The study of Internal Combustion Engines (ICE) has been a topic of interest for researchers and engineers for many years. One of the key components of an ICE is the valve system, which controls the flow of air and fuel into the combustion chamber. The dynamics of the valve lift play a crucial role in determining the performance and efficiency of the engine [1], [2]. The ICE has been a crucial component in the automotive industry for over a century. With the increasing demand for more efficient and environmentally friendly vehicles, researchers have turned to computational studies for improved engine performance. The four-stroke engine, also known as the Otto cycle, is the most common type of ICE used in automobiles [3], [4]. It consists of four stages: intake, compression, power, and exhaust. The engine's efficiency is determined by how well these stages are executed. Computational Fluid Dynamics (CFD) is a powerful tool that allows researchers to simulate the flow of air and fuel within the engine. By analyzing the flow patterns, researchers can optimize the engine's design to improve performance and reduce emissions [5], [6]. One of the key parameters that researchers focus on is the combustion process. By simulating the combustion process, researchers can fully comprehend the principles of an in-cylinder fuel-air mixture to ensure complete combustion and maximum power output [7], [8].

This is crucial for improving the efficiency of the engine. The valve lift dynamics refer to the motion of the valves as they open and close during the engine cycle [9], [10]. The valve lift profile is crucial in determining the amount of air and fuel that enters the combustion chamber and the timing of the combustion process [11], [12]. CFD simulations can analyze the valve lift dynamics and optimize the engine's performance. On the other hand, the Stoichiometric behaviour of an engine refers to the ratio of air to fuel required for complete combustion [13], [14]. The stoichiometric ratio is the ideal ratio at which all the fuel is burned completely with the available oxygen in the air [15], [16].

In a four-stroke engine, the stoichiometric ratio is typically around 14.7:1, meaning that 14.7 parts of air are required for every part of fuel [17], [18]. By studying the stoichiometric behaviour of the engine, researchers can optimize the fuel injection timing and air intake to improve the efficiency and performance of the engine. The Renault IC engine is popular for automotive applications due to its reliability and performance [19], [20]. By conducting a computational study of the valve lift dynamics and stoichiometric behaviour of the Renault IC engine, valuable insights into its performance can be gained, leading to informed decisions on improving its efficiency [21], [22]. Over the years, several studies have been conducted on valve lift dynamics and stoichiometric behaviour of four-stroke IC engines. For example, Ikpe and Bassey [23] conducted a study on CFD of the charging behaviour in the cylinder of a four-stroke spark ignition reciprocating engine, focusing on different valve lift opening clearances. The CAD model of the engine was designed using SOLIDWORKS 2019, while the in-cylinder charge behaviour was simulated using ANSYS Fluent 14.5. The increase in valve lift opening clearance resulted in a greater amount of air-fuel mixture entering the cylinder via the intake valve. This led to a rise in the temperature of the mixture inside the cylinder and a notable enhancement in the efficiency of the combustion process, both in terms of volume and mechanical performance. Additionally, it was noted that the cylinder's ability to retain heat may be most efficient at a lower valve lift, resulting in minimal or no losses. Conversely, a considerably high cylinder charge temperature may lead to a decrease in the density of the intake charge. Clenci et al. [24] experimented on a port-injected engine to investigate the effects of varying intake valve lifts during low-lift idle conditions. The study's findings indicated that regulating the maximum intake valve lift makes managing the intake quality and intake flow rate possible, leading to enhancements in the air-fuel mixing process and in-cylinder vortex dynamics. The study also showed significant fuel efficiency enhancements and cycle variability reduction. Hence, adjusting the lift of the intake valve can compensate for the decrease in flow rate caused by the valve clearance, which can have a negative impact on the efficiency and stability of combustion.

Ikpe and Owunna [25] designed a model for a single-cylinder ICE that accurately depicted the four stages of a two-stroke cycle: intake, compression, expansion, and exhaust. In their model, they considered the engine to be a closed system. The temperature of the combusted gas in the cylinder of the ICE was seen to be precisely proportional to the in-cylinder gas pressure when the air-fuel combination was close to optimum circumstances (14.7:1), and both compression and expansion were co-occurring. Temperature of the combusted gas ranged from 293.92 to 3000.60 K, while the cylinder gas pressure ranged from 60.76 to 80.20 bar. The maximum temperature of the engine at equilibrium was found to be 2367.56 K, and the maximum shear stress was determined as 176 x 102 MPa. These calculations were made using a heat transfer coefficient of 581.236 W/m2K. Sawant and Bari [10] investigated the effects of modifying the Intake Valve Timings (IVT) and valve lift at various engine speeds on engine performance, especially regarding torque and power. It was discovered that the modifications led to a mean improvement in performance of 6.02% over the whole spectrum of engine velocities, ranging from 3000 to 9000 rpm. Furthermore, the modifications made to the diverse Valve Lifts (VVL) and Variable Valve Timings (VVT) resulted in a reduction in Brake-Specific Fuel Consumption (BSFC) of about 0.35% across all engine speeds.

Ikpe and Owunna [26] employed MATLAB 2018b to develop a four-stroke Renault ICE model and conducted simulations on the model's operational efficiency, which was Mercedes-Benz 250SE W108. The displacement volume and the lowest volume filled by the in-cylinder charge were 4.65x10-4 mm3 (equivalent to 4.65x10-7 cm3) and 0.5x10-4 mm3 (equivalent to 5x10-8 cm3). The simulated data captured maximum pressure at a crank angle of 30 degrees, but the experimental data recorded it at 22 degrees. Kumar and Jayashankar [27] conducted a CFD simulation to examine how valve lift affects fluid flow in an ICE cylinder. The engine had an intake port diameter of 46 mm, a valve diameter of 43 mm, and a cylinder length and diameter of 562 mm and 93.65 mm, respectively. The findings demonstrated that the valve lift significantly impacted the flow velocity regime within the cylinder. Therefore, when the valve lift increased, flow separation became more crucial, resulting in increased losses in the vicinity of the valve opening.

Akele et al. [28] conducted a flapper flow analysis on ICE to ascertain the flow and swirl characteristics at various valve lifts. The model's shape was designed using ANSYS Design Modeller, featuring a single cylinder, intake port, exhaust port, and valves. The airflow within the cylinder experienced turbulence as it moved against the cylinder wall, undergoing a stroke motion. This motion helped to provide consistent combustion within the cylinder while also causing an increase in the intake mass flow as the valve lift also increased. Ikpe et al. [29] performed a port flow study on ICE that incorporated a valve lift of 8 mm, utilizing ANSYS R-16 software. The velocity and mass flow rate magnitude were observed using simulated profiles and cut planes. The angular velocity of the cycle was computed using SOLIDWORKS 2017. The crankshaft's average angular velocity was determined to be 1315 rpm, exhibiting a percentage variance of less than 20%. The velocity of charge, calculated by considering each component's area, was found to be 11 m/s. The equivalent mass flow rate was determined to be -0.055479 kg/s. The flow rate at a diameter of 8 mm was determined as 0.005417 kg/s.

The swirl intensity in the engine cylinder grew linearly along the stroke length. A higher swirl number led to a more evenly distributed radial temperature and a decrease in the flame temperature within the cylinder. The analysis of the influence of valve lift on the performance of a single-cylinder ICE using fluid dynamics is an intricate and time-consuming process, frequently necessitating data from experimental operations [30]. Nevertheless, employing computer-aided modelling and simulation to connect theoretical concepts with the in-cylinder thermodynamics of the ICE can enhance efficiency and minimize simulation time, leading to optimal outcomes.

This study aimed to employ modelling, simulation, and computational techniques in studying the effects of valve lift dynamics and stoichiometric behaviour of the four-stroke Renault IC engine. The study also included the relationship between valve lift openings and flow coefficient, engine speed and volumetric efficiency at various valve lift openings, engine speed and Specific Fuel Consumption (SFC) at various valve lift openings, and engine speed. It indicated power at various valve lift openings.

The subject of the investigation was a Nissan Primera inline engine, hypothesized to function based on a four-stroke cycle. The cylinder ports, valve seats, and head were designed using SOLIDWORKS 2018 and then imported into the IC engine workbench on ANSYS R-15. The cylinder head was partially modelled due to its symmetry, which reduces the computational time required for analysis. Figs. 1(a) and 1(b) display the front and end views of the ICE model, while Fig. 1(c) illustrates the cylinder port, including the intake and exhaust valves. The ICE parameters and specifications are presented in Table 1.

The poppet valve shuts progressively as the reciprocating piston descends in the cylinder due to the increasing momentum of the crankcase pressure. Prior to the completion of the stroke, the pressurized in-cylinder air-fuel mixture within the crankcase undergoes high-temperature-high-pressure flame expansion, as illustrated in Fig. 2. The expanded air-fuel mixture enters the primary cylinder and experiences compression and expansion at elevated temperatures and pressures before being expelled from the ICE due to the intake port being uncovered by the reciprocating piston as it proceeds towards the end of its stroke. The Navier-Stokes and nonlinear continuity equations are fundamental partial differential equations that govern the behaviour of incompressible and Newtonian fluids [31], [32]. These equations provide a comprehensive description of the in-cylinder fluid flows.

cut section showing in-cylinder flame temperature, b. cut section showing in-cylinder flame pressure.

Governing continuity and Navier-Stokes equations are typically used as closed-form nonlinear solutions for complex flow problems like the in-cylinder flow in spark ignition engines. These solutions consider pertinent assumptions, suitable boundary conditions, order of magnitude analysis, and dimensionless parameters [33], [34]. The flow was assumed to be turbulent, three-dimensional, incompressible, and steady. The analysis is based on a closed cycle with a constant volume of working fluid, but the elements are nonlinear and not uniformly spaced. Based on 3D Continuity and Navier Stokes Eqs. (1)-(3), represented in Cartesian coordinates, the mass and pressure dynamics of the in-cylinder charges at varying valve lifts were simulated while applying the boundary conditions:

I. Continuity equation: a continuity equation defines a conservation law by equating the net flux over the surface with a loss or gain of material within the surface [35]. In this case, the continuity equation is represented by Eq. (1) as either an integral or a differential equation:

∂u ∂u ∂u

+ + = 0. (1)

∂x ∂y ∂z II. Energy equation: this equation demonstrates that the change in energy of the fluid moving through the control volume is equal to the rate of heat transfer into the control volume plus the rates of work done by surface forces plus the rates of work done by gravity [36], [37] as given in Eq. (2).

∂ 1 2 ∂ 1 2 ∂ 1 2 ∂ 1 2 ∂ T

(ρe + ρv ) + (ρue + ρuv ) + (ρve + ρvv ) + (ρwe + ρwv ) = k ( +

∂t 2 ∂x 2 ∂y 2 ∂z 2 ∂x2

2 2 2 2

∂ T ∂ T ∂ρ ∂ρ ∂ρ ∂ u ∂ ∂v ∂w ∂ u ∂ ∂u

+ ) − (u + v + w ) + μ [u + (v + w ) + v + (u +

∂y2 ∂xz2 ∂x ∂y ∂z ∂x2 ∂x ∂x ∂x ∂y2 ∂y ∂y

2 2 2 2

∂w ∂ u ∂ ∂u ∂v ∂ u ∂u ∂v ∂ v ∂v ∂w ∂ w ∂w ∂u

w ) + w + (u + v )] + 2μ [u + + + + + ] +

∂y ∂z2 ∂z ∂z ∂z ∂x2 dy ∂x ∂y2 ∂z ∂y ∂z2 ∂x ∂z

ρugx + ρvgy + ρwgz.

III. Equations for momentum (Navier Stokes): the momentum equation, which forms the foundation of Newton's Second Law, links the overall force acting on a fluid element to its acceleration or rate of change of momentum [38], [39]. Newton's second law of motion, F = ma, is the foundation for the x, y, and z momentum equations, depicted in Eqs. (3a)-(3c).

2 2 2

∂u ∂u ∂u ∂ρ ∂ u ∂ u ∂ u

pu + ρv + ρw = + μ + μ + μ . (3a)

∂x ∂y ∂z ∂x ∂x2 ∂y2 ∂z2 2 2 2

∂v ∂v ∂v ∂ρ ∂ v ∂ v ∂ v

pu + ρv + ρw = + μ + μ + μ . (3b)

2 2 2

∂x ∂y ∂z ∂y ∂x ∂y ∂z 2 2 2

∂w ∂w ∂w ∂ρ ∂ w ∂ w ∂ w

pu + ρv + ρw = + μ + μ + μ . (3c)

2 2 2

∂x ∂y ∂z ∂z ∂x ∂y ∂z The rate of mass flow which enters the IC engine cylinder is resolved by Eq. (4a). Therefore, the rate of mass flow rate transiting the cylinder is shown in Eq. (4b).

m(x) = puF. (4a)

m(x + dx) = puF + (puF)dx. (4b)

The momentum conservation equation for the swirl velocity is expressed by Eq. (5). Thus, The strength of the swirl recorded can be evaluated by the swirl number (Sn) as shown in Eq. (6), while the ratio of axial flux (tangential momentum to the axial flux) of axial momentum times the effective nozzle radius as expressed as swirl intensity (Si) which is shown in Eq. (7).

∂ 1 ∂ 1 ∂ 1 ∂ ∂w 1 ∂ 3 ∂ w vw

(ρw) + (rρuw) + (rρvw) = [rμ ] + [r μ ( )] − ρ . (5)

∂t r ∂x r ∂r r ∂x ∂x r2 ∂r ∂r r r

∫ rwv ⃗ . d⃗A ⃗

Sn = . (6)

R ̅ ∫ uv ⃗ . d⃗A ⃗ Axial flux of tangential momentum 2π ∫ ρWUr dr

Si = = . (7)

Axial flux of axial momentum ∗ radius 2 R ∗ 2π ∫ ρWUr dr

The momentum equation states that the total of the pressure and shear forces within the cylinder of an ICE is equal to the sum of the rate of change of momentum within the cylinder and the net momentum that leaves the cylinder [40], [41]. Thus, the pressure and shear forces can be represented by Eqs. (8) and (9).

∂p ∂F dF ∂ dF

pF − (p + dx) (F + dx) + p dx = − (pF)dx + p dx. (8)

∂x ∂x dx ∂x dx pu

τ πDdx = −f πDdx. (9)

Thus, D can be expressed as the equivalent diameter which the wall shear stress τw is related to the friction factor, as shown in Eq. (10). Hence, the rate of change in momentum in the cylinder is shown in Eq. (11).

τw f = .

1 (10)

pu

(pFudx). (11)

Thus, the net efflux of momentum (net) in the cylinder is shown in Eq. (12), and the momentum equation forms the basis for the equations given in Eq. (13).

∂p ∂u dF ∂

2 2 (12)

(p + dx) (u + dx) (F + dx) − pu F = (pu F)dx.

∂x ∂x dx ∂x ∂ dF 1 ∂ ∂

2 2 (13)

− (pF)dx + p dx − f pu πDdx = (pFudx) + (pFu )dx.

∂x dx 2 ∂t ∂x Moreover, the specific stagnation enthalpy, specific internal energy, and energy equation for a fixed volume with the heat transfer rate are expressed by Eqs. (14)-(17).

CvT + + . (14)

C T + . (15)

∂(E)cv

Q − W = + (Net efflux of stagnation enthalpy). (16) Q = qρFdx. (17) Thus, q represents the heat transfer energy per unit mass per unit time, and Ws is the extemal rate of shear work. The rate of change in time (intemal energy in the cylinder )is given by Eq. (18), and the net efflux of stagnation enthalpy (in the cylinder) is shown in Eq. (19).

∂(E)cv ∂ u

= {(ρFdx) (CvT + )}. (18)

∂t ∂t 2 ∂ u p

{(ρuF) (CvT + + )} dx . (19)

∂x 2 ρ Resolving the substitution of Eqs. (17)-(19) with Eq. (16), the energy equation becomes ∂ u ∂ u p

qρFdx = {(ρFdx) (CvT + )} + {(ρuF) (CvT + + )} dx. (20)

∂t 2 ∂x 2 ρ The volumetric efficiency expressed in Eq. (21) can be expressed as the air mass (inducted) ratio into the cylinder and to the air mass that the cylinder volume can accommodate [42].

mg mg v9

 = = = . (21)

mtn vth ∗ ρth vth Thus, ηv is the volumetric efficiency, mg is the actual mass of air inducted, mtn is the theoretical mass of air that the cylinder can accommodate, ρth is the density of ambient air, and v9 is the volume of air inducted while vth is the swept volume. The Effective Cam Duration (ECD) is the degree of cam rotation, as shown in Eq. (22).

(N ∗ RV ∗ Leff)

ECD = ( ) − 0.5D. (22)

(ECD ∗ 0.25 ∗ C ∗ 2) Thus, C is the speed of sound at intake temperature, N is the engine speed, RV is the number of reflections, D is the average runner diameter, and Leff is the effective length of the runner as expressed by Eq. (23) [43], [44].

(ECD ∗ 0.25 ∗ C ∗ 2)

Leff = ( ) − 0.5D. (23)

(N ∗ RV) The in-cylinder adiabatic flame temperature during combustion for a lean mixture is specified by Eqs. (24a)- (24c), and the in-cylinder adiabatic flame temperature for a rich mixture is specified by Eq. (25) [45].

m . LHV + (m + m )C ̅ (T − T )

f a f P.R R o

TR ≅ To + . (24a)

(m + m )C ̅

a f P.P

mf . LHV mf / ma . LHV

TR = TR + . (24b)

(m + m )C ̅ P (1 + m / m )C ̅ P

a f P. f a P.

f. LHV ∅ . fs . LHV

TR + = TR + . (24c)

(1 + f)C ̅ P (1 + ∅ . f )C ̅ P

P. s P.

fs . LHV fs . LHV

TP = TR + = TR + , (25)

(1 + f)C ̅ P (1 + ∅ . f )C ̅ P

P. s P.

where mf and ma are expressed as the mass of air and fuel, C ̅ is an average value of specific heat calculated at the average temperature of reactants and standard temperature, fS is the stoichiometric fuel/air ratio by mass, and TP is the adiabatic flame temperature. Intake of the four-stroke engine is governed by isentropic flow through a restriction, which is the poppet valve of the engine [46]. The equation governing this process is given by Eq. (26). However, it is a critical parameter in IC engines, as represented by Eq. (27).

dm CDARPO PT k 2k PT k−1

= ( ) { (1 − ( ) )} . (26)

( )0.5 dθ 6N RTO PO k − 1 PO

Cd = . (27)

(A ∗ sqrt(2 ∗ g ∗ h)) Cd is the flow coefficient, Q is the actual flow rate, A denotes the cross-sectional area of the flow passage, g denotes acceleration due to gravity, and h represents the pressure drop across the IC engine cylinder. The cylinder volume is a function of the crank angle  and the piston rod length ratio to the crank (see Eq. (28)). However, the cylinder volume at any crank angle is represented by Eq. (29) [47].

Vd l l

√ 2 (28)

V = Vc + (1 + − cos θ − − sin θ).

2 c c

r − 1 1

2 2 0.5

V(θ) = Vc {1 + {1 − cosθ + [1 − (1 − ε sin θ) ]}}, (29)

where Vc is the clearance volume, r is the compression ratio, and  is the piston stroke [48]. The internal energy of burned and unburned gases (see Eq. (30)) is expressed in terms of the specific heat (C ̅ ) in Eq. (31).

vi

o ̅ ′ ′

u ̅ = ∆u ̅ (T ) + ∫ C (T )dT . (30)

i fi o vi To

∫ (ai + biT)dT a b

T1 i i (31)

C ̅ = = + (T + T ),

vi 1 2

Mi (T2 − T1) Mi 2Mi where u ̅ denotes the internal energy of in-cylinder burned and unburned gases, while C ̅ is the specific heat

i vi

of the in-cylinder combusted gases.

Fig. 4 illustrates the periodic fluctuations in the cylinder temperature during periods of 25% idle or low engine load. In contrast, Fig. 5 depicts the variations in-cylinder temperature during periods of 100% full engine load. The temperature within the cylinder ranged from 707-841oC at low load conditions and increased significantly to 2154-2254oC when the engine was at full load. This occurs due to the reduced temperature and pressure within the cylinder at idle load when the throttle is closed. Consequently, when the intake valve is shut, there is a diminished amount of air and fuel in the cylinder, resulting in decreased power output.

Conversely, increasing the throttle will quickly increase temperature and pressure within the intake cylinder, leading to a significant air and fuel mix intake to optimize engine performance [54], [55]. Therefore, the temperature and pressure within the cylinder are vital factors in the engine's performance. Fig. 6 illustrates the variations in the trajectory of the flame, whereas Fig. 7 depicts variations in the flame's propagation within the cylinder. The flames in an ICE cycle exhibit turbulent and unstable patterns when the premixed air-fuel reaches the combustion chamber. Turbulent conditions in the flame pressure enhance the dispersion of flame temperature as well as the flame speed, thus increasing the rate at which thermal reactions occur in the combustion vessel [56]. The transformation from the flame generation phase to the flame propagation phase is marked by a progressive rise in temperature and turbulence velocity within the cylinder. Elevated temperatures and prolonged engine operation also mark the flame propagation phase and, therefore, heightened engine load and velocity. Another research found that expanding the temperature of the cylinder resulted in a higher number of inflow vortices (ranging from 0.2 to 0.6 seconds). This, in turn, enhanced the recirculating zone in the furnace and induced the synthesis of combustion compounds within the internal recirculation zone [57]. This enables the effective blending of fuel-air mix, resulting in enhanced combustion efficiency by minimizing the regions of high temperature that generate Nitrogen Oxides (NOx) in the ICE. Furthermore, by augmenting the quantity of vortices, the radial dispersion of the flow is enhanced, leading to an expansion in the heat transfer surface area of the flame. Simultaneously, the highest temperature of the flame is diminished, resulting in an enhancement of the flow's radiation efficiency. The radial expansion of the flow in the combustion chamber leads to a uniform temperature distribution due to the rise in vortices generated by the drop in axial velocity and increase in tangential velocity [58]. Volumetric efficiency in ICEs measures the ratio or percentage of air inflow into the cylinder compared to the air released. Basically, it is the ratio of the mass of air-fuel mix in the cylinder during the intake stroke to the mass that would fill the same volume if the air density inside the cylinder matched that of the air around it. Fig. 8 illustrates the variations in volumetric efficiency inside the ICE cylinder. The valve lift variation ranging from 5 to 13 mm results in volumetric efficiencies ranging from 0.315 to 0.822, with 0.315 being the least and 0.822 being the highest. The optimum volumetric efficiency refers to the ideal possible quantity of air-fuel mix that can be introduced into the cylinder during the intake stroke cycle. This is due to the engine's need for the valve to open at higher rates to facilitate the inflow of charge into and out of the engine during the extended cycle. Volume efficiency can reach a maximum of 1.00 or 100%. With this figure, the engine can effectively assimilate the necessary amount of charge required for optimal operation.

Indicated Power (Kw)

1500 2500 3500 4500 5500

Engine Speed (rpm)

This research paper on the computational study of valve lift dynamics and stoichiometric behaviour of four-stroke Renault IC engines has provided valuable insights into the performance and efficiency of this engine. The study has highlighted the significance of maintaining stoichiometric behaviour in the combustion process to ensure optimal fuel efficiency. One of the key findings from these studies is that, by adjusting the valve lift profile of the intake and exhaust valves, the engine's power output and efficiency can be improved. Furthermore, the study demonstrated the importance of maintaining proper stoichiometric ratios in the combustion chamber to complete the combustion of the fuel-air mixture. The findings also underscore the importance of continuous research and development in engine optimization. By further exploring and refining these concepts, engineers, and researchers can continue to improve the performance, efficiency, and environmental impact of ICEs; future studies must build upon the existing research to drive innovation and advancements in the automotive industry. In light of the findings of this study, the following recommendations are suggested to improve the design, operation, and performance of the Renault IC engine:

I. It is vital to optimize the valve lift dynamics of the engine to ensure efficient combustion and maximum power output. This can be achieved by carefully designing the camshaft profiles and valve timing to ensure the valves open and close optimally during the engine cycle.

II. The stoichiometric behaviour of the engine must be carefully monitored and controlled to ensure that the air-fuel mixture is at the ideal ratio for combustion. This can be achieved using advanced engine management systems that adjust the fuel injection and ignition timing in real time to maintain the stoichiometric ratio under varying operating conditions.

III. Considering the impact of engine speed and load on the engine's valve lift dynamics and stoichiometric behaviour is crucial. This study has shown that these factors can significantly affect the performance and efficiency of the engine and must be carefully considered during the design and tuning process.

IV. Future research should focus on developing advanced control strategies to dynamically adjust the valve lift profile based on the engine's operating conditions.

By implementing the recommendations outlined in this study, engineers can optimize the design and operation of these engines to achieve maximum power output and fuel efficiency.

Hence, this study has contributed to understanding the valve lift dynamics and stoichiometric behaviour of IC engines, paving the way for more efficient and environmentally friendly engine designs.

Aniekan Ikpe: Methodology, modelling, and computation; Enefiok Usungurua: Writing, conceptualization, and editing; Imoh Ekanem: Interpretation of result. All authors have read and agreed to the publication of this research work.

The authors affirm that they received no funding or support for this research work, including any administrative, technical, or material assistance.

This manuscript contains all the data supporting the various conclusions from this research work.

The authors affirm no conflicts of interest with the findings derived in this research work. No second or third party was involved in the conceptualization, data collection, analysis, data interpretation, or decision-making on the publication of results achieved.