Dynamics of heat release in a dual-fuel engine

The increasing attention to the use of dual-fuel engines with compression ignition leads to the need to study the thermal engineering processes occurring in them. A model for calculating the thermal engineering stages in a cylinder of a dual-fuel engine with a refined composition of the working fluid is presented, including the determination of fuel supply characteristics, fuel injection and evaporation functions and allowing theoretically to determine with high accuracy the pressure function, cycle operation, power, efficient and thermal criteria for the operation of a dual-fuel engine. The paper attempts to show the mutual relationship between the individual processes of heat generation, their influence on the design parameters under the operating conditions characteristic of a dual-fuel engine, as well as on the operating conditions of components and parts.


Introduction
The conversion of thermal energy into mechanical energy in a dual-fuel engine is a rather complex process.Its course in real conditions is associated with the occurrence of additional losses that are not taken into account by the second law of thermodynamics.To assess the perfection of individual processes in a real dual-fuel engine and their totality, which determines the actual cycle, it is necessary to identify the possible use of heat, characteristic of the thermodynamic cycle, in which the return of heat to a cold source is a mandatory and the only type of loss [1][2][3].
The presentation of the material is based on the classical method of theoretical analysis of the processes occurring in a dual-fuel engine, the kinematics and dynamics of the crank mechanism and the calculation of the criteria under consideration, taking into account the alternating load.The fundamentals of the theory are considered taking into account the specifics of the operation of dualfuel engines with compression ignition, taking into account the peculiarities of their operation under operating conditions and the nature of the flow of individual processes in them.The analysis of individual processes and the experimental coefficients recommended for use in calculations are based on modern data obtained by researchers [4][5][6].

Methodology
The method of calculating heat release based on an experimental indicator diagram using the first law of thermodynamics is well known, but the methods used do not take into account differences in the chemical composition of the fuel used, which leads to significant errors.The working fluid in a dualfuel engine is a mixture of gases, the volume fractions of which continuously change during the combustion stages.As the injected fuel burns out, the mass of the working fluid changes [7][8][9].Simply imagine that the working fluid at the beginning of combustion consists of air and residual gases, and as the fuel burns, the concentration of the products of complete combustion of CO2 and H2O increases in the working fluid.A to solve this problem, we will not take into account the heat dissipation for heating droplets and subsequent evaporation of fuel.The rate of heat release will have only positive values, the rate of fuel combustion will be taken in proportion to the rate of heat release [10][11][12].
When considering thermal engineering processes, we will make the following assumptions.In the cylinder of a dual-fuel engine there is a constant, irremovable amount of a working fluid that performs a closed cycle.In fact, in order to carry out the cycle, it is necessary to remove the gases spent in the previous cycle from the cylinder and ensure the receipt of a fresh portion of the working fluid.It takes work to complete this gas exchange process, which is not provided for in the theoretical cycle [13][14][15][16].Heat is supplied from the outside during a certain period of the cycle in accordance with the selected nature of its flow.In real cycles, heat in the corresponding period of the cycle is released as a result of the chemical reaction of fuel with oxygen in the air [17][18][19].The stages of combustion are complex, as a result of which it is not always in the process of chemical reaction that the fuel is completely oxidized before the release of the final combustion products.All this causes additional heat loss.The heat capacity of the non-replaceable working fluid in the cylinder is constant and does not depend on temperature.In fact, the heat capacity is variable and depends on the temperature and composition of the working fluid.The processes of compression and expansion proceed without heat exchange with the external environment.In real conditions, during these processes, as well as during gas exchange and combustion, due to significant temperature differences between the working fluid and the cylinder walls, cylinder head, piston bottom, intense heat exchange occurs, as a result of which part of the heat is lost [20][21][22].

Results and considerations
According to the first law of thermodynamics, the heat supplied Q to the working fluid is spent on changing the internal energy U of the gas and performing the work L by the gas: The internal energy of a gas mixture can be defined as the sum of the products of the expression: , where i N -the amount of i gas in the working fluid; t -working fluid temperature, K.
The temperature of gases can be determined from the classical equation: , where  -compression ratio function; a  -compression ratio at the end of the intake.
On the other hand, the basic equation of state of an ideal gas:

GRT pv 
, where G -working fluid weight, kg; R -gas constant of a mixture of gases, J/kg K. Gas constant of the substance: The mass of the working fluid changes at the stages of combustion.If the mass composition of the fuel is written as follows, as the sum of carbon, hydrogen and oxygen, then the working fluid will consist of: where q -cyclic fuel supply, g/cycle; C m , Н m -molar masses of these substances, g/mol.
The functions of the components of the working fluid, taking into account the content of residual gases, can be determined by the equations: Internal energy of the working body Let us determine the derivatives of the functions of the change in the composition of gases, then the first law of thermodynamics can be written: Heat dissipation rate: -computational studies on gas engine fuel; -experiment on gas engine fuel -calculated studies on methanol; -methanol experiment -calculated studies on ethanol; -ethanol experiment

Conclusion
The calculation of the heat release rate of a dual-fuel engine proposed in the work gives a satisfactory coincidence of experimental and calculated data, while the difference does not exceed 5-7%.
change of the mixture: withdrawn from the working fluid due to heat exchange; x -integral characteristic; 2 a , 3 a ,  -design parameters; W T -average equivalent temperature.

4
The results of the calculation according to the presented methodology are shown in figure1.

Figure 1 .
Figure 1.Results of combined computational and experimental studies of the heat release rate of a dual-fuel engine.