Building a research model for the combustion process of fuel in a constant volume combustion chamber

ABSTRACT

Blending biodiesel at different ratios leads to fluctuations in properties such as oxygen content, cetane number, speed, density, and calorific value, affecting performance and emissions. Therefore, studying the combustion process of biodiesel is necessary. This study describes the construction of a CVCC (Constant volume combustion chamber) model to study the fuel combustion process and the impact of temperature on the characteristic parameters of the combustion process. Fuels used for simulations included diesel fuel and B10 biodiesel derived from palm oil. The calculated results from the model are compared with experimental data to verify, analyse, and evaluate the combustion process in CVCC. Analysis of the influence of combustion chamber temperature shows that increasing the temperature from 300K to 450K leads to a decrease in the mixing time of the mixture, a decrease in the spray length, an increase in the fuel evaporation rate, and the combustion process occurs. Faster, the peak pressure appears earlier and higher, and the heat transfer rate is faster. Pressure increases faster during the delayed combustion phase. At the same time, increasing the oxygen concentration from 10% to 20% also leads to an increase in pressure rate, reaching an earlier peak, and the combustion process occurs faster.

KEYWORDS:

• CVCC
• diesel fuel
• pressure
• burning process

1. Introduction

Diesel engines serve as a prevalent power source in agricultural and construction machinery, as well as vehicles, owing to their superior adaptability, performance, and fuel efficiency compared to gasoline engines. Primary exhaust pollutants from diesel engines include particulate matter (PM) and nitrogen oxides (NOx) (Thiyagarajan et al. 2020; X. Wang et al. 2010, 2011). However, the widespread use of diesel engines faces constraints imposed by both energy and environmental considerations (Dhinesh and Annamalai 2018; Dhinesh et al. 2018; Krishnamoorthy et al. 2020; X. G. Wang et al. 2010). Stringent emission regulations and the prospective depletion of petroleum reserves have compelled researchers to explore new technologies for developing alternative fuels and mitigating greenhouse gas emissions (T. H. Lee et al. 2020; Liu, Yao, and Yao 2015; Santhosh et al. 2020). Notably, biodiesel for engines and vehicles has emerged as a promising avenue. Biodiesel for engines and vehicles, in particular, is receiving great attention.

On the one hand, biofuel contributes to solving the future energy shortage problem. On the other hand, biofuel contributes to rural economic development, increasing income for people in remote areas and places with great potential for agriculture, forestry, and fishery (Bailey et al. 1997; Hardenberg and Schaefer 1981). Biodiesel fuel is made by converting triglyceride fats into esters. The triglyceride fats used for biodiesel production can be any vegetable oil, animal fat, or cooking or industrial waste oil (Graboski and McCormick 1998; Kumar Agarwal et al. 2014). Biodiesel can be used directly in any unmodified diesel engine mixed or compact form (Babu and Devaradjane 2003; Rakopoulos et al. 2006). Many studies have been done to examine the emissions from biodiesel (Chen et al. 2006; Cheng, Buchholz, and Dibble 2003; Khoa et al. 2023; McCormick et al. 2001; Tsolakis et al. 2007; Verhaeven et al. 2005). Most of these studies show that biodiesel can effectively reduce particulate matter (PM), dry carbon black (DS), carbon monoxide (CO), and unburnt hydrocarbons (HC), but with a slight increase in nitrogen oxide (NOx) compared to diesel fuel.

Several studies have presented specific findings. Yesilyurt’s research (Kadir Yesilyurt 2020) assessed a one-cylinder, four-stroke, water-cooled, naturally aspirated diesel engine with direct injection (DI). The study evaluated engine performance, exhaust emissions, and combustion characteristics. Test fuel samples were prepared using a spray mixing technique, including a 20% biodiesel blend from peanut oil and 1-heptanol added to diesel fuel. The results revealed that incorporating 1-heptanol as an oxidation additive reduced unburned CO and HC emissions while increasing CO₂, O₂, and NO_x emissions compared to diesel fuel.

In a separate experimental study by Zhao et al (Zhao et al. 2020), a single-cylinder diesel engine was utilised to investigate the intelligent charge compression ignition (ICCI) mode using biodiesel fuel and n-butanol. Results indicated that, at medium load, adjusting the biodiesel injection timing improved the indicated thermal efficiency (ITE) and shortened combustion time, reaching a maximum ITE of 50.7% and increasing the butanol energy ratio reduced nitrogen oxide (NO_x) emissions due to local high-temperature reduction while maintaining low NO_x emissions. The injection pressure of butanol significantly impacted the combustion and emission characteristics of the ICCI mode. Increasing butanol injection pressure improved ITE and reduced emissions, but excessive pressure damaged combustion, increasing hydrocarbon and carbon monoxide emissions.

Each type of biodiesel made from different sources will have other physical and chemical properties, such as oxygen content, cetane number, viscosity, density, thermal value, etc., and thus affect emissions performance. Therefore, studying the emission differences between biodiesel from different sources and their relationship with fuel properties is necessary. To achieve this, the constant volume combustion chamber (CVCC) is considered a valuable tool for researchers to understand the complexities of engine injection and combustion processes (Hu et al. 2018; Rizwanul Fattah et al. 2019; Shi et al. 2020; Shi, Lee, Wu, Li, et al. 2019; Zhong et al. 2019). To serve the manufacture and study of combustion processes in a constant combustion chamber, it is necessary to conduct numerical simulations of the working process of a constant combustion chamber, which plays an essential role in the design and improvement of the chamber. Combustion and initial evaluation of the combustion process parameters (C.-F. Lee et al. 2019; Lim and Suh 2022; Shi, Lee, Wu, Wu, et al. 2019; L. Wang, Vinod, and Fang 2021). The constant combustion chamber CFD (Computational Fluid dynamics) simulation can provide a comprehensive view of the physical and physical phenomena occurring in the constant combustion chamber, such as the mixing of fuel and air, ignition, and the chemical combustion reaction. Knowing in detail the process of physical phenomena occurring in the combustion process will help us analyse, predict, and accurately evaluate the factors affecting the working process of the combustion chamber unchanged, making the engine basis to improve and improve the efficiency of the combustion process and reduce emissions to the environment.

In this study, the authors used a theoretical basis to build a CVCC combustion chamber model to study the combustion process of different fuel types and evaluate the effects of various parameters on the combustion process. To assess the model’s accuracy, the author conducted a combustion chamber experiment on a test bed in the laboratory and compared the results with simulation results. The model construction utilised Simcenter software Star-CCM+, which has an additional dedicated tool (Add-on) tailored for cylinder combustion issues. The combustion within the engine was simulated using the Extended Coherent Flame Model Three Zone (ECFM-3Z), which is capable of replicating the intricate mechanisms of fuel mixture mixing, ignition, flame propagation, and diffusion combustion inherent in CVCC. The combustion simulation in the CVCC chamber involved calculations with diesel fuel and biodiesel B10 derived from palm oil. The simulated results were then compared with experimental findings to verify, analyse, and evaluate the combustion processes within the CVCC.

2. Theoretical foundations of model building

Fuel combustion is a multi-physics process, a combination of phenomena: reaction between chemical substances, flow convection, and heat transfer. To accurately simulate the combustion process, it is necessary to clearly define the physical quantities in the model, the physical phenomena related to those physical quantities, and the equations describing the relationships of these quantities. Physical quantity in the form of partial differential. In this simulation, the piston stroke is set to a value small enough that the volume variation is minimal, so the dV is now infinitely small. Then the combustion chamber will become equivalent to CVCC.

The system of equations relating physical quantities describing the combustion of fuel in a finite volume V surrounded by a closed surface A includes the following integral equations:

The fluid flow momentum variation equation describes the relationship between the gas and fuel mixture velocity with pressure, temperature, and mass force (Ferziger, Perić, and Street 2002). ®

(1) $\frac{\mathrm{\partial }}{\mathrm{\partial }\mathit{t}}{\int }_V^{\mathit{\hspace{0.17em}}}\mathit{\rho vdV}+{\oint }_A^{\mathit{\hspace{0.17em}}}\mathit{\rho v}\mathit{v}.\mathit{da}=-{\oint }_A^{\mathit{\hspace{0.17em}}}\mathit{pI}.\mathit{da}+{\oint }_A^{\mathit{\hspace{0.17em}}}\mathit{T}.\mathit{da}+{\oint }_V^{\mathit{\hspace{0.17em}}}{f}_b\mathit{dV}+{\int }_V^{\mathit{\hspace{0.17em}}}{s}_u\mathit{dV}$(1)

In there:

p: is the pressure

T: is the viscous stress tensor

fb: is the total force vector

Su: is the source of the liquid

Continuity equation of liquid flow:

(2) $\frac{\mathrm{\partial }}{\mathrm{\partial t}}{\int }_V^{\mathit{\hspace{0.17em}}}\mathit{\rho dV}+{\oint }_V^{\mathit{\hspace{0.17em}}}\mathit{\rho v}.\mathit{da}={\int }_V^{\mathit{\hspace{0.17em}}}{S}_u\mathit{dV}$(2)

The energy equation describes the reciprocal relationship between flow kinetic energy and temperature

(3) $\frac{\mathrm{\partial }}{\mathrm{\partial t}}{\int }_V^{\mathit{\hspace{0.17em}}}\mathit{\rho EdV}+{\oint }_A^{\mathit{\hspace{0.17em}}}\mathit{\rho Hv}.\mathit{da}=-{\oint }_A^{\mathit{\hspace{0.17em}}}\mathit{q}.\mathit{da}+{\oint }_A^{\mathit{\hspace{0.17em}}}\mathit{T}.\mathit{v}.\mathit{da}+{\int }_V^{\mathit{\hspace{0.17em}}}{f}_b.\mathit{vdV}+{\int }_V^{\mathit{\hspace{0.17em}}}{S}_u\mathit{dV}$(3)

In there:

E: is the total energy

H: is the total enthalpy

q: is the heat flux

Equation of state for natural gases Van der waals

(4) $\left(\mathrm{p}+\frac{\mathrm{a}}{{\mathrm{v}}^2}\right).\left(\mathrm{v}-\mathrm{b}\right)=\mathrm{R}.\mathrm{T}$(4)

In there:

a/b: is the correction factor for pressure when there is an intermolecular attraction

b: the factor that takes into account the volume of molecules

The coefficients a and b are determined through the critical state of the gas and calculated by the formula:

(5) $\mathrm{a}=\frac{27}{64}.\frac{{\mathrm{R}}^2.{\mathrm{T}}_{\mathrm{k}}}{{\mathrm{p}}_{\mathrm{k}}};\mathrm{b}=\frac{1}{8}.\frac{\mathrm{R}.{\mathrm{T}}_{\mathrm{k}}}{{\mathrm{p}}_{\mathrm{k}}}$(5)

In there:

Tk and pk are the temperature and pressure of the medium at the critical state.

Equation of motion

Transport equations of kinetic energy and rate of chaotic dispersion.

(6) $\frac{\mathrm{\partial }}{\mathrm{\partial }\mathit{t}}\left(\mathit{\rho k}\right)+\mathrm{\nabla }.\left(\mathit{\rho k}\nabla \right)=\mathrm{\nabla }.\left[\left(\mathit{\mu }+\frac{{\mu }_t}{{\sigma }_k}\right)\mathrm{\nabla k}\right]\text{break}+P_k-\mathit{\rho }\left(\mathit{\epsilon }-{\epsilon }_0\right)+S_k$(6)

(7) $\frac{\mathrm{\partial }}{\mathrm{\partial t}}\left(\mathit{\rho \epsilon }\right)+\mathrm{\nabla }.\left(\mathit{\rho \epsilon }\bar{\mathrm{\nabla }}\right)=\mathrm{\nabla }.\left[\left(\mathit{\mu }+\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\mathrm{\nabla \epsilon }\right]+\frac{1}{T_e}{C}_{\mathit{\epsilon }1}{P}_{\epsilon }-C_{\mathit{\epsilon }2}{P}_2\mathit{\rho }\left(\frac{\epsilon }{T_e}-\frac{{\epsilon }_0}{T_0}\right)+S_{\epsilon }$(7)

In there:

$\bar{v}$: is the average speed.

μ: is the kinematic viscosity.

${\sigma }_k,{\sigma }_{\epsilon },C_{\mathit{\epsilon }1},C_{\mathit{\epsilon }2}$: is the model coefficient.

P_k và P_ε: are simulation conditions.

f₂: damping function.

S_k and S_ε are the source conditions.

ε₀ is the ambient disturbance value in the source condition against perturbation decay. The ability to impose the term source around also leads to the definition of a particular time scale being defined as:

(8) $T_0=\mathit{max}\left(\frac{k_0}{{\epsilon }_0},C_t\sqrt{\frac{v}{{\epsilon }_0}}\right)$(8)

In there:

C_t: is the model coefficient.

Equation of energy in a liquid

Simcenter STAR-CCM + implements the energy equation in the following integral form.

(9) $\frac{\partial }{{\partial }_t}{\displaystyle {\int }_V^{ }\mathit{\rho }}\mathit{EdV}+{{\displaystyle \oint }}_A^{ }\mathit{\rho Hvda}=-\oint \mathit{Aq}\prime \prime .\mathit{da}+{{\displaystyle \oint }}_A^{ }\mathit{T}.\mathit{vda}+{\stackrel{.}{{\displaystyle \int }}}_{\mathit{V}}{f}_b.\mathit{vdV}+{\displaystyle {\int }_V^{ }{S}_u}\mathit{dV}$(9)

In there:

E: is the total energy.

H: is the total enthalpy.

${\dot{q}}^{{ }^{\prime \prime }}$: is heat flux vector.

T: is the viscous stress tensor.

v: is the velocity vector

S_u: is the combined force vector for the remaining components: rotation, gravity, fan…

Su is energy source, such as a radiation source, an alternating energy source, or an energy source due to a chemical reaction. User-defined volume sources also enter through this term.

The total energy related to the full enthalpy H is equal to:

(10) $\mathit{E}=\mathit{H}-\frac{p}{\rho }$(10)

(11) $\mathit{H}=\mathit{h}+{\left|v\right|}^2/2$(11)

To simulate fuel combustion, the ECFM-3Z (Extended Coherent Flame Model Three Zone) model is applied thanks to its ability to affect complex mechanisms of fuel mixture mixing, ignition, and flame propagation. Flame and diffuse combustion characteristics of internal combustion engines.

The reactions taking place in the combustion chamber:

${\mathrm{C}}_2{\mathrm{H}}_2+{\mathrm{O}}_2+{\mathrm{N}}_2\to \mathrm{C}{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}+{\mathrm{N}}_2$

$C_8{C}_{18}+2{\mathrm{O}}_2\to \mathit{C}{O}_2+H_2\mathrm{O}$

$C_{17}{H}_{32}{O}_2+{\mathrm{O}}_2\to \mathit{C}{O}_2+H_2\mathit{O}$

3. CVCC combustion chamber model and boundary conditions

3.1. Model of fire chamber CVCC

The numerical simulation model is built based on the geometrical design parameters of the combustion chamber with constant volume. Experience. Therefore, the numerical simulation results can be used to compare, evaluate, and analyse the experimental results.

The constant volume combustion chamber built for simulation has a diameter of 80 mm, a height of 90 mm, a thickness of 60 mm, an intake and exhaust valve diameter of 5 mm, and a nozzle mounting hole diameter of 8 mm.

Using the geometric parameters in Table 1, the computational mesh model is built using the 3D-CAD tool integrated into Star-CCM+. According to In-Cylinder’s regulations, the CAD model must contain three components: Cylinder – the volume of the combustion reaction of the fuel in the combustion chamber; IntakeValve, ExhaustValve – are defined as valve valves that feed the energy and discharge the product mixture after combustion. The spatial domain where the combustion reaction occurs (Cylinder) and the intake and exhaust valves in the simulation model are shown in Figure 1.

Figure 1. CVCC simulation model.

This figure shows a 3D model of the CVCC combustion chamber for research purposes.

Table 1. Defined boundary conditions for simulation model.

Boundary conditions	Physical variable	Type of boundary condition to be applied
Boundary cylinder	Gas	Wall
Injector	Gas	Output
Air inlet	Gas	Output
Exhaust gas margin	Gas	Output

To simulate fuel injection in the cylinder, the In-Cylinder tool allows the injector model to be modelled with one or more injectors with different injection patterns and located anywhere inside the combustion chamber. In this simulation, the injected fuel is adjusted according to 4 parameters: jet velocity, injection ratio, temperature, and particle size of fuel injected into the combustion chamber. The temperature and particle size parameters were interpolated directly from the input data sheet. The parameters of speed and injection ratio are determined as follows:

Equation of velocity:

(12) $u_i=\frac{\dot{m}/\mathit{n}}{C_{\mathit{d}.\mathit{i}}\mathit{P}{\left(d_i/2\right)}^2\mathit{\pi }}$(12)

Trong đó:

$\dot{m},\mathit{n},C_{\mathit{d},\mathit{i}},\mathit{P},d_i$ are injection ratio, number of injectors, exhaust coefficient, fuel density, and hydraulic diameter of the fuel, respectively and spray area.

The injection rate is determined by:

(13) $\dot{m}=F_{\mathit{interpolate}}\left(\mathit{C}{A}_{\mathit{cycle}}-\mathit{ICAT}+\mathit{ICAA}\right)$(13)

Trong đó: $\dot{m};F_{\mathit{interpolate}};\mathit{C}{A}_{\mathit{cycle}},\mathit{ICAT},\mathit{ICAA}$ are interpolated functions from the data table, respectively, crankshaft rotation angle in degrees (0–720°), crankshaft rotation angles determine fuel injection timing.

3.2. Calculation conditions

Combustion in the engine is a process that evolves, in the current simulation model uses the PISO (Pressure-Implicit with Splitting of Operators) algorithm to descramble the dominant equations. Accordingly, the equations of the velocity components are solved in turn before solving the continuity equation, the energy equation, and the combustion reaction equation. The combustion of the fuel is simulated using the ECFM-3Z model, which allows for the simulation of complex turbulent mixtures, flame propagation, diffuse combustion, and typical pollutant emissions for modern mechanisms of the internal combustion engine.

Simulation of the effect of temperature on the mixture formation and combustion of fuel includes the time of fuel injection, injection termination, and complete fuel evaporation. Temperatures vary from 300K to 1200K with splits: 300K, 450K, 600K, 900K, and 1200K. Amount of fuel injected into the combustion chamber: 0.039 (g).

Simulate the effect of oxygen concentration on fuel combustion in two cases: 10% oxygen and 20% oxygen before and after the pre-combustion of fuel.

3.2.1. Boundary conditions

Boundary conditions at cylinder housing, intake valve, exhaust valve, and injector for different physical variables are given in Table 1.

Initial conditions for the simulation process correspond to the experiment: the pressure and temperature in the combustion chamber space are set at 18 bar, and the temperature is 300K. The flow velocity in the combustion chamber is considered to be small enough to be considered static. The intake and exhaust valves are closed.

Because the combustion process occurs very quickly with the simultaneous evolution of many physical phenomena, the selection of the simulation time steps to ensure the simulation accuracy and the reasonableness of the simulation run time plays an important role. Important role. In this simulation, the time settings are set as shown in Table 2.

Table 2. Fuel injector related time step.

Time	Angle (deg)	Time step (s)
Before spraying	1	1.0E–6
Spray process		1.0E–6
After spraying	20	5.0E–6

• Minimum time step: 1.0 E −7 s.

• Time step related to valve movement.

• Time step relative to fuel injector.

3.2.2. Computational grid model

The simulation space has meshed with the Trimmed Mesher, which maximises the number of rectangular grid elements and optimises the process of solving systems of discrete equations. To improve the accuracy of the medium flowing near the walls, orthogonal prismatic grids are created close to these boundaries. For locations where complex physical phenomena (such as injected fuel, high-temperature combustion zones, Etc.) or corners with complex shapes may occur, the calculation grid in this area will be smoothed for increased accuracy. Proper meshing is also applied to improve mesh quality in the volume region around the intake/exhaust valve. Small mesh size is used to increase the fineness of the mesh in this area, resulting in more accurate results, especially when opening and closing the valve. Grid settings are adjusted to ensure high grid accuracy with the least number of grid cells. The grid settings used in the CVCC simulation model are described in Table 3. The simulated mesh parameters and mesh quality are shown in Tables (4, 5)

Table 3. Mesh settings used for the CVCC simulation model.

	Parameter	Value
	Base Grid	1mm
Contiguous mesh	Mesh Thickness	0.25mm
	Number of classes	2
	Layer elongation rate	1

Table 4. Simulation mesh parameters and quality.

Parameter	Value	Note
Number of vertex	4859160	Number of grid nodes
Smallest cell	0.25mm	Minimum grid element size
Largest cell	1mm	Maximum grid element size
Tetrahedral cells	1199	Tetrahedral element
Hexahedral cells	4626685	6-sided box element
Wedge cells	56543	Triangular prism element
Pyramid cells	75	Pyramid element
Polyhedral cells	56220	Polyhedral element
Cells total	4740722
Interior faces	14157523 (64045 triangular 14,019,369 quadrilateral 74,109 polygonal)	Number of faces in the calculated volume region
1.00 ≤ Face Validity	4740722	The number of sides is of good quality
1.000000e-02 ≤ Volume Change < 1.000000e-01	15932	The number of grid cells with an increase in volume with adjacent grid cells is in the range [0.01–0.1]
1.000000e-01 ≤ Volume Change ≤ 1.000000e+00	4724790	The number of grid cells with an increase in volume with adjacent grid cells is in the range [0.1–1.0]

Table 5. Mesh parameters and mesh quality of boundary surfaces.

Edge face	The number of grid cells on the edge	Maximum grid angle (degrees)
Default Wall	97313 faces (3219 triangular 92,161 quadrilateral, 1933 polygonal)	64.3
Intake Valve 1	4325 faces (1054 triangular, 2893 quadrilateral, 378 polygonal)	53.7
Exhaust Valve 1	4313 faces (1053 triangular, 2882 quadrilateral, 378 polygonal)	55.1
Inlet	464 faces (28 triangular, 424 quadrilateral, 12 polygonal)	0.7
Outlet:	464 faces (28 triangular, 424 quadrilateral, 12 polygonal)	0.8

The mesh is properly divided so the simulation can occur and ensure accuracy. The simulation domain is divided into 821,475 grid cells 2,454,260 faces 860,612 node points. The number of grid cells, faces, and nodes are quite large to meet the continuous variation in simulation results. Using the Trimmed Mesher, the calculated mesh is generated based on the meshing algorithm derived from the original square mesh. The mesh quality is high on almost the entire simulation domain. The largest grid geometry twist is 47.83 degrees, at an appropriate level (<90 degrees) to meet good mesh conditions. This reduces the error due to non-perpendicularity between the line connecting the centres of two adjacent mesh elements and the contact surface. In areas where many physical phenomena appear, such as the area around the valves, fuel injector heads, and finer meshing to fully capture the phenomenon and ensure the calculation process converges (Figures 2 to 5).

Figure 2. Calculation grid used for simulation model.

To calculate the CVCC combustion chamber model, the authors conducted meshing with the corresponding grid number 4,740,722 grid cells 14,157,523 faces, and 4,859,160 node points.

Figure 3. Smooth the mesh.

The computational grid is smoothed in the spatial region where complex physical phenomena occur.

Figure 4. Detail of calculation grid at intake and exhaust valve areas.

The intake and exhaust valves will have a discontinuous structure, so this location has its own mesh pattern.

Figure 5. Calculation conditions.

After declaring the boundary conditions, the result is shown in this figure.

4. Evaluate model reliability

4.1. Diagram and test equipment

The test subject is CVCC. This combustion chamber has been safely designed, manufactured, and tested with a pressure of 80 bar inside the chamber. This combustion chamber can control the air residue coefficient, temperature, pressure, and fuel injection timing. The combustion chamber can observe the process of mixing and burning inside through the observation window. The combustion chamber is a unified combustion chamber with a diameter of 80 mm, a height of 90 mm, and a wall thickness of 60 mm (Figure 7).

The experiment was performed using CVCC with a 6-hole nozzle, nozzle hole diameter 0.14 mm, injection pressure kept constant 1500 bar, fuel injection time 3 ms, ambient temperature change 300K, 450K. The oxygen concentration is kept at 10% or 20% for the test. The test scheme is shown in Figure 6, and during the research process, the authors used diesel fuel; 10% bio-diesel means 90% diesel fuel and 10% biodiesel. With a nozzle diameter of 0.14 mm and an injection time of 3 ms, The injection pressure is 150 MPa, and the ambient temperature is 300K, 450K. With 20% oxygen concentration, the experiment was repeated ten times.

Figure 6. Diagram of test equipment.

Describe the equipment layout diagram when testing the CVCC combustion chamber.

Figure 7. Fire image in CVCC.

Demonstrates experimental equipment to verify and calibrate the CVCC model.

4.2. Model reliability

Figure 8 shows experimental and simulated pressure graphs. The results show that the graphs between simulation and experiment tend to be similar. Peak pressure values , when simulated and experimental, differ by no more than 3%. This proves that the model is reliable when simulating fuel combustion in CVCC.

Figure 8. Experimental and simulated pressure graphs.

Indicates the accuracy between calculated and experimental results.

REC1-Experiment B0: experimental pressure of fuel B0; REC1- Experiment B10: experimental pressure of fuel B10; REC1-Simulation B0: simulated pressure of fuel B0; REC1- Simulation B10: simulated pressure of fuel B10.

5. Investigate some parameters in the constant combustion chamber model

With the accuracy of the generated model, the authors went to study the evaporation and mixing of the fuel in the combustion chamber; Investigate the influence of temperature and the effect of oxygen concentration on the combustion process in the CVCC combustion chamber. During the simulation, the temperature in the combustion chamber is changed from 300K to 1200K. This is the temperature corresponding to the compression process of a commonly used non-turbocharged diesel engine.

5.1. Evaporation of fuel in CVCC

Figure 9 shows the evaporation process of fuel B0 in the condition that the injection pressure into the combustion chamber is the same 1500 bar and the temperature changes from 300K to 1200K. It can be seen that when the temperature is increased, the total evaporation time of the fuel in the CVCC combustion chamber decreases (Figure 10), and the area of the vaporised fuel in the CVCC combustion chamber decreases. The image also shows that, as the temperature increases, the more spaced part of the fuel near the injector tends to spread more widely. In addition, the effect of temperature on the spray length at the end of spraying. As the temperature increases, the length of the jet in the combustion chamber is reduced.

Figure 9. Effect of temperature on fuel evaporation in CVCC.

Shows the influence of temperature at the time of injection on the evaporation process in the CVCC combustion chamber.

Figure 10. Graph of the effect of temperature on fuel evaporation in CVCC.

Shows the law of fuel evaporation over time depending on temperature.

5.2. Fuel mixing process in CVCC

Figure 11, with the colour spectrum in Table 6, shows the initial fuel injection time into the combustion chamber. At this time, the entire combustion chamber contains the gas mixture (red).

Figure 11. Mixture formation process in CVCC at the beginning of fuel injection.

Shows that the CVCC combustion chamber is red, meaning it is filled with air.

Table 6. Colour spectrum corresponding to A/F ratio.

A/F	40	40–32	32–24	24–16	16–8	8–0
Color	Red	Yellow-orange	Blue	Green_yellow	Sea green	Green_blue

Figure 12 and the colour spectrum in Table 6 show that the fuel is injected after a minimal time. The image shows that the fuel (blue) is injected, and the air in the combustion chamber has a film. Separate the contact layer between the inside air and the injected fuel forms a carburettor with an A/F ratio of about 32–24 (green_yellow) and a mixture that darkens (A/F gets smaller) in the direction of the fuel injector. On the other hand, the image shows that fuel particles of different sizes with different kinetic energies move chaotically when coming out of the injector; particles with sizeable kinetic energy tend to go beyond the carburettor layer and move forward, further into the space in the combustion chamber to create a local air-conditioning space.

Figure 12. Mixture formation at 1.0E–6(s) after fuel injection.

Shows the development of fuel after injection in the CVCC combustion chamber.

Figure 13 and the colour spectrum in Table 6 show that the dispersion of fuel particles in the combustion chamber is more intense, the space where the fuel fights in the combustion chamber is more significant, and some fuel particles have substantial kinetic energy that surpasses them. Membrane boundary and further into the combustion chamber beyond the boundary of the exposed carburettor to create more carburettor volume in the combustion chamber. The image also shows that the fuel particles with larger sizes (yellow and brown) have gone beyond the contact layer boundary to develop more carburettor zones in the combustion chamber.

Figure 13. Mixture formation at 2.0E–6(s) after fuel injection.

Additional development of the air-mixing zone in the combustion chamber.

Figure 14 and the colour spectrum in Table 6 show that the mixing process is almost the entire combustion chamber. All injected fuel has been uniformly mixed with the air inside the combustion chamber. However, in the corners of the combustion chamber, there is still a tiny amount of fuel that is not evenly mixed (the corners of the combustion chamber).

Figure 14. Mixture formation at 5.0E–6(s) after fuel injection.

Shows that all fuel is mixed evenly.

5.3. Effect of temperature on combustion in CVCC

5.3.1. Combustion chamber pressure

Figure 15 illustrates that with an increase in temperature, the jet penetration length decreases, resulting in a shortened mixing time. This phenomenon contributes to an augmented combustion rate, primarily attributable to the accelerated evaporation of the fuel. Conversely, at lower ambient temperatures, the fuel has a prolonged mixing period, allowing the air around the inlet to coil into the formed mixed fuel. This extended mixing time leads to a higher peak temperature and peak pressure.

Figure 15. Effect of temperature on combustion chamber pressure.

Specifically:

Temperature-Dependent Jet Penetration:

As temperature rises, the jet penetration length decreases. This reduction in penetration length is instrumental in diminishing the mixing time, ultimately fostering a faster combustion process through the quicker evaporation of the fuel.

Impact on Peak Temperature and Pressure:

Lower ambient temperatures afford the fuel more time to mix, allowing the surrounding air to coil into the formed mixed fuel. This extended mixing duration results in a higher peak temperature and peak pressure.

Elevated Initial and Peak Pressure at Higher Temperatures:

The values of both initial and peak pressure are notably elevated in the high-temperature case. This is indicative of the intensified combustion process and faster evaporation dynamics, leading to a more pronounced increase in pressure.

In summary, Figure 15 highlights the intricate relationship between temperature, jet penetration length, mixing time, and combustion rate. Higher temperatures correspond to reduced jet penetration, shorter mixing times, and faster combustion, ultimately resulting in elevated peak temperature and pressure values.

5.3.2. Pressure rise rate

In Figure 16, it is evident that the pressure rise rate for fuel B10 exhibits a more pronounced incline compared to that of fuel B0. Notably, at a temperature of 450K, the pressure rise rate for B10 surpasses that observed at 300K. This acceleration results in a faster increase in pressure, with B10 reaching its peak pressure earlier.

This phenomenon can be attributed to the following factors:

Shortened Mixing Time at High Temperatures:

The shorter mixing time of the fuel-air mixture at elevated temperatures contributes to the heightened pressure rise rate for B10. The faster mixing facilitates a more efficient combustion process.

Increased Oxygen Content in B10:

B10 fuel, containing a higher proportion of oxygen, plays a crucial role in expediting the combustion process. The elevated oxygen levels contribute to a swifter combustion, leading to a temporary reduction in combustion delay.

In summary, the steeper slope in the pressure rise rate for B10, particularly at 450K, is a consequence of the combined effects of reduced mixing time at higher temperatures and the enhanced oxygen content in the fuel. These factors collectively result in a more rapid combustion process and an earlier attainment of peak pressure for B10 fuel compared to B0.

Figure 16. Pressure increase rate in the combustion chamber.

5.3.3. Heat release rate

Figure 17. The effect of temperature on the heat release rate shows that the graphs in the two cases have the same trend; the fuel receiving heat leads to the combustion process taking place faster than the blazing speed increasing suddenly, making the fuel burn more quickly. The heat release also increases. Therefore, the fuel’s heat release rate at 450K is greater than the fuel’s heat release rate at 300K.

Figure 17. Effect of temperature on heat release rate.

Shows the effect of temperature on the heat release rate in the combustion chamber.

5.4. Effect of oxygen concentration on combustion in CVCC

5.4.1. Combustion chamber pressure

Figure 18. The effect of oxygen concentration on combustion chamber pressure under the same ambient temperature conditions shows that, when increasing the oxygen concentration to 20%, the temperature increase rate in the combustion chamber is faster, corresponding to the fuel. Because the pressure increases more rapidly, peak pressure and peak temperature are reached sooner. The reason is that many oxygen particles are sprayed around the fuel particles, leading to the combustion reaction speed occurring earlier than in the case of 10% oxygen concentration.

Figure 18. Effect of oxygen concentration on combustion chamber pressure.

5.4.2. Heat release rate

Figure 19. In the case of fuel injection before CNLM, the heat release rate between simulation and experiment has the same trend, and the graph shows two extreme peaks corresponding to two HCCI-like combustion stages. The heat release rate in the case of 20% oxygen begins to earlier and reaches its maximum value. The reason is that the combustion process is supplied with more oxygen, which makes the reactions take place earlier and give off more heat.

Figure 19. Heat release rate in case of fuel injection before igniting primer fuel.

Shows the effect of oxygen concentration on the heat release rate in the combustion chamber.

6. Conclusions

Fuel combustion is a complex, multi-physics process encompassing various phenomena, including the reaction between chemical substances, flow convection, and heat transfer. The study employed a model to investigate the combustion process within a constant combustion chamber and assess the impact of temperature and oxygen concentration on combustion dynamics.

The research addressed the following key issues:

1. Model construction and evaluation:

   Developed a simulation model for the Constant Volume Combustion Chamber (CVCC) and compared its reliability with the actual combustion chamber.

   The simulation demonstrated a minimal deviation, with the most significant variation in simulating the pressure evolution within the combustion chamber being less than 3%.

2. Temperature influence on combustion:

   The study explored the effect of temperature on combustion pressure, pressure rise rate, and specific heat transfer rate.

   Increasing the temperature from 300K to 450K resulted in reduced mixing time, shorter combustion delay, faster fuel evaporation, and an earlier and higher peak pressure. This led to an overall increase in combustion speed, particularly during ignition delay.

3. Oxygen concentration impact on combustion:

   The study examined the effects of increasing oxygen concentration from 10% to 20% on combustion dynamics.

   Higher oxygen concentration accelerated the pressure increase rate, achieving an earlier peak pressure. The increased presence of oxygen particles surrounding fuel particles promoted faster combustion reactions, resulting in higher fuel speeds. The homogeneous mixture formed before burning indicated a Homogeneous Charge Compression Ignition (HCCI) combustion process.

4. Theoretical basis for experimental studies:

   They have affirmed that the simulation study results serve as a theoretical foundation for experimental investigations into the combustion process within the CVCC combustion chamber and internal combustion engine.

In summary, the comprehensive findings contribute valuable insights into the intricacies of the combustion process, providing a basis for theoretical understanding and practical experimentation in the context of CVCC combustion chambers and internal combustion engines.

Author contributions

Nguyen Phi Truong: Software, Data curation, Methodology, Writing-review & editing, Nguyen Xuan Khoa: Formal analysis, editing, Formal analysis; Nguyen Van Tuan: Data curation, Methodology, Writing-review & editing, Investigation, Formal analysis, Writing-original draft. All authors have read and agreed to the published version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Authors agree to make data and materials supporting the results or analyses presented in their paper available upon reasonable request.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Notes on contributors

Nguyen Phi Truong

Nguyen Phi Truong received his M.S. in Mechanical Engineering from Ha Noi University of Industry, Viet Nam 2015. He then received his Ph.D. from Hanoi University of Science and Technology, Vietnam, in 2022. Dr. Truong is a researcher at the Hanoi University of Industry in Vietnam. Dr. Truong’s research interests include internal combustion engines, alternative fuels, and thermodynamics.

Nguyen Xuan Khoa

Nguyen Xuan Khoa received his M.S. degree in Mechanical Engineering from Kanazawa University, Japan 2010. He then received his Ph.D. from Ulsan University, South Korea, in 2021. Dr. Khoa is a researcher at the Hanoi University of Industry in Vietnam. Dr. Khoa’s research interests include internal combustion engines, alternative fuels, and thermodynamics.

Nguyen Van Tuan

Nguyen Van Tuan received a Master’s in Dynamics Engineering from Hanoi University of Science and Technology, Vietnam 2008. Then, he received a Ph.D. from Le Quy Don Technical University, Vietnam, in 2015. Dr. Tuan is a lecturer and researcher at the University of Transport Technology, Vietnam. Dr. Tuan’s research interests include internal combustion engines, alternative fuels, thermodynamics, and hybrid and electric cars.