bowl, the 
peak AHRR, CE, and CD are lower than for the cylinder shape, 
but the total AHR is 5.19% higher.  

 
Figure 5. Cylinder Temperature variation for three different piston 
bowl shapes 

 

 

Figure 6. AHRR variation for three different piston bowl shapes 

 



AA. Rifat et al. /Future Energy                                                                                                February 2026| Volume 05 | Issue 01| Pages 01-09 

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CE demonstrates how much chemical energy is released 
from fuel into useful work. CE for stepped bowl signifies 
mixing is poor and a larger amount of fuel is oxidizing 
incompletely. Figure 9 shows the highest percentage of UHC 
and VOC emissions from the stepped bowl. A strong late 
diffusion burn can give a large area under the AHRR curve 
without a significant amount of complete oxidation. Peak 
pressure rise rates (PPRR) are almost the same for both the 
cylinder and the modified re-entrant bowl, as shown in Figure 
7(c). The modified re-entrant bowl has high PPRR with high 
CE. Besides, the cylinder has similar PPRR, but less overall 
oxidation, demonstrating it is less favorable than the modified 
re-entrant bowl. 

 
Figure 7. Comparison of, (a) combustion efficiency, (b) combustion 
duration, (c) maximum pressure rise rate, and (d) total AHR for three 
different bowl shapes 

3.2 Bowl shape effect on performance 
The amount of fuel consumed per kWh is indicated by 

specific fuel consumption (ISFC). The ISFC is 1.5% and 7.05% 
higher in the cylinder bowl than in the stepped and modified 
re-entrant shapes, respectively, as shown in Figure 8 (a). 
Thermal efficiency is the fraction of fuel energy that is 
converted into work. The thermal efficiency for the modified 
re-entrant is 4.86% and 6.5% higher than the stepped and 
cylinder bowl, respectively, as shown in Figure 8 (b). 
Enhanced swirl and turbulence are generated by the re-
entrant lip, which improves mixing and sustained oxidation 
during the diffusion phase in the modified re-entrant bowl. A 
modified re-entrant bowl yields lower ISFC and higher 
thermal efficiency, enabling a significant fraction of chemical 
energy to be converted into useful work. Despite the 
intermediate CE and CD of the cylinder bowl, it has a higher 
ISFC and lower thermal efficiency. The rapid burning of 
premixed fuel increases NOX, as shown in Figure 9 for the 
cylinder bowl shape, and weaker diffusion burn decreases 
total AHR, as shown in Figure 7(d). 

3.3 Bowl shape effect on emission 
NOx emissions of the cylinder bowl are 15.91% and 

15.16% higher than those of the stepped and modified re-
entrant bowls, respectively, as shown in Figure 9. The PCT of 
the modified re-entrant shape is 1.24% and 0.46% higher, and 
the PCP is 0.28% and 0.7% higher than the cylinder and 
stepped bowl, but NOX emission is higher in the cylinder bowl. 

The PCT and PCP differences are not enough to define NOx 
formation dependency due to temperature. In the cylinder 
bowl, PCP and PCT occurred at 3° CA and 4° CA, respectively, 
as in Figure 5. But, in the modified re-entrant bowl, PCP and 
PCT occurred at 4° CA and 7° CA, respectively, and in the 
stepped bowl, they occurred at 4° CA and 6° CA, respectively. 
The cylinder-shaped bowl’s PCP and PCT occurred earlier, 
close to top dead center (TDC), and PPRR was also high. Early 
PCP and PCT conditions strongly favor Zeldovich thermal NOx 
formation. Early PCP and PCT with PPRR indicate a very fast 
premixed burn near TDC. Although the modified re-entrant 
has a longer CD than the cylinder bowl, the stronger, earlier, 
and instantaneous combustion in the cylinder bowl provides 
a larger integrated NOx. The superior mixing inside the 
modified re-entrant shape lowers local fuel-rich hot spots; 
this lowers local NOx formation. 

 
Figure 8. Comparison of (a) ISFC, and (b) thermal efficiency, for three 
different bowls 

 

Figure 9. Comparison of emissions for three different piston bowl 
shapes at 0.44 MPa load 

The CO emission of the modified re-entrant is 6.32% and 
37.41% higher than that of the cylinder and stepped bowl, 
respectively, as shown in Figure 9. The presence of highly 
active O and OH free radicals increases the oxidation of CO 
into CO2 [37,38]. Figure 10 shows the active O and OH radicals 
for three different bowls. From -165° CA to 125° CA 
simulation, the stepped bowl has a higher amount of O and OH 
radical formation than the cylinder bowl, and then the 
modified re-entrant bowl shape. As free radical formation is 
lower in the modified re-entrant, CO emission is higher, as 
shown in Figure 9. CO emission is lower in stepped bowls due 
to higher O and OH radicals. In a steeped bowl, though radical 
formation is delayed, the cumulative radical formation is 
large and effectively converts CO into CO2. 



AA. Rifat et al. /Future Energy                                                                                                February 2026| Volume 05 | Issue 01| Pages 01-09 

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Figure 10. Reactive species, (a) OH radical, and (b) O radical 

The UHC emission of the stepped bowl is 17% and 
35.62% higher than that of the cylinder and modified re-
entrant bowl, respectively, as shown in Figure 9. A modified 
re-entrant bowl enhances very good mixing, and a longer CD 
and total AHR demonstrate a sustained diffusion phase and 
enable more oxidation, which lowers UHC. A short CD in a 
stepped bowl means weak diffusion-controlled combustion. 
The VOC emission of the stepped bowl is 16.48% and 34.4% 
higher than that of the cylinder and modified re-entrant bowl, 
respectively, as shown in Figure 9. VOC evaporates easily, and 
UHC is a specific type of VOC that results from the byproduct 
of incomplete combustion. 

3.4 Qualitative analysis 
At 3° CA, the stepped bowl has a higher small fuel vapor 

mass fraction (FVMF) shown in Figure 11, which 
demonstrates that locally rich pockets remained unmixed 
into oxidant streams. The cylinder and modified re-entrant 
have fewer pockets; comparing these two, the modified re-
entrant provides slightly better mixing. At 7° CA, there are 
local rich hot zones for the cylinder and stepped bowl, and the 
rich cold zones of the steeped are highest at the head. Overall, 
FVMF is the highest in the stepped bowl and then the cylinder 
bowl. From 11° to 19°, FVMF pockets almost remained 
unreacted by the cylinder and stepped bowl; that is a sign of 
much lower diffusion oxidation. FVMF still burns slowly from 
11° CA to 19° CA, suggesting sustained diffusion oxidation. All 
bowls showed the FVMF reduction towards the centerline. 
FVMF concentrated near the cylinder axis much more for the 
stepped, then the cylinder, and then the modified re-entrant 
bowl. The modified re-entrant bowl better summarizes net 
mixing and steps down the lower net mixing. Piston bowls 
showed higher and wider temperature distribution along the 
spray direction, as shown in Figure 12, representing the 
premixed combustion region. The stepped bowl has a higher 
temperature zone near the bowl axis for 3° CA. At 11° CA, 
bowls have hot spots at the center, and stepped bowls show 
higher temperature distribution at the center.  

 

 
Figure 11. Fuel vapor mass fraction for different piston bowl shapes 

 

 
Figure 12. Temperature distribution for three different piston bowl 
shapes 

 

 

 

 



AA. Rifat et al. /Future Energy                                                                                                February 2026| Volume 05 | Issue 01| Pages 01-09 

8 

 

The stepped bowl has a hot spot at the squish zone and 
has a higher temperature distribution along the step 
curvature, but a much lower temperature distribution at the 
bowl radius periphery. The modified re-entrant bowl showed 
the higher temperature distribution along the bowl radius 
periphery and in the squish zone. Cylinder bowls have a much 
higher temperature distribution along the lower bowl depth 
surface. At 19° CA, the modified re-entrant maintains a wide 
and uniform range of higher temperatures, reflecting 
sustained diffusion oxidation. Around 3° CA, early wide 
hotspots with high PPRR produce higher amounts of thermal 
NOx. The contours demonstrate that the stepped bowl 
captures and maintains higher fuel vapor in the near middle, 
which remains unreacted because of the short diffusion phase 
and causes higher UHC and VOC levels. The cylinder generates 
intense, early hotspots that cause the greatest NOx levels, 
while its weaker diffusion burns result in modest UHC. The 
modified re-entrant generates a more uniform vapor 
distribution and sustains late oxidation, decreasing UHC and 
VOC and boosting thermal efficiency. 

4. Conclusion 

This study investigates how a dual-fuel (DF) engine at 
50% MES is affected by different bowl geometries on 
combustion, emission, and performance attributes. The 
piston bowls are investigated with 45° sections for eight 
injectors with periodic boundary conditions at the periodic 
faces to reduce computational time. Ansys Forte 2023 R1 
software was used for the analysis of the cylinder, stepped, 
and modified re-entrant bowl. There are some observations 
that have been found in this investigation as follows: 
• Modified re-entrant’s longer combustion duration with 

higher combustion efficiency indicates enough time to 
oxidize fuel, more sustained combustion, and an increase in 
total heat release. For the stepped bowl, the peak AHRR, 
combustion efficiency, and combustion duration are lower 
than those of the cylinder shape, but the total AHR is 5.19% 
higher. The cylinder bowl has a similar PPRR but less 
overall oxidation, demonstrating it is less favorable than 
the modified re-entrant bowl. 

• The modified re-entrant bowl has the highest thermal 
efficiency with lower ISFC. The enhanced swirl and 
turbulence in the modified re-entrant chamber improve 
mixing and sustained oxidation during the diffusion phase. 

• In the cylindrical bowl, NOx emissions peaked. NOX 
emissions in stepped and modified re-entrant bowls are 
close enough. The UHC and VOC emissions peaked in the 
stepped bowl with a larger fraction; the modified re-
entrant bowl was the lowest by 35.62% and 34.4%, 
respectively. The modified re-entrant bowl has the lowest 
amount of free radical formation results and the highest 
amount of CO fraction. 

• A larger amount of FVMF remained unreacted in the middle 
of the stepped chamber, and a low temperature 
distribution at 19° CA results in a higher percentage of UHC 
and VOC emissions. The temperature distribution from 
7°CA to 19°CA, modified re-entrant bowl, showed a stable 
and uniform temperature distribution throughout the 
combustion chamber, demonstrating diffusion burn is 
superior to the cylinder-shaped bowl. 

It is noted that the best performance was shown by the 
modified re-entrant bowl. Its lower ISFC ensures the best fuel 
economy with higher combustion efficiency and thermal 
efficiency. Sustained diffusion burning confirms complete 
fuel oxidation; that’s why there are lower UHC and VOC. The 

only drawback is the higher CO emission for delayed 
oxidation. 

Acknowledgements 
This work is financially supported by Chittagong University of 
Engineering & Technology (CUET), Bangladesh through 
research grant no. CUET/CHSR-47-47.4.11. The 
corresponding author is responsible for ensuring that the 
descriptions are accurate and agreed by all authors. 

Ethical issue 
The authors are aware of and comply with best practices in 
publication ethics, specifically concerning authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere in any language. 

Data availability statement 
The manuscript contains all the data. However, more data will 

be available upon request from the corresponding author. 

Conflict of interest 

The authors declare no potential conflict of interest. 

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