The Performance of an Air-Cooled Diesel Engine with a Variable Cross-Section Dual-Channel Swirl Chamber

Abstract

In order to improve the performance of a mini-type air-cooled diesel engine in terms of the overall efficiency and engine emissions, a swirl chamber of a variable cross-section dual-channel model was developed. This study proposed nine turbulent swirl chambers with a variable cross-section for a dual-channel combustion solution, which applied a dual-channel cross-section to the insert between the original swirl chamber and the main chamber. Model-based design, simulation and experiments were applied as a feasible approach to address this issue to find out the influence of the dual-channel inclination angle and divergence angle on the swirl rate in the swirl chamber, the power and the emissions performance, including the fuel efficiency. By comparing the tests, the performance of the diesel engine with a variable cross-section dual-channel swirl chamber was superior to the original one with a single channel in terms of the swirl rate, fuel consumption rate and emissions.

1. Introduction

An air-cooled diesel engine with a swirl chamber has a lot of characteristics, such as a good working performance, low noxious emissions, minimal noise and low manufacturing cost. This kind of engine is widely applied in all kinds of small agricultural machinery, engineering machinery and ships [1,2]. However, there are still some defects in the swirl chamber diesel engine compared with a DI, such as a higher thermal load, lower charring efficiency and about 5% lower average effective pressure [3,4,5]. The increasingly urgent requirements for low emissions in recent years also prompted the improvement of the working performance of the diesel engine with a swirl chamber. This is what the present research intended to accomplish [6,7,8].

The key element that influences combustion is the mixture of air and fuel, and the quality of the mixture relies on the injection character, injection rule, swirl inside the combustion chamber, chamber shape, etc. Di Blasio [9,10,11] studied the effect of DFI combustion systems, dual-fuel (CNG–diesel) and ethanol–diesel blends, etc., that were shown to improve the CO₂ output, among other emissions. In the combustion system of a diesel engine with a swirl chamber, some factors, such as the shape, size and position of the insert connection channel, have obvious influences on the developing features and intensity of the swirl in the chamber [5]. Therefore, having a command of the design principle and requirements of the insert connection channel and adopting the research method of numerical simulation and test coupling will be extremely conducive to and provide a reference for the improvement of the performance of the combustion system of a diesel engine with a swirl chamber [12].

During the development history of the air-cooled diesel engine with a swirl chamber, lots of studies have been conducted in terms of its combustion system. The majority of studies focused on the following three points: (1) swirl chamber improvement, (2) main combustion chamber improvement and (3) connection channel improvement [13,14]. For the swirl chamber improvement, the major measure that was taken was to introduce a spray insulation layer on the surface of the swirl chamber, connection channel and at the bottom of the cylinder to reduce the thermal loss. As far as the combustion structure is concerned, major changes were made to the design of a better shape and size of the chamber, and on the other hand, the total volume of the combustion chamber and air utilization ratio were also enlarged and increased to improve the combustion process in the swirl chamber [15,16,17,18]. Finally, referring the improvement of the combustion chamber, the main measures were made to change the main combustion chamber’s shape into wedge, double-wedge or asymmetric types to match the swirl chamber and connection channel structure to ultimately promote the combustion process and improve the economic efficiency, power and exhaust situation of the engine [19,20,21,22].

However, the research showed that the connection channel had the most important influence on the combustion system of the swirl chamber. It can be said to be a double-edged sword since it is not only mainly responsible for the throttle and thermal loss of the swirl chamber but also serves as the key element for the formation of the swirl. Numerous experimental and numerical studies were conducted to investigate the connection channel of diesel engines and achieved many great results. The Japanese Komatsubara adopted the three-dimensional simulation method to analyze the air flow field distribution in the swirl chamber and was the first to recognize the connection channel’s great influence on the flow field in the swirl chamber [23]. The Japanese Mitsubishi Corporation designed a connection channel junction with two different dip angles, and the results showed that the change in the connection channel dip angle altered the penetration length of the main chamber flow. Furthermore, a smaller dip angle led to worse stability of the flow coefficient during the expansion stroke, while a larger dip angle resulted in less flow diffusion in the main chamber, as it could enlarge the channel flow coefficient during the expansion stroke. According to the results, the double-stage channel design was put forward, namely, the dip angle toward the swirl chamber was bigger than that toward the main chamber. For this structure, the channel flow coefficient, as well as the diffusion and penetration of the air in the main chamber, were improved, which had a positive influence on the economy and power performance of the diesel engine with a swirl chamber [24]. The Kubota Company optimized the connection channel shape and the piston top pit to obtain an eddy three-vortex-swirl combustion (ETVSC) system and further optimized the fuel injection characteristics. The results showed that the optimized diesel engine with the swirl chamber had a better economy and power performance than the original one [25]. In the same period, Tadao Okazaki and some other researchers studied the connection channel shape performances [26]. J. J. Hu et al. researched the swirl chamber flow characteristics influenced by the connection channel sectional area. A small sector shape structure was added to one side of the main connection channel, and the testing results showed that the improved channel enlarged the flow efficiency under high load conditions and reduced the throttle loss, which therefore reduced the fuel consumption ratio and enhanced the economy performance [27].

Based on the previous studies of the swirl chamber insert connecting channel, this study proposed a turbulence combustion solution for the air-cooled diesel engine with a swirl chamber that had a variable cross-section dual-channel, which applied a dual-channel cross-section to the insert between the original swirl chamber and the main chamber; we then set up and calculated the mathematical model for the combustion to find out the influence of dual channel’s inclination angle and divergence angle on the swirl rate in the swirl chamber, the power and emissions performance, and the fuel efficiency of the diesel engine.

2. Swirl Chamber Turbulence Combustion System with a Variable Cross-Section Dual Channel

2.1. Swirl Chamber Turbulence Combustion System

In order to make the best of the swirl chamber combustion system and avoid the disadvantages of low heat release rate in the main chamber, great loss of channel throttle, and high fuel consumption rate, etc., the concept of swirl chamber turbulence combustion was put forward based on the advantages of turbulence combustion. In other words, the combustion process of the swirl chamber and main combustion chamber was improved by increasing the turbulence intensity in the swirl chamber, and thus, increasing the engine’s performance [28,29,30]. To be specific, the engine’s performance can be improved through the following aspects after introducing the appropriate turbulence: strengthening the turbulence in the swirl chamber to expand the contact area between the fuel spray and the air, as well as lower the steam concentration around the fuel drop and promote the evaporation; a high-intensity compound air movement occurs in the combustion chamber due to the turbulence strengthening in the swirling movement, which substantially promotes the mixture of fuel and gas, accelerates the physical preparation for ignition, shortens the ignition lag and increases the combustion rate, while the addition of turbulence can lower the swirl intensity and further reduce the throttling and heat loss.

2.2. Structural Design

Based on the above principle, this study proposed a kind of swirl chamber turbulence combustion system with cross-section multi-channel structures (as shown in Figure 1), namely, adding a dual-channel cross-section structure on the insert of the original swirl chamber combustion system to intensify the turbulence in the combustion chamber, increase the turbulent flow on the basis of the large-eddy movement, strengthen the turbulence in the air movement, accelerate the fuel atomization and enable the concentration field in the combustion chamber so that it moves evenly. The research results of the swirl chamber turbulence combustion system of a mini-type air-cooled diesel engine will provide a theoretical foundation and technical reference for improving the combustion process and developing a swirl chamber diesel engine that has low cost, high economical and emissions efficiency, and a low requirement for diesel fuel quality.

This method of adding a variable-section double-channel structure to the insert of the original swirl chamber type combustion system was mainly done to increase the degree of turbulence in the combustion chamber by changing the inclination and expansion angle of the double-channel. Adding the turbulence on the base of the original large eddy fluid motion accelerates the atomization of the fuel and can promote a more uniform distribution of the concentration field in the combustion chamber. However, this kind of structure has high requirements regarding the processing technology, which increases the application cost.

3. Mathematical Model for Combustion

3.1. Model Hypothesis

The swirl chamber and main combustion chamber were assumed to be two independent transient thermodynamic equilibrium systems, ignoring the pressure, temperature and concentration differences between each set of two points in the cylinder and considering it as a homogeneous state. Moreover, the changes in the thermodynamic parameter of the mixed working fluids in the cylinder were dependent on the gas temperature and its composition [31,32,33]. The influence of the pressure and temperature fluctuations was neglected during the intake and exhaust, and the air flowing into the cylinder was immediately mixed with the residual gas in the cylinder during intake, where the gas flow was regarded as a quasi-stable flow. Without considering leakage of the working fluid at the piston ring and valve, all flows passing through throttle parts (including the air inlet, air outlet and the connecting channel between the main and auxiliary combustion chambers) were quasi-stable and adiabatic [15]. The working fluid was almost at an ideal state, and the mass exchange rates of the gas fuel, combustion product, and liquid fuel between the swirl chamber and main combustion chamber were always proportional to the total mass exchange rate without considering the volume ratio of liquid fuel in both the swirl chamber and main combustion chamber [34,35].

3.2. Thermodynamic Process in the Cylinder

Based on the above assumptions, two independent variable mass thermodynamic systems for the swirl chamber and main combustion chamber were established, as shown in Figure 2. An equation for the energy and quality control in both the swirl chamber and main combustion chamber, as well as an almost ideal state equation by using the control volume method, were created, and the quality and energy exchange between two combustion chambers or between the system and the outside could be derived from the quality flow and enthalpy flow equations of the working fluid flow in the throttle part. Then, the working fluid thermodynamic process in the swirl chamber and main combustion chamber was obtained as follows [36]:

$$\frac{d{T}_i}{d\phi }=\frac{1}{m_i{c}_{V_i}}\left[\begin{array}{l}\frac{d{Q}_{B_i}}{d\phi }+\frac{d{Q}_{W_i}}{d\phi }-p_i\frac{d{V}_i}{d\phi }+h_{E_i}\frac{d{m}_{E_i}}{d\phi }\\ +h_{A_i}\frac{d{m}_{A_i}}{d\phi }+h_i\frac{d{m}_{U_i}}{d\phi }+h_{F_i}\frac{d{m}_{F_V{}_{{}_i}}}{d\phi }\\ -u_{F_i}\frac{d{m}_{F_i}}{d\phi }-u_{G_i}\frac{d{m}_{G_i}}{d\phi }-m_{G_i}\frac{\partial u_{G_i}}{\partial {\lambda }_{G_i}}\cdot \frac{d{\lambda }_{G_i}}{d\phi }\end{array}\right]$$

(1)

$$\frac{d{m}_i}{d\phi }=\frac{d{m}_{E_i}}{d\phi }+\frac{d{m}_{A_i}}{d\phi }+\frac{d{m}_{U_i}}{d\phi }+\frac{d{m}_{F_V{}_{{}_i}}}{d\phi }$$

(2)

$$p_i{V}_i=m_i{R}_i{T}_i$$

(3)

where T—thermodynamic temperature, K; m—quality, kg; φ—crank angle, °CA; Q—heat, kJ; R-gas constant, R = 8.314 J/(mol·K); V—volume, cm³; h—specific enthalpy, kJ/kg; u—specific internal energy, kJ/kg; C_Vi—specific heat at constant volume, kJ/(kg·K); and λ—instantaneous excess air coefficient.

The subscript meanings are described as follows:

B—fuel combustion; W—wall; E—intake; A—exhaust; U—connecting channel; F—fuel gas; F_V—fuel evaporation; G—air and combustion product mixture; i = 1.2 expressed the main combustion chamber parameters in the swirl chamber; and when P₁ < P₂, j = 2, and when P₁ > P₂, j = 1.

In terms of the swirl chamber, the following were constant: $d{V}_1=0$, $d{m}_E{}_{{}_1}=0$ and $d{m}_A{}_{{}_1}=0$.

Based on the conservation of mass, the relationship between the swirl chamber and the main combustion chamber is shown as follows:

$$\frac{d{m}_{U_1}}{d\phi }+\frac{d{m}_{U_2}}{d\phi }=0$$

(4)

To supplement all the sub-models for the above differential equations and work out the numerical problems after closing, the changes in the temperature, pressure and quality of the working fluids in the swirl chamber and main combustion chamber with respect to the crank angle changes could be obtained.

3.3. Sub-Model

(1)

The change rate of the cylinder volume $\frac{d{V}_1}{d\phi }$

The change rule of the piston’s swept volume with respect to the crank angle is as follows:

$$V_1=\frac{V_s}{2}\left[\begin{array}{l}\frac{2}{{\epsilon }_c-1}+1-\cos \phi \\ +\frac{1}{{\lambda }_s}\left(1-\sqrt{1-{\lambda }_s^2{\sin }^2\phi }\right)\end{array}\right]$$

(5)

where $V_s$—cylinder displacement, $V_s=\pi D^{2}S/4$, cm³; D—piston diameter, cm; S—piston stroke, cm; ${\epsilon }_c$—compression ratio; and ${\lambda }_s$—crank–link rod ratio ${\lambda }_s=S/2l$, where $l$—connecting rod length, cm.

Formula (5) was derived with respect to $\phi$ to obtain Formula (6):

$$\frac{d{V}_1}{d\phi }=\frac{V_s}{2}\left[\sin \phi +\frac{{\lambda }_s\sin 2\phi }{2\sqrt{1-{\lambda }_s{}^2\sin 2\phi }}\right]$$

(6)

(2)

Combustion heat release rate $\frac{d{Q}_{B_i}}{d\phi }$

The Wiebe function heat release rule was used [27], as shown in Formula (7):

$$\begin{array}{l}\frac{d{Q}_{B_i}}{d\phi }=\\ H_u{g}_b{\eta }_u\times 6.908\frac{m+1}{{\phi }_z}{\left(\frac{\phi -{\phi }_0}{{\phi }_z}\right)}^m{e}^{-6.908{\left(\frac{\phi -{\phi }_0}{{\phi }_z}\right)}^{m+1}}\end{array}$$

(7)

where H_u—lower calorific value of fuel, J/kg; $g_b$—fuel supply per cycle, kg; ${\eta }_u$—combustion efficiency; $m$—burning rate shape factor, normally 0.2–3.0; ${\phi }_z$—burning duration, °CA; and ${\phi }_0$—timing of combustion, °CA.

(3)

Heat exchange $\frac{d{Q}_{W_i}}{d\phi }$

The heat transfer model of the working fluid, swirl chamber wall, block wall, the top surface of the piston, cylinder wall and cylinder bottom was described using Formula (8):

$$\frac{d{Q}_{W_i}}{d\phi }=\frac{1}{6n}{\displaystyle \sum _{k=1}^5{a}_w{A}_{Fk}\left(T_{Wk}-T\right)}$$

(8)

where $A_{Fk}$—each heat transfer surface, m²; $T_{Wk}$—wall temperature, K; and $a_w$—heat transfer coefficient, W/(m²·K), which could be found using Woschni’s experimental formula:

$$\begin{array}{l}{a}_w=\\ 130D^{-0.2}{p}^{0.8}{T}^{-0.53}{\left[\begin{array}{l}{C}_1{c}_m\\ +C_2\frac{V_s}{P_{c1}}\cdot \frac{T_{c1}}{V_c}\left(p-p_{c0}\right)\end{array}\right]}^{0.8}\end{array}$$

(9)

where $c_u$—cylinder vortex speed, m/s; $c_m$—mean piston speed, m/s; $C_1$ and $C_2$—coefficient, $C_1$ = $2.28+0.308c_u/c_m$, $C_2$ = 6.22 × 10⁻³; $p_{c0}$—cylinder pressure while starting the diesel engine, MPa; $T_{c1}$—the cylinder temperature while closing the inlet valve, K; $p_{c1}$—the cylinder pressure while closing the inlet valve, MPa; and $V_c$—combustion chamber volume, cm³.

(4)

Thermodynamic properties of working fluids

For convenience, the working fluids in the swirl chamber and main combustion chamber were grouped as unburned fuel steam and a mixture of combustion product with air, and the specific heat capacity of the former one was known:

$$h_F=c_{pF}T$$

(10)

$$u_F=c_{VF}T$$

(11)

Then, for the thermodynamic property calculation of the latter one, the thermal parameters, such as the specific heat, specific internal energy and specific enthalpy, could be regarded as a function of the temperature and gas mixture, and the specific internal energy $u_G{}_{{}_i}$ could be roughly defined using the Justi formula, as shown in Formula (12):

$$\begin{array}{l}{u}_{G_i}=\\ 4.1868\times \left[\begin{array}{l}-\left(0.0975+\frac{0.0485}{{\lambda }_G^{0.75}}\right){\left(T-273\right)}^3\times {10}^{-6}\\ +\left(7.768+\frac{3.36}{{\lambda }_G^{0.8}}\right){\left(T-273\right)}^2\times {10}^{-4}\\ +\left(4.896+\frac{46.4}{{\lambda }_G^{0.93}}\right)\left(T-273\right)\times {10}^{-2}\\ +1358.6\end{array}\right]\end{array}$$

(12)

where ${\lambda }_G{}_i$—the instantaneous excess air coefficient:

$${\lambda }_{G_i}=\frac{1}{l_0}{\displaystyle {\int }_{{\phi }_{IVO}}^{{\phi }_{IVC}}\frac{d{m}_{E_i}}{d\phi }}/{\displaystyle {\int }_{{\phi }_0}^{\phi }\frac{d{m}_{B_i}}{d\phi }}$$

(13)

where ${\phi }_{IVC}$ and ${\phi }_{IVO}$ are, respectively, the opening and closing crank angles of the air inlet, °CA.

Further, $\partial u_i/\partial T$ and $\partial u_i/\partial {\lambda }_{G_i}$ were obtained using Formula (13).

We defined $Y_{F_i}$ and $Y_{G_i}$ as the mass fractions of unburned fuel steam and air-combustion product mixture in the swirl chamber and main combustion chamber, respectively; after working out the thermal parameters of the unburned fuel steam and air-combustion product mixture ($R_F{}_{{}_i}$—gas constant of fuel gas; $R_G{}_{{}_i}$—gas constant of air and combustion product mixture; $c_{VF}{}_{{}_i}$—specific heat at constant volume of fuel gas; $c_{VG}{}_{{}_i}$—specific heat at constant volume of air and combustion product mixture; $u_F{}_{{}_i}$—specific internal energy of fuel gas; $u_G{}_{{}_i}$—specific internal energy of air and combustion product mixture; $h_F{}_{{}_i}$—specific enthalpy of fuel gas; $h_G{}_{{}_i}$—specific enthalpy of air and combustion product mixture), the overall working fluid thermal parameter in the swirl chamber and the main combustion chamber could be calculated using the following Formulas (14)–(18):

Gas constant:

$$R_i=Y_{F_i}{R}_{F_i}+Y_{G_i}{R}_G{}_{{}_i}$$

(14)

Specific heat at constant volume:

$$c_{V_i}=Y_{F_i}{c}_{V{F}_i}+Y_{G_i}{c}_{V{G}_i}$$

(15)

Specific heat at constant pressure:

$$c_{p_i}=c_{V_i}+R_i$$

(16)

Specific internal energy:

$$u_i=Y_{F_i}{u}_{F_i}+Y_{G_i}{u}_{G_i}$$

(17)

Specific enthalpy:

$$h_i=Y_{F_i}{h}_{F_i}+Y_G{}_{{}_i}{h}_{G_i}$$

(18)

(5)

Model of the resistance loss $\Delta p$ in the connecting channel

The flow velocity of the working fluid in the connecting channel was described as follows:

$$v_i\left(\alpha ,\gamma ,\phi \right)=\frac{60nd{m}_{U_i}}{\rho \left(\phi \right)d\phi }/A\left(\alpha ,\gamma \right)$$

(19)

where $\alpha$—channel angle (which is between the center line of the cylinder and the center line of the channel), °; $\gamma$—expansion angle, °; $v_i\left(\alpha ,\gamma ,\phi \right)$—mixed gas flow velocity in the connection channel, m/s; $n$—diesel engine rotation speed, r/min; $\rho \left(\phi \right)$—density of the mixed gas, kg/m³; and $A\left(\alpha ,\gamma \right)$—sectional area of the connecting channel, cm².

The resistance loss $\Delta p$ in connecting the channel mainly refers to the fractional flow loss of the gas mixture from the main and auxiliary combustion chambers when flowing through the connecting channel, which is given as follows:

$$\Delta p=p_1-p_2=2F\cdot \zeta \cdot \frac{\upsilon }{A\left(\alpha ,\gamma \right)}{v}_i\left(\alpha ,\gamma ,\phi \right)L$$

(20)

where $F$—friction coefficient, generally $F$ = 28.454; $\zeta$—correction coefficient, $\zeta$ = 1/3; $\upsilon$—gas viscosity; and $L$—connection channel length, m.

(6)

Model of the swirl ratio ${\Omega }_k$

$$\begin{array}{l}{\Omega }_k=\frac{R_1}{R_2^2}\frac{{\delta }_k{V}_s\omega }{4\mu A{\left(\alpha ,\gamma \right)}_k(\epsilon -1)}\\ \begin{array}{cc}& \end{array}\times \left[\left(\frac{1}{\epsilon -1}\right)+\frac{1-\cos \phi +0.5{\lambda }_s{\sin }^2\phi }{2}\right]\\ \begin{array}{cc}& \end{array}\times {\displaystyle {\int }_{\pi }^{{\phi }_x}\frac{{\sin }^2\phi {\left(1+0.5{\lambda }_s\right)}^2}{{\left[1/\left(\epsilon -1\right)+\left(1-\cos \phi +0.5{\lambda }_s{\sin }^2\phi \right)/2\right]}^3}d\phi }\end{array}$$

(21)

When it is compressed to the top dead center (TDC), i.e., ${\phi }_x=2\pi$, the swirl ratio at this point ${\Omega }_{kc}$ is approximately

$${\Omega }_{kc}=\frac{R_1}{R_2^2}\frac{{\delta }_k{V}_s}{4\mu A\left(\alpha ,\gamma \right){(\epsilon -1)}^2}\cdot \frac{\pi }{180}\left(565\epsilon -3500\right)$$

(22)

where $R_1$—the vertical distance from the connection channel center line to the center of the swirl chamber, cm; $R_2$—inertia radius of the swirl chamber volume, which is, respectively, $0.636R_k$ and $0.707R_k$ for a spherical and cylindrical vortex chamber, cm; $R_k$—radius of the swirl chamber, cm; ${\delta }_k$—volume ratio ${\delta }_k=V_k/V_c$, where $V_k$—swirl chamber volume and $V_c$—compression endpoint volume; $V_s$—cylinder volume, cm³; $\mu$—the discharge coefficient of the connecting channel $\mu$ = 0.5–0.6; $\epsilon$—compression ratio; $\phi$—crank angle, °CA; and $\omega$—angular velocity of the crankshaft, °/s.

This mathematical model involved a reasonable simplification of complex issues, namely, the system was deemed to have a uniform and stable flow of the insulation, which allowed for mainly exploring the effects of the thermal process and the influence of the vortex ratio on the burning. This simplification of the essence of grasping the problem was summarized into a solution-available mathematical model, reducing the cost of simulation calculation. However, the model ignored the important impact of a certain factor on the entire model.

4. Model Solutions

To solve the nonlinear differential equations with multi-variable coupling and guarantee the solution accuracy, stability and astringency, this study adopted a central difference discretization scheme with the computational domain $\phi$ = 0–720° and V₁ = $V_c$ − $V_s$ + $V_c$, whose step lengths were Δφ and ΔV, respectively. Combined with the engine’s working condition, this research made a presupposition about its initial quantity of air and residual gas coefficient in the cylinder, and started with the initial point of the compression stroke, namely, at the moment when the air inlet closes. Considering that the working fluid quality remained the same during the stroke and no chemical combustion occurred during this period with almost identical gas thermodynamic properties, i.e., $\frac{d\left(m_1+m_2\right)}{d\phi }=0$ and $\frac{d{\lambda }_{G_i}}{d\phi }=0$, this study, combined with the working fluid’s thermal property Equations (10)–(18), carried out an iterative solution process using Equations (1), (3), (6) and (13) and created the coupled solution of resistance loss model (20) in the connecting channel between the swirl chamber and the main combustion chamber until the iteration result met the requirement of Formula (4), or else we revised the initial quantity and re-iterated again until the model converged.

To set the above results as the initial value during the combustion expansion phase, using the pre-set combustion heat release rule as given by the Wiebe function in Equation (7) for the working fluid’s quality change during combustion that arises from fuel combustion, Equation (2) could be simplified as follows:

$$\frac{d{m}_{i_i}}{d\phi }=\frac{1}{H_u}\frac{d{Q}_B{}_{{}_i}}{d\phi }$$

(23)

Formula (24) was obtained from Formula (13):

$$\frac{d{\lambda }_G{}_{i_i}}{d\phi }=-\frac{m_1}{l_0{m}_F^2{H}_u}\frac{d{Q}_B}{d\phi }$$

(24)

Formulas (1), (3), (6)–(8), (23) and (24) were solved in turn until the iteration result met the requirement of Equation (4) and $d{\lambda }_G{}_{i_i}/d\phi =0$ in the combustion chamber during the later expansion phase.

As for the gas exchange, according to [37], the suffuse–empty volume method was adopted while calculating Equations (1)–(3), and the quaternion Runge–Kutta method was employed to accelerate the process of the calculation and convergence.

After calculating the whole working cycle, to set the compression initial point as the reference, the calculation process compared the successively results to find out whether they met the calculation accuracy requirement; if not, the calculation process set the computed terminal point as the initial parameter and re-iterated again using the process described above until the result met the specified accuracy.

After the calculation of the change rules of pressure $P_I$ and temperature $T_I$ with respect to the crank angle in the cylinder, the performance indicators of this engine were worked out, such as the power $P_e$ and fuel consumption g_e, under this working condition according to its simulation result and mechanical efficiency.

Further, the swirl ratio ${\Omega }_{kc}$ was calculated in the swirl chamber according to Equations (21) and (22).

5. Testing System

5.1. Engine Performance Testing System

Based on the BH175F-1-type single-cylinder agricultural diesel engine’s test bench, as shown in Figure 3, we examined the impact of the swirl chamber’s variable cross-section dual-channel structure on the engine’s performance. We used 0# diesel fuel, and under the atmospheric temperature of 25 ± 5 °C and relative humidity of 45 ± 5%, the load characteristics and the emission characteristics were tested while referring to GB/T18297-2001 Performance Test Code for Road Vehicle Engines and GB14761-2001 Limit and Measurement Methods for Exhaust Pollutants from Compression Ignition (C.I.) Engines and Vehicles Equipped with C.I., respectively. To guarantee the test accuracy, all the performance data collections were done under stable conditions. The response accuracy changes of a test system should be in a linear relationship within the sensor’s static accuracy grade range, and sensors with a large discharge time constant were used to minimize its test distortion [38,39]. When processing the test data, data with a large deviation were eliminated as bad values in accordance with the Lauta rule.

5.2. Swirl Ratio Testing System

Based on the ZNQD-V intelligent test bench of the swirl chamber diesel engine airway, as shown in Figure 4, we examined the impact that the inclination and extending angle of the swirl chamber’s variable cross-section dual-channel structure had on the swirl ratio. By using the Eddy Momentum Instrument to test the eddy momentum M, the eddy momentum M was converted into an equivalent blade speed $n_D$ according to the formula $n_D=240M/\left(\pi \rho V/D^2\right)$. Corresponding sensors were used to detect the change in the valve lift, pressure, temperature, flow rate and eddy current speed; signals could be directly displayed on the instrument, and at the same time, signals were sent to a computer after an A/D conversion. The measuring analysis system could obtain the curve of the relationship between the swirl rate $\Omega$, flow $\mu \sigma$ and dimensionless valve lift $l_v/d_v$ ($l_v$ is the valve stem diameter (m), $d_v$ is the valve seat inner ring) to obtain the Ricado swirl ratio and AVL swirl ratio.

6. Results Analyses

6.1. Swirl Ratio

We set the inclination angle of the dual-channel α (along the tangent line of the swirl chamber) to 15°, 30° and 45°, and the divergence angle γ to 10°, 20° and 30°.

Table 1. Schemes of dual-channel structure.

Scheme Numbering	Channel Angle α	Expansion Angle γ	Scheme Numbering	Channel Angle α	Expansion Angle γ
1 (C15E10)	15°	10°	6 (C30E30)	30°	30°
2 (C15E20)	15°	20°	7(C45E10)	45°	10°
3 (C15E30)	15°	30°	8 (C45E20)	45°	20°
4 (C30E10)	30°	10°	9 (C45E30)	45°	30°
5 (C30E20)	30°	20°	10 ※ (C30E0)	30°	0°

Note: An item marked with the symbol ※ is a single-connecting channel scheme.

shows the nine dual channel structural schemes formed by the different α and γ combinations (e.g., C15E10 for channel angle 15° and expansion angle 10°) and single-connecting channel scheme of the original engine. The swirl ratio Ω_k values of the nine (as shown in Table 1) dual-channel structural schemes and single-connecting channel scheme of the original engine formed by different α and γ combinations (e.g., C15E10 for channel angle 15° and expansion angle 10°) were simulated and calculated in the swirl chamber at an engine rotation speed of 2000 r/min, as shown in Figure 5.

As shown in Figure 5, at a certain inclination angle α, the swirl ratio in the swirl chamber Ω_k decreased with the increase in the divergence angle during the compression stroke, and thus, it could decrease the divergence angle to enlarge the swirl ratio, but this reduced the divergence to narrow the channel’s flow area too much and further lowered the flow coefficient, which strengthened the throttling action in each channel and caused more flow resistance losses, and at the same time, the swirl ratio decreased. Therefore, there was an optimal divergence angle that could maximize the swirl ratio. Here, taking the channel’s inclination angle α = 15° for example, according to the simulation results, the optimal divergence angle should be around 11.6°, at which the swirl ratio could reach 31.8. After the piston surpassed the top dead center, all the swirl ratios Ω_k of three different variable cross-section channels with γ set to 10°, 20° and 30° decreased sharply due to the diffusive combustion, expansion of the gas mixture, turbulence flow fluctuation degree, etc.; furthermore, the corresponding swirl ratio Ω_k of the bigger divergence angle γ fell even faster. As shown in Figure 5. The descending slopes of the swirl ratio in C15E30 could reach 0.35.

At a certain divergence angle γ of the connecting channel, the swirl ratio Ω_k of the compression stroke in the swirl chamber rose with the increase in angle α up to a maximum but decreased if the angle α increased further. Taking the divergence angle γ = 20° for example, the maximum swirl ratio Ω_k at the top head center went up from 25.7 to 31.4 as the inclination angle α increased from 15° to 30°, which meant that it was favorable to form the highest swirl ratio along the swirl chamber tangent line, and then it was beneficial to improve both the gas mixture quality and the air utilization rate. However, when the inclination angle α increased further up to 45°, the maximum swirl ratio Ω_k decreased to 21.8. Moreover, the swirl ratio Ω_k in each scheme decreased faster after the piston descended.

Compared with the C30E0, except for the swirl ratio in C15E30 and E45C30 in which no obvious changes or decreases were discovered, the swirl ratio of all other schemes went up. In addition, according to the simulation results, the flow coefficients of C15E10, C15E20, C30E10 and C45E20 that adopted the dual-channel structure improved from the original 0.66 to 0.68–0.84, which was beneficial for improving the overall performance.

6.2. Load Characteristics

To investigate the influence on the load characteristics of the original air-cooled diesel engine with the above nine kinds of dual-channel cross-section swirl chamber structures, the load characteristics of the engine at speeds of 1200 r/min, 1800 r/min and 2400 r/min were analyzed based on the solution and experimental verification of the above mathematical model of the combustion process.

To examine the rationality of the mathematical model and the accuracy of the numerical calculation, three structures, namely, C15E10, C30E30 and C45E30, were randomly selected, and then the computational simulation value and the measured value under the working condition of the engine rotation speed as 1200 r/min were compared, as shown in Figure 6.

As indicated in the comparison results in Figure 6, the simulation value of the load characteristics was consistent with the experimental result under medium and small loads. Among the three schemes, the simulation accuracy slightly decreased and the maximum error between the simulation value of the load characteristics and the experimental result was less than 4.8% as the channel’s inclination angle α went up under medium and small loads. Under a large load, however, the deviation was bigger. The reason could have been that the above model and the numerical solution were both based on the assumption of zero dimension, while the gas mixture state and composition in the swirl chamber and auxiliary combustion chamber cannot be even and constant in practical work. In addition, the lack of recognition of the fuel atomization particle collision aggregation model and fuel film evaporation during the solution led to the simulation value of the fuel consumption rate being higher than the actual experimental value. The deviation between the corresponding fuel consumption became bigger, especially with the further addition of diesel engine power. However, since the deviation range was not big, it was generally within 0–18 g/kw·h according to the swirl chamber combustion structure in the randomly selected C15E10, C30E20 and C45E30, the calculation accuracy was also acceptable.

The simulation values of the load characteristics at other rotation speeds, namely, 1400 r/min, 1600 r/min, 1800 r/min, 2000 r/min and 2400 r/min, were also studied, and the simulation results all fitted the experimental results well. Therefore, the former model had better predictability.

According to the above nine kinds of schemes, a simulation of influence on the engine’s load characteristics was undertaken and the results are shown in Figure 7, Figure 8 and Figure 9. From the figures, it can be seen that at a certain channel’s divergence angle γ, the influence of the inclination angle α on the engine’s load characteristic was larger, the channel’s inclination angle α deviated in the tangential direction (30°) more in the swirl chamber and the fuel consumption was larger overall. The fuel consumption rate was smaller when α = 30°, and as the inclination angle α rose from 30° to 45°, the fuel consumption change was smaller when α decreased from 30° to 15°; the change trend at this time was the same as that of swirl ratio, that is, Ω_k increased as the channel’s inclination angle went up, which is helpful to improve the gas mixture quality, promote the combustion performance and reduce the fuel demand under the same power (the fuel consumption was minimized when α = 30°). When the angle α went up from 30° to 45°, according to the former analysis, the corresponding swirl ratio dropped faster, the swirl intensity decreased, the mixed energy weakened and the fuel consumption increased.

At a certain dual-channel inclination angle α, the swirl ratio decreased and the fuel consumption with the same power increased with the increase in divergence angle γ. The fuel consumption rate of each scheme hit the minimum when the divergence angle γ = 10°.

Therefore, according to the comparison results of C15E10–C45E30, the fuel consumption rate decreased at different rotation speeds when transferred from a small load to a medium load, and under a large load, the fuel consumption rate went up further. Meanwhile, the fuel consumption of C30E10 was the least under the same load and much more economical under a medium load.

Furthermore, relative to the original single connection channel structure illustrated in C30E0, under different rotational speeds but with the same power, the fuel economy was exclusively improved, except for C15E30 and C45E30, in which the economy increased by 2.3–13.2% compared with the original engine.

Compared with the load characteristics of C15E10–C45E30 under the three different speeds shown in Figure 7, Figure 8 and Figure 9, in which the engine increased from 1200 r/min to 1800 r/min under small and medium loads, the fuel consumption in all schemes also increased. For example, the minimum fuel consumption in C30E10 at 1800 r/min was 36.5 g/kw·h, which was lower than that at 1200 r/min. However, when the rotation speed was increased to 2400 r/min, the fuel consumption went up under the same power instead.

6.3. Smoke Emissions Characteristics

Smoke emissions have always been the key to controlling a diesel engine’s emissions. Whether the diesel engine can be developed well in the long run largely depends on whether the smoke emissions can be efficiently controlled. Therefore, this study investigated the smoke emissions characteristics based on the above nine kinds of swirl chamber structures to offer a new kind of approach that could reduce the emissions of a diesel engine with a swirl chamber.

Figure 10 shows the smoke emissions of a diesel engine at the rotation speeds of 1200 r/min, 1800 r/min and 2400 r/min when the load rate was 25%; it indicates that at a steady rotation speed and a certain dual-channel divergence angle γ of the swirl chamber insert, the smoke emission decreased as the channel’s inclination angle α increased from 15° to 30°. Taking 1200 r/min for example, the maximum falling range of the corresponding BSU25% could reach 43.9%, while when the inclination angle α reached 45°, the swirl intensity weakened at this time and the smoke emissions increased with a relatively evident rising trend. The corresponding increasing ratio of the smoke emissions at the three rotation speeds were 106.3%, 62.8% and 50%, respectively. Therefore, in terms of reducing the emissions pollution, an inclination angle α that is relatively small and almost tangent to the swirl chamber should be used. However, when the connecting channel angle α was constant, the smoke emissions increased with the increase in the dual-channel divergence angle γ and the BSU25% increase rate could reach 34.4% when α was 30° and γ increased from 20° to 30°. Therefore, the divergence angle γ should not be too big to reduce the smoke emissions, but not too small to avoid making the processing more difficult. Therefore, γ should be selected appropriately when considering the best performance compromise between emissions and processing.

In addition, the smoke emissions decreased with the increase in the rotation speed with the same swirl chamber structure, and due to the fact that the increasing rotation speed was beneficial to improve the swirl intensity, this reduced the residual gas in the cylinder, as well as promoted the intake charge, and thus, the smoke emissions were further efficiently reduced by 3.6–12.5%.

According to the experimental results, all schemes except for scheme 3 and scheme 9 had lower emissions than the original diesel engine under the same working conditions and the smoke emissions could be reduced by approximately 59.7%.

Experiments under other operating conditions were also done, where

Table 2. BSU50% and BSU75% for a rotation speed of 1800 r/min.

No.	BSU50%	BSU75%	No.	BSU50%	BSU75%
1	2.3	3	6	1.9	2.4
2	2.5	3.2	7	2.5	3.2
3	2.9	3.6	8	2.7	3.4
4	1.2	1.8	9	3.1	3.7
5	1.6	2.0	10 ※	3	3.7

Note: An item marked with the symbol ※ is a single-connecting channel scheme.

illustrates the change in BSU50% and BSU75% of the 50% and 75% load rates at a rotation speed of 1800 r/min. The table shows that the smoke emissions characteristics were almost the same with the above change rule, and the emissions value increased with the load rate rise. At a certain load, the BSU50% and BSU75% in scheme 4 were both minimized; combined with the above analysis results, a cross-section dual-channel swirl chamber with a smaller divergence angle that is almost tangent to the swirl chamber is favorable for reducing diesel engine emissions.

Through the experimental and simulation analysis, this dual-channel structure played an important role in improving the performance of the engine and the discharge of smoke emissions. There were also insufficiencies in this scheme. The first was the idealized state of the mathematical models. The impact of changes in the pressure and temperature of the exhaust process on the entire combustion process was not considered. Second, the model assumed that a quasi-stable flow was present, and the work quality was the ideal gas state. There is a gap between these assumptions and the actual operation of the engine and may be an important factor that affects the combustion. In future work, we can fully consider the changes in the turbulence of the ventricular and main combustion chamber, further reveal the effects of the influence and emissions of the vortex disturbance, and analyze the causes from the perspective of thermodynamics and combustion.

7. Conclusions

Drawn from all the experiments discussed above, we can summarize the major findings of the present research as follows:

(1)

The scheme of a variable dual-channel cross-section swirl turbulence combustion system was put forward and its structural design was carried out. Based on proper hypothesis and simplification, a model of the swirl chamber turbulence combustion with a zero-dimensional thermal process was established and the corresponding numerical solution was obtained. The test results showed that the model had good predictability.

(2)

This combustion system is vital to the working performance of a diesel engine. Among the nine designs of a variable cross-section dual-channel swirl chamber, the theoretical swirl rate increased first and then fell as the channel’s inclination angle rose at a certain divergence angle, and its variation in the expansion stroke was more substantial than that in the compression stroke. As for the load characteristics, the fuel consumption rate under small and medium power decreased as the inclination angle increased, but increased under large power. According to the test results, the smoke emissions of the diesel engine went down first and then up with the increase in the inclination angle. At a certain inclination angle, the theoretical swirl rate decreased with the increase in the divergence angle, the variation in the expansion stroke was more substantial than that in the compression stroke, and both the corresponding fuel consumption and smoke emissions went up under the same power.

(3)

By comparing the tests, the performance of the diesel engine with a variable cross-section dual-channel swirl chamber was superior to the original one with a single channel.

The results of this research provide a technical reference for performance improvement and beneficial guidance for the design and optimization of a mini-type air-cooled diesel engine.