Advanced System Determined for Utilisation of Sustainable Biofuels in High-Performance Sport Applications

Abstract

It is of current importance to reach carbon neutrality in various transport sectors as soon as possible, with regard to the fact that transport, characterized by the utilization of piston combustion engines, is one of the main polluters in urban agglomerations. Piston combustion engine pollution also significantly influences the quality of the living environment and human health. The application of biofuels containing bioethanol or biodiesel essentially contributes to the reduction of air pollution caused by exhaust gases, also taking into consideration the renewability of these fuels. Therefore, the modification of spark ignited engines is necessary for the correct operation of ethanol combustion and to remove risks during operation and combustion, mainly the possibility of detonation combustion. To date, there has been a gradual development of engines intended for the combustion of the fuel mixture gasoline–bioethanol, mainly the fuel E85. This fuel mixture contains 85% ethanol and 15% gasoline. This paper is focused on construction modifications of a specific combustion engine, which operates with a two-stroke working cycle, which is predominantly intended for installation in category L motor-sport vehicles and kart race vehicles. A new construction solution specifically for this engine was developed and consequently patented. The results obtained while testing this engine in real racing conditions confirmed the correctness and purposefulness of the proposed engine concept.

1. Introduction

The Otto cycle is used to theoretically describe a spark ignition engine’s combustion cycle. During this process, the fresh air-fuel mixture is sucked into the combustion chamber when the piston is at top dead center (in a real engine, the air-fuel mixture intake occurs nearly before the piston reaches top dead center) and rapidly burns at a constant volume, which causes the pressure to rise [1,2].

Adiabatic compression of the mixture inside the cylinder occurs when the piston moves from bottom dead center after intake, and exhaust channels are closed (points 1 and 2 in Figure 1). Both temperature and pressure increase during this process [3,4,5].

$$\frac{p_2}{p_1}={\left(\frac{V_1}{V_2}\right)}^{\kappa }\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\Rightarrow \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{p}_2\hspace{0.17em}=p_1{\epsilon }^{\kappa } (\mathrm{Pa})$$

(1)

$$\frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{\kappa -1}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\Rightarrow \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{T}_2\hspace{0.17em}=T_1\cdot {\epsilon }^{\kappa -1} (\mathrm{K})$$

(2)

where $\epsilon =\frac{V_{\mathrm{z}-\mathrm{k}}+V_{\mathrm{k}}}{V_{\mathrm{k}}}$ is the compression ratio, p is the pressure (Pa), T is the thermodynamic temperature (K), and V is the volume of working charge (m³).

A spark generated by a spark plug ignites the mixture, which instantly burns. The spark is generated at the top dead center, at point 3 at Figure 1. Theoretically, combustion is replaced by rapid heat input Q_2,3. The pressure rises, at nearly constant volume, from value p₂ to p₃. Input heat is calculated by equation:

$$Q_{2,3}=m\cdot c_v\cdot \hspace{0.17em}\left(T_3-T_2\right) \left(\mathrm{J}\right)$$

(3)

where Q_2,3 is heat brought between points 2 and 3 in p–V diagram (J), m is the working charge weight (kg), and c_v is the specific heat capacity at constant volume (J·kg⁻¹·K⁻¹).

$$p_3=\frac{p_2}{T_2}\cdot T_3 (\mathrm{Pa})$$

(4)

Adiabatic gas expansion follows—the mechanical power of gas occurs between points 3 and 4. Temperature and pressures decrease during the expansion, while the volume increases to Vk + Vz–k. The following equations describe the relation between the stated variables:

$$\frac{p_3}{p_4}={\left(\frac{V_4}{V_3}\right)}^{\kappa }$$

(5)

$$\frac{T_3}{T_4}={\left(\frac{V_4}{V_3}\right)}^{\kappa -1}$$

(6)

Just before the piston reaches the bottom dead center, the exhaust channel opens and gases leave the combustion chamber (points 4 and 1). Isotropic rapid cooling can be used instead. The pressure at point 4 is described by the equation:

$$p_4=\frac{p_1}{T_1}\cdot T_4 (\mathrm{Pa})$$

(7)

When the intake channels open, an isobaric process occurs which is theoretically described by the Otto cycle of the two-stroke engine between points 1 and 0. When the fuel is sucked into the combustion chamber, the remaining waste gases are exhausted through the exhaust channel and the total heat is adequate to decrease the temperature to the value of T₁.

$$Q_{4,1}=m\cdot c_v\cdot \hspace{0.17em}\left(T_4-T_1\right) \left(\mathrm{J}\right)$$

(8)

The volume of the mechanical work of charge (fuel mixture), W, performed by the engine is described by the following equation:

$$W=Q_{2,3}-Q_{4,1}=m\cdot c_v\cdot \hspace{0.17em}\left(T_3-T_2\right)-m\cdot c_v\cdot \hspace{0.17em}\left(T_4-T_1\right) \left(\mathrm{J}\right)$$

(9)

$$W=m\cdot c_v\cdot \hspace{0.17em}\left(T_3-T_2-T_4+T_1\right) \left(\mathrm{J}\right)$$

(10)

By modifying the equation, a new equation describing the work is obtained:

$$W=m\cdot c_v\cdot \hspace{0.17em}{T}_1\cdot \left[\tau \left(1-\frac{1}{{\epsilon }^{\kappa -1}}\right)+1-{\epsilon }^{\kappa -1}\right] (\mathrm{J})$$

(11)

where $\tau =\frac{T_3}{T_1}$ is the temperature ratio and describes the relation between maximum and minimum temperature.

From Equation (11), it is clear that the higher the temperature ratio, the greater the work cycle is. Mechanical work firstly increases, then subsequently decreases while the compression ratio increases. If we differentiate the work according to the compression ratio and set it as equal to zero, we obtain a local extreme to determine the optimal compression ratio at a constant temperature ratio [6]:

$$\frac{\partial W}{\partial \epsilon }=m\cdot c_v\cdot \hspace{0.17em}{T}_1\cdot \left[\left(\kappa -1\right)\cdot \frac{\tau }{{\epsilon }^{\kappa }}-\left(\kappa -1\right){\epsilon }^{\kappa -2}\right]=0$$

(12)

Equation (13) determines the optimal compression ratio (for constant temperature ratio T₃/T₂).

$${\epsilon }_{\mathrm{opt}}={\tau }^{\frac{1}{2\cdot \left(\kappa -1\right)}}$$

(13)

The maximum volume work (Figure 2) obtained by cycle is calculated by connecting Equations (12) and (13):

$$W_{\max }=m\cdot c_v\cdot \hspace{0.17em}{T}_1\cdot {\left(\sqrt{\tau }-1\right)}^2 (\mathrm{J})$$

(14)

Heat efficiency of the spark ignition combustion engine can be calculated by Equation (15):

$${\eta }_t=\frac{Q_{2,3}-Q_{4,1}}{Q_{2,3}}=1-\frac{Q_{4,1}}{Q_{2,3}}=1-\frac{m\cdot c_v\cdot (T_4-T_1)}{m\cdot c_v\cdot (T_3-T_2)}=1-\frac{(T_4-T_1)}{(T_3-T_2)}$$

(15)

By modification of the previous equation, it is possible to obtain the equation used for thermal efficiency determination based on the compression ratio:

$${\eta }_{\mathrm{t}}=1-\frac{1}{{\epsilon }^{\kappa -1}}=1-{\left(\frac{p_1}{p_2}\right)}^{\frac{\kappa -1}{\kappa }}$$

(16)

The thermal efficiency of the spark ignition combustion engine increases with the rising compression ratio and does not depend on the amount of heat supplied or the load. The more compressed the mixture is before ignition, the better the use of the heat supplied, and the more economical the engine will be. It is obvious that the temperature needed for ignition of the mixture is not possible to achieve only by compression [7].

According to results of the article, it is convenient to keep the optimal value of compression ratio, though from an efficiency point of view, it is convenient to reach the maximum possible value of ε. Therefore, a compromise between these two parameters is needed [8].

The compression ratio of a real combustion engine is constant and does not rise with increasing inlet pressure. The supplied amount of fuel can be increased by rising inlet pressure to adhere to the stoichiometry of combustion, which correlates with higher heat input [9,10].

High performance engines used in racing vehicles (category L) have a very short period of time to fill the cylinder with fresh air–fuel mixture and remove the waste products (exhaust gases) of combustion from the combustion chamber. The exchange process of fresh air–fuel mixture and waste products occurs when the piston is in the bottom dead center position. Typical piping for high performance two-stroke engines consists of four exhaust pipes and five intake pipes or channels. Excessive piston thermal expansivity and insufficient fresh mixture intake are the two main disadvantages of the aforementioned displacement of channels. As a result, possible engine destruction caused by the detonation combustion of the E85 biofuel may occur [11,12,13]. The new system’s main principle is to implement an additional cooling channel into the exhaust pipe, which would provide an additional amount of fresh air–fuel mixture into the combustion chamber. This additional cooling pipe or channel has a rectangular shape in cross-section. The main purpose of this system is to dramatically reduce the detonation combustion risk while using suitable fuels in common and performance two-stroke engines [11,14]. The new system can possibly increase the power output of the engine, but this is not a goal. The concept of this innovation is shown in Figure 3.

Compression progresses as a polytrophic process, while polytrophic exponent n acquires a value of 1.17 based on the experimental data.

The volume of air–fuel mixture is compressed between distances L₁ and L₂. The equation that describes the relation between length, L, and crankshaft angel rotation with radius, a, is:

$$L=a\cdot \left(1-\cos \theta -\frac{R_{\mathrm{c}}}{2}\cdot {\sin }^2\theta \right) (\mathrm{m})$$

(17)

where θ is the angle of crankshaft rotation angle (m), and R_c is the relation between crankshaft radius and connecting rod length (a/L_k).

The distance L₄ belongs to θ₄, which is possible to calculate by Equation (18):

$${\theta }_4=360°-\arccos \frac{1-\sqrt{1-2\cdot R_{\mathrm{c}}\cdot \left(1-\frac{R_{\mathrm{c}}}{2}-\frac{L_4}{a}\right)}}{R_{\mathrm{c}}} (°)$$

(18)

2. Fuel Mixture and Exhaust Gases Exchange Described by Computation

Gas flow and heat exchange of two-stroke engines are the biggest and most difficult problems for the mathematical description of the Otto cycle, due to their complexity. A suitable numerical tool is needed to describe basic state values during the movement of the piston due to its complex movement behavior. An applied numerical tool operates with the model of the cylinder, and to achieve the required results, the method of finite volume was used [15].

To reach the solution was used the simulation software. Individual elements´ energy flows can be simulated in this software based on differential equations described by Navier-Stokes [16]. Simulation of turbulence models is also possible in this simulation software. Network shape changes, which are the result of piston movement during Otto cycle points 4 and 1, are taken into account during the simulation process. An inverted model of the tested engine, showing the inner area of cylinder, is shown in Figure 4. The model also shows the intake and exhaust pipes where the additional intake pipe is implemented into the exhaust pipe [17]. The inverted model was created by METROTOM (scanning equipment).

Simulation software used the inverted model (adjustments needed), created by the scanning procedure and based on the geometric parameters of in-cylinder area. To reduce the computation time, the model was simplified and the in-cylinder area remained without change, to gain the best results. The only change of the in-cylinder area was a shortening of the intake and exhaust channels. In the simulation, when the piston reached a distance of 25.2 mm from TDC, the exhaust channels started to open, transferred into the crankshaft rotation angle of θ₄ = 91.6°. The listed distance or angular rotation of the crankshaft stated the initialization conditions which represent a zero starting time of τ = 0 s. By rotating the crankshaft and increasing the angle, the piston moved to the BDC which led to the exhaust channels closing. At a crankshaft angle of θ = 268.4° the exhaust channels were closed [18,19,20].

The simulation process was set to an engine speed of 11,000 rpm. A relative piston shift (axis z) is described by Equation (19) (dependence of relative piston movement and time of the simulation):

$$z=-z_0+a\cdot \left(1-\cos \theta -\frac{R_{\mathrm{c}}}{2}\cdot {\sin }^2\theta \right) (\mathrm{mm})$$

(19)

where z is the piston movement (mm), and z₀ is the piston position at the start of the simulation (mm).

The dependence of the crankshaft angular rotation at the given engine speed is described by Equation (20).

$$\theta =\frac{2\cdot \mathsf{\pi }\cdot n}{60}\cdot \tau +{\theta }_4 (\mathrm{rad})$$

(20)

Combining Equations (19) and (20) results in the mathematical equation directly used in the simulation program describing the dependence of the piston movement and time. Equation (21) shows the final mathematical equation used in the simulation software:

$$z=-z_0+a\cdot \left[1-\cos \left(\frac{2\cdot \mathsf{\pi }\cdot n}{60}\cdot \tau +{\theta }_4\right)-\frac{R_{\mathrm{c}}}{2}\cdot {\sin }^2\left(\frac{2\cdot \mathsf{\pi }\cdot n}{60}\cdot \tau +{\theta }_4\right)\right] (\mathrm{mm})$$

(21)

$$z=-25.2+27.25\cdot \left[1-\cos \left(\frac{2\cdot \mathsf{\pi }\cdot 11\times {10}^3}{60}\cdot \tau +1.609\right)-\frac{0.2271}{2}\cdot {\sin }^2\left(\frac{2\cdot \mathsf{\pi }\cdot 11\times {10}^3}{60}\cdot \tau +1.609\right)\right]$$

At approximately the crankshaft angle of 176.8° (3.0857 rad), the exhaust and intake channels are opening and closing. The time of simulation process represents the required time interval for a given angular rotation. The difference form of equation, Equation (22), is used to obtain the time interval by which the angular speed is described:

$$\Delta \tau =\frac{30\cdot \Delta \theta }{\mathsf{\pi }\cdot n}=2.679\times {10}^{-3} (\mathrm{s})$$

(22)

Opening and closing time dependence of exhaust channels is shown in Figure 5.

When the piston moves in the direction of axis z (the axis identical to the vertical axis of cylinder), the exhaust channels are opening (closing).

After the expansion of exhaust gases, intake channels start to open along with the newly patented cooling channel, implemented in the exhaust channel with slight delay, which results in the embossing of the residual burnt exhaust gases from the in-cylinder area [21].

Simulation software allowed the division of the cylinder model into various individual parts. The main purpose of the fragmentation was the necessity of the piston shifting movement regarding the bottom area of the cylinder volume. By connecting all parts, one functional entity was created. The crucial part for obtaining results was the inner part of the cylinder. When the piston moves in the direction of axis z, the exhaust channels are opened.

After the expansion phase of combustion, intake channels open in addition to the newly implemented cooling channel opening, but with slight delay, which helps to push out residual exhaust gases from the in-cylinder area [22].

Three various types of networks were used for sampling parts of the cylinder. The hexagonally based network Sweep was used to split the cylinder into upper and bottom parts.

The network used for the sample consisted of 1.38 × 10⁶ elements and 1.27 × 10⁶ nodal points. Because the cylinder was the most important part of the simulation, a substantial number of elements were used to create the network.

3. Determining Unicity Conditions Used in Simulation Solution

The model was modified to secure unicity of geometrical conditions during testing. Material characteristics of individual parts are important for the simulation solver, boundaries and initializations, and also for heat transfer and streaming.

Combustion stoichiometry sets the material characteristics of the air–fuel mixture and exhaust gases, while physical specifications are specified by pressure and temperature. At τ = 0 s, the in-cylinder was filled with 100% of the exhaust gases characterized by a temperature of 530 °C and pressure of 5.105 Pa [23]. Velocity, v_p, specifies piston velocity at any time, τ, which was set to value of 30.92 m·s⁻¹ at τ = 0, and was calculated on the basis of Equations (23) and (24):

$${\upsilon }_{\mathrm{p}}=\frac{\mathrm{d}L}{\mathrm{d}\tau }=\omega \cdot \frac{\mathrm{d}L}{\mathrm{d}\theta } (\mathrm{m}·{\mathrm{s}}^{-1})$$

(23)

$${\upsilon }_{\mathrm{p}}=\omega \cdot a\cdot \left[\sin \left(\frac{2\cdot \mathsf{\pi }\cdot n}{60}\cdot \tau +{\theta }_4\right)-\frac{R_{\mathrm{c}}}{2}\cdot \sin \left(\frac{4\cdot \mathsf{\pi }\cdot n}{60}\cdot \tau +2\cdot {\theta }_4\right)\right] (\mathrm{m}·{\mathrm{s}}^{-1})$$

(24)

According to the First Law of Thermodynamics, calculations of total parts energy were necessary, mainly for performing volumetric work. The modifications showed positive results in reducing the calculation time (1 μs) of the linear solver with the ability to keep convergence stability.

The software required 2.679 × 10⁻³ s of total time to solve the problem, which was subsequently divided into 2679 time steps, using four iterations per one time-step. The total number of iterations was 10,700. Shear stress transport (SST) was needed to model the turbulent flow of gas, which is also used in supersonic streaming with large pressure gradients, typical for exhaust processes.

Equation (6) defines the movement time dependence of the in-cylinder bottom surface volume and its contact with the piston. Changing cylindrical surface within the piston movement was defined by “unspecified” shift.

There was a possibility of supersonic streaming of the exhaust gas outlet, which was defined by boundary conditions of the exhaust channel. Intake channels’ boundary conditions for air–fuel mixture suction were set to a value over 60 kPa. The high value of pressure was caused by mixture compression under the piston during its movement. Pressure increased 8/5 times when the initial mixture volume was compressed to 5/8, meaning that the pressure rose from 100 kPa to 160 kPa [24].

Iteration correctness and maximum number of iterations were important to define before commencing the numerical solution process. The short time step secured high correctness after only 4 iterations, even though there were 10 iterations set before the process commenced [25,26].

4. Numerical Solutions Analysis

The solver starts by calculating the results needed to test the new design by a gradual solution of difference equations and the display of iteration steps created for each individual time step [27,28]. Isosurfaces can be displayed once the solver has finished processing all the inserted data for the calculation of the equations. Values that cannot be achieved analytically (Otto cycle points 4 and 1) are calculated by the solver. Isobaric surfaces are shown in cross-section view of the in-cylinder area in Figure 6. Patented suction channel (bottom left), exhaust channel (top left), suction channels (bottom right) and cylinder are shown in Figure 6.

The crankshaft rotation angle of 21.13°, which represents time 3.2 × 10⁻⁴ shows a reduction of pressure at around 350 kPa. This pressure decrease is caused by gas leakage through the exhaust channel and the changed cylinder volume (increased). The temperature falls with pressure reduction, represented by the in-cylinder cross-section Figure 7 showing the temperature areas.

The exchange of fuel mixture and exhaust gases is shown in Figure 8 in the form of velocity vectors. Figure 8 clearly shows the perforation of fresh fuel mixture into the exhaust gases in the area of the added intake channel. Otto cycles points 4 and 1 are achieved by pressure values analysis while the piston shifts between BDC and TDC. The pressure values analysis is presented by Figure 9.

Pressure rapidly decreases during the initial phase when the exhaust channels are starting to open. When the intake channel starts to open, the pressure starts to rise, adequately, due to fresh mixture inside the intake channel and its overpressure [28,29]. Pressure reduction occurs near the bottom dead center. The average pressure increase is caused by the upwards repetitive movement of the piston, which results in forcing the remaining exhaust gases out of the exhaust channel [30]. Temperature and volume dependence of the cylinder is shown in Figure 10.

This view on the time dependence of exhaust and intake of gases allows a complex view of calculated results and their evaluation for two-stroke engines. Thereby, it is possible to know the quantity of exhaust gases remaining in the cylinder, and the quantity of fresh mixture which is sucked into the cylinder and blown out through the exhaust channel without undergoing combustion.

5. Conclusions

Insufficient fresh air–fuel mixture and redundant piston thermal expansivity are the main two problems of high-performance engines that can be solved by implementing an additional intake channel into the exhaust canal, which also decreases the risks connected with the combustion of E85, used as biofuel [31]. This solution has important advantages for engine operation. Firstly, the modification highly optimizes the filling of the cylinder with a fresh mixture of air and fuel through the cooling channel and improves the performance of the engine. Secondly, the additional cooling channel reduces the surface temperature of the piston, which lessens the possibility of engine destruction due to uncontrollable thermal expansion of the piston.

The positive results of this construction modification allow the use of alternative fuel mixtures (biofuels) without problems during engine operation. This modification has undergone long development, has been implemented and used in a real engine with great success, and has become the subject of a patent application.