Seiliger cycle

Pressure-volume diagram of the Seiliger process

Temperature-entropy diagram of the Seiliger process

The Seiliger cycle is a mixed comparison process ( constant space and constant pressure process ) that is used to represent the processes in internal combustion engines . It depicts the so-called perfect engine. Both the constant pressure process and the constant space process are included as special cases in the Seiliger process.

The constant pressure process (diesel process) with its purely isobaric heat supply cannot be implemented in practice, since heat supply is not possible without increasing the pressure. The constant- space process (Otto process) with its purely isochoric heat supply cannot be implemented in practice, since heat supply at any rate is not possible. The partially isobaric and partially isochoric heat supply in the Seiliger process provides a good approximation of the real processes in diesel and gasoline engines.

Process flow

The comparison process proposed by Myron Seiliger in 1922 is divided into five process steps for engines without engine charging :

• (1 - 2) isentropic compression. Energy transfer in the form of labor . ${\displaystyle w>0}$
• (2 - 3) isochoric combustion. Energy transfer in the form of heating . ${\displaystyle q>0}$
• (3 - 4) isobaric combustion. Energy transfer through heating and useful work through expansion. . ${\displaystyle q>0,w<0}$
• (4 - 5) isentropic relaxation. Energy transfer in the form of useful work . ${\displaystyle w<0}$
• (5 - 1) isochoric exhausts. Energy transfer in the form of waste heat and workload . ${\displaystyle q<0,w>0}$

Positive heat or work energy values ​​mean an energy supply and negative work or heat energy values ​​mean energy output to the working gas. The gas exchange cycle (isobaric discharge and suction) is not taken into account.

Efficiency

The thermal efficiency of the Seiliger process depends not only on the volume ratio (expansion ratio, compression ratio) and the isentropic exponent, but also on the distribution of the amount of heat supplied for the pressure increase ratio and the amount of heat for the full or constant pressure ratio and can be determined as follows: ${\displaystyle \varepsilon }$ ${\displaystyle \kappa }$ ${\displaystyle \xi }$ ${\displaystyle \psi }$

${\displaystyle \eta _{th\,\mathrm {Seiliger} }=1-{\frac {1}{\varepsilon ^{\kappa -1}}}\cdot {\frac {\psi ^{\kappa }\xi -1}{\xi -1+\kappa \xi (\psi -1)}}}$

The first major factor is the thermodynamic loss for the constant space process. The second main factor is the additional loss due to the constant pressure process and thus greater than 1. The constant space process is more efficient than the constant pressure process. The thermal efficiency of the Seiliger process lies between the constant space process and the constant pressure process.

${\displaystyle \varepsilon ={\frac {V_{1}}{V_{2}}}}$; V ₁ is the expansion volume or the expansion space. V _{2 is} the compression volume or the compression space.

${\displaystyle \kappa ={\frac {c_{p}}{c_{V}}}}$; Isentropic exponent (fuel gas or exhaust gas at 1000 ° C has a value of approx. 1.3). The higher the ratio of c _p to c _V, the higher the efficiency.

${\displaystyle c_{p}}$; Specific heat capacity at constant pressure (combustion or exhaust gas at 1000 ° C has approx. 1.25 kJ / (kg K).

${\displaystyle c_{V}}$; Specific heat capacity at constant volume (combustion or exhaust gas at 1000 ° C has approx. 0.96 kJ / (kg K).

${\displaystyle R_{s}=c_{p}-c_{V}}$; Specific gas constant . It remains constant over a wide temperature range and is approx. 0.29 kJ / (kg K) for fresh gas and exhaust gas.

${\displaystyle \xi ={\frac {p_{3}}{p_{2}}}={\frac {T_{3}}{T_{2}}}}$; Pressure and temperature increase ratio with isochoric combustion. The greater the pressure and temperature increase, the higher the thermal efficiency.

${\displaystyle p_{2}=p_{1}\cdot \varepsilon ^{\kappa }}$; Compaction pressure. p ₁ is the initial pressure, e.g. B. 1 bar.

${\displaystyle T_{2}=T_{1}\cdot \varepsilon ^{\kappa -1}}$; Compression temperature. T ₁ is the starting temperature in Kelvin (fresh gas and residual exhaust gas) before the compression stroke, e.g. B. 400 K (approx. 127 ° C).

${\displaystyle p_{3}=p_{2}{\frac {T_{3}}{T_{2}}}}$   and   ; Pressure and temperature after combustion in the same room. p ₃ and T ₃ result from the selected amount of heating energy for the isochoric temperature and pressure increase. ${\displaystyle T_{3}=T_{2}{\frac {p_{3}}{p_{2}}}}$

${\displaystyle \psi ={\frac {V_{4}}{V_{3}}}={\frac {T_{4}}{T_{3}}}}$; Space and temperature increase ratio (expansion, full pressure ratio) with isobaric combustion. T ₄ and V ₄ result from the selected division of constant space and constant pressure ratio. The lower the constant pressure factor, the higher the efficiency.

${\displaystyle \eta _{th\,\mathrm {Carnot} }=1-{\frac {T_{1}}{T_{4}}}}$; The Carnot efficiency determines the theoretical upper limit of all thermodynamic cycle processes .

To illustrate the state variables, an ideal gas with temperature-independent and equal heat capacity is used for compression and expansion in the following.

Division of pressure increase - increase in space

The heat input of the mixed process is composed as follows:

${\displaystyle Q_{zu}=Q_{V}+Q_{P}=m\left[c_{V}({\frac {T_{3}}{T_{2}}}-1)T_{2}+c_{p}({\frac {T_{4}}{T_{3}}}-1)T_{3}\right]}$Heat supply (kJ) for the entire work cycle. Q _V is the heat conversion at constant volume and Q _P is the heat conversion at constant pressure. In the case of diesel engines with multiple direct injection, the division can be freely selected. In the case of a petrol engine without direct injection, the split can only be influenced via the ignition point. m is the heating or mixture mass of the working gas (kg).

Instead of calculating with absolute heating energies and masses, specific heating energies and masses are used in the following.

${\displaystyle \!H_{u}=H_{V}+H_{P}}$; specific heating energy (kJ / kg) for the entire work cycle. H _V is the heating energy component for the constant space phase and H _P for the constant or full pressure phase. For example: 42,000 kJ / kg H _u = 20,000 kJ / kg H _V + 22,000 kJ / kg H _P . The more energy for the constant space phase, the higher the efficiency.

${\displaystyle T_{3}=T_{2}+{\frac {H_{V}}{m_{H}c_{V}}}}$; Temperature after combustion in the same room. m _H is the specific heating mass to fuel mass (kg / kg). For an air ratio of = 1, 18 kg of air and residual exhaust gas are required per kg of gasoline , i.e. about 20% more than the minimum for air. c _V = c _p / κ. ${\displaystyle \lambda }$

${\displaystyle T_{4}=T_{3}+{\frac {H_{P}}{m_{H}c_{p}}}}$; Maximum temperature after constant pressure combustion. m _H is the specific heating mass per fuel mass (kg / kg). An air ratio of = 1.4 requires 25 kg of air and excess air and residual exhaust gas per kg of diesel . c _p = c _V * κ. The specific heat capacity c _{p of} the heating mass (fuel gas or exhaust gas at approx. 1000 ° C) is around 1.2 kJ / (kg K), for c _v around 0.9 kJ / (kg K). ${\displaystyle \lambda }$

Pressure increase ratio

The pressure increase p ₃ / p _{2 also} corresponds to the temperature increase T ₃ / T ₂ during the constant space phase. The absolute increase in pressure p ₃ -p ₂ is directly dependent on the selected specific energy supply H _V .

${\displaystyle \xi ={\frac {H_{V}}{m_{H}c_{V}T_{2}}}+1}$; Pressure increase number. H _V is the heating energy (kJ / kg) for the constant space phase. The higher the pressure increase, the higher the efficiency.

${\displaystyle p_{3}=p_{2}\cdot \xi }$   and   ; Pressure and temperature after combustion in the same room. p ₃ is the maximum pressure. ${\displaystyle T_{3}=T_{2}\cdot \xi }$

Space increase ratio

The volume increase V ₄ / V _{3 also} corresponds to the temperature increase T ₄ / T ₃ during the equal-pressure phase. The absolute increase in temperature T ₄ -T ₃ arises directly from the remaining (H _u - H _V ), specific energy input H _P .

${\displaystyle \psi ={\frac {H_{P}}{m_{H}c_{p}T_{3}}}+1}$; Temperature and volume increase number for the equal pressure process. T ₁ is the initial temperature after the intake cycle before compression and H _{u is} the specific heating energy supplied (kJ / kg) for the entire work cycle. If known, the following formula can also be used: ${\displaystyle \xi }$

${\displaystyle \psi ={\frac {H_{u}}{m_{H}c_{p}T_{1}\varepsilon ^{\kappa -1}\xi }}-{\frac {1}{\kappa }}+{\frac {1}{\kappa \xi }}+1}$

${\displaystyle T_{4}=T_{3}\cdot \psi }$   and   ; Temperature and volume after equal pressure combustion. T ₄ is the maximum temperature. ${\displaystyle V_{4}=V_{3}\cdot \psi }$

Diesel engine

In the diesel engine, these five process steps are implemented as follows:

• (1 - 2) The piston moves towards top dead center. The air in the cylinder is compressed. That is, work is done in the air.
• (2 - 3) The diesel fuel is injected into the combustion chamber before top dead center. The high temperature of the compressed air ignites the injection jet and the internal energy of the fuel is released in the form of heat. In this process step, this is initially done with approximately the same volume.
• (3 - 4) Due to the continuous combustion beyond top dead center, the temperature is further increased at approximately the same pressure of the combustion gases.
• (4 - 5) The combustion now ends and the combustion gas relaxes while the entropy remains the same. Technical work is carried out on the piston (force times displacement). The volume of the combustion gas increases, the pressure and temperature decrease until the piston reaches bottom dead center.
• (5 - 1) The exhaust valve is opened, the hot exhaust gas leaves the combustion chamber with overpressure. Residual gas and heat are expelled with little back pressure.

Gasoline engine

In the gasoline engine, these five process steps are implemented as follows:

• (1 - 2) The piston moves towards top dead center and the air-fuel mixture is compressed. This means that work is done on the air-fuel mixture.
• (2 - 3) The spark plug starts the combustion of the air-fuel mixture before top dead center and the internal energy of the fuel is released in the form of heat and pressure. This is initially done with approximately the same volume (isochoric).
• (3 - 4) After the top dead center of the piston, the combustion reaches the maximum pressure before the maximum temperature, which is maintained (isobaric) until the main part of the mixture is burned and the temperature drops again.
• (4 - 5) The mixture now burns completely and the fuel gas continues to relax while the entropy remains the same until the piston reaches bottom dead center. In this process phase, technical work is carried out on the piston (work cycle).
• (5 - 1) The exhaust valve is opened and the exhaust gas escapes first by the residual pressure and then by the upward movement of the piston. Energy is dissipated in the form of residual pressure and heat.

Real process in the four-stroke

Logarithmic pV diagram for four-stroke engines (including gas exchange)

Sucking in and pushing out is associated with friction and pumping losses (counter-clockwise loop in the pV diagram for the gas exchange work). The pre-injection and pre-ignition take place well before top dead center, which also has a negative impact on the useful work balance. Part of the combustion energy (in addition to the endothermic formation of nitrogen oxide and other harmful exhaust gases) is lost without any work through heat transfer to the combustion chamber walls. The maximum pressure is lower than the calculated one because of sealing losses. The expansion curve is thus below the ideal course. The outlet valve is opened before the bottom dead center, which rounds off and reduces the process area (work performance).

See also

• Carnot process (theoretical maximum thermodynamic efficiency)

literature

• Wolfgang Kalide: Pistons and flow machines . 1st edition. Carl Hanser Verlag, Munich / Vienna 1974, ISBN 3-446-11752-0 .
• Richard van Basshuysen, Fred Schäfer: Handbook Internal Combustion Engine Basics, Components, Systems, Perspectives. 3. Edition. Friedrich Vieweg & Sohn / GWV Fachverlage, Wiesbaden 2005, ISBN 3-528-23933-6 .
• Heinz Herwig: Technical Thermodynamics . 1st edition. Pearson Studium, Munich 2007, ISBN 978-3-8273-7234-5 .
• Heinz Grohe: Otto and diesel engines . 11th edition. Kamprath series, Vogel Buchverlag, ISBN 3-8023-1559-6

Web links

• Seiliger cycle .
• The perfect engine . ( Memento from November 8, 2009 in the Internet Archive ) FH-Frankfurt
• Thermodynamics . (PDF; 9.7 MB) University of Munich
• University of Duisburg-Essen (PDF; 2.6 MB)