Investigation of the combustion process in a dual-fuel engine

Modeling of in-cylinder processes occurring in a dual-fuel engine is necessary to obtain the ignition delay period as a function of the angle of rotation of the crankshaft and the subsequent calculation of its effective and environmental indicators. There is a need to identify the theoretical dependence of the fuel combustion process on the parameters that determine the operating modes of a dual-fuel engine, which leads to the need to create a mathematical model that allows the most accurate description of the combustion process, taking into account the maximum possible number of factors. The paper considers the optimization of the parameters of the workflow and the prediction of the performance of the projected and existing dual-fuel engines.


Introduction
In existing combustion models in dual-fuel engines based on the separation of the combustion stages into two or three characteristic sections, the principle of superposition of these stages in the initial and main phases is used, which is due to the complexity of the separation of combustion into these sections.Thus, in the mathematical model for a dual-fuel alcohol engine with ignition fuel, it is assumed that the stages of fuel combustion are the sum of two combustion processes developing by different mechanisms [1][2][3][4].At the same time, there is kinetic combustion of alcohol vapors entering the diesel engine and evaporating by the time ignition begins, and diffusion combustion of the ignition fuel with burning alcohol droplets that did not have time to evaporate before ignition, where each of the processes is supposed to use its own value of the parameter m.However, in a real engine, the combustion process of two fuels occurs simultaneously, affecting each other, so it is quite difficult to reliably determine when which fuel burns [5][6][7][8].In real conditions, the indicator m is not a constant value, which is due to the complex, non-stationary nature of the combustion stages, which consist of the interaction of fuel injection mechanisms and the formation of a mixture, starting with the distribution of the fuel jet of evaporation and mixing, the ignition delay period and oxidation.In addition, do not forget that the processes in the cylinder are carried out simultaneously, affecting each other [9][10][11].

Methodology
According to the model of professor Ivan Vibe, heat generation in integral form is described by the equation:  The process indicators change as follows.After the ignition delay period φi, a short-term flash and burnout of fuel vapors and their incomplete oxidation products formed during this period φi follows.
There is an explosive increase in the concentration of active reaction centers associated with the decay of intermediates and intensive branching of chains.Shortly after ignition, the concentration of active centers and the rate of combustion reach a maximum, after which they also decrease sharply due to the burnout of fuel vapors formed during the period φi [12][13][14][15][16].
If we assume that the parameter m is constant throughout the combustion process, then we can determine the integral and differential heat generation, as well as the relative density of effective centers.At a constant value of the parameter m, the density of effective centers will increase sharply, followed by its monotonous decrease, while in a real engine the combustion process may already have time to complete by this time and, accordingly, the concentration of active centers will fall to a minimum.In real conditions, the indicator of the nature of combustion changes during the combustion process m is not a constant value, which is associated with a change in the rate of combustion and the limiting role of the physical processes of evaporation and diffusion [17][18][19][20][21].
The study of heat release allows us to conclude that combustion takes place in difficult conditions.Initially, the fuel ignites and burns quickly at the periphery of the torch, then the flame penetrates to the core, local foci of flame appear around local accumulations of evaporating fuel.The intensity of combustion of the main portion of fuel enclosed inside the flame largely depends on the intensity of oxygen entering the combustion zone and the removal of combustion products [22][23][24].At the same time, the combustion products formed on the periphery of the torch or the local flame focus isolate this focus and hinder the flow of oxygen into the combustion zone.In this regard, at the initial moment with the rapid development of combustion reactions, oxygen consumption in the combustion zone exceeds the flow of free oxygen from the periphery or the surrounding zone.Combustion is incomplete in this case, an increase in the volume fraction of carbon monoxide and other incomplete combustion products is recorded in the cylinder.Due to this, it can be concluded that when describing the combustion process in dual-fuel engines, it is impossible to operate with the oxygen concentration averaged over the entire volume of the cylinder [25][26][27].

Results and considerations
The characteristics of burnout practically do not depend on the type of fuel used and are determined mainly by the utilization factor of the air charge: , where С and h -proportionality coefficients; Z  -the ratio of the current angle of rotation of the crankshaft to the actual duration of combustion.
The proportionality coefficients are determined by the formulas: Since the branched chain process of oxidation and decomposition of fuel depends on the concentration of the oxidizer in the combustion zone, it is necessary to determine the concentration of oxygen and the local coefficient of excess air.The oxygen concentration in the combustion zone depends on the intensity of oxidation, heat release and the rate of turbulent exchange between the sections of the combustion chamber.The rate of oxidizer supply to the combustion zone can be approximated by the function of the air charge utilization factor, experimentally verified by Nikolai Razleitsev by the expression.At the same time, the number of active centers increases proportionally as the vaporized fuel enters the combustion zone and decreases as the fuel burns out [28][29][30].
Then the concentration of active centers can be determined by the equation: , where A and B -proportionality coefficients; E -activation energy of the formation of new active centers, J/mol; σ -amount of vaporized fuel.
The density of active centers during the operation of a diesel engine by a dual-fuel process can be defined as the sum of active centers formed as a result of pre-flame processes in the flare of both fuels by the expression: , where E1, E2 -conditional activation energy for the first and second fuels, J/mol; σ1, σ2 -the amount of vaporized first and second fuel.
To calculate the relative density of the active centers, it is necessary to determine the masses of the fuel that entered the cylinder and evaporated.The evaporation rate significantly depends on the characteristics of fuel injection and atomization, as well as the physical properties of the fuel-air charge.Vaporization of a sprayed fuel torch under conditions of a dual-fuel engine is a complex process characterized by unsteadiness, complex dynamics of the torch and individual droplets, a complex structure of the torch in length and cross-section, the presence of droplets of different diameters with different residence times, as well as significant temperature and concentration heterogeneity.An accurate analytical calculation of the fuel torch, taking into account all the above features, is a rather laborious task, therefore we will use an approximate method for calculating the evaporation of a spray fuel torch with well-studied patterns of evaporation of individual droplets.This approach to solving the problem is due to the fact that the fuel torch has a droplet structure, and its evaporation rate is the sum of the evaporation rates of individual droplets [31][32][33][34][35].
The evaporation of each drop before and after ignition of the fuel is subject to the following law: The fuel torch is an ensemble of droplets of various diameters, however, the fuel equipment of modern forced diesel engines provides a fairly uniform atomization of fuel, especially at the main injection site, so the calculation of fuel evaporation can be carried out by a drop of medium diameter according to the Zauter method d32: In the absence of experimental data, the value of the diffusion coefficient can be approximately calculated using the Gilliland formula: The evaporation function of a drop of mass m on the basis of Sreznevsky 's law will take the form For further investigation of the combustion process, it is necessary to determine the angle of the ignition delay period.To calculate the ignition delay period, we suggest using the following methodology based on this dependence: -computational studies on gas engine fuel; -experiment on gas engine fuel -calculated studies on methanol; -methanol experiment -calculated studies on ethanol; -ethanol experiment  The figures show the results of combined computational and experimental studies of the ignition delay period of a dual-fuel engine.

Conclusion
This technique allows the most complete analysis of changes in the ignition delay period, maximum pressures, pressure rise rate and temperatures depending on the composition of the fuels used, as well as depending on changes in fuel supply conditions.Additionally, this calculation allows us to take into account the cooling of the working fluid associated with the evaporation of fuel, and also takes into account intermediate parameters differing in their physical properties according to the principle of additivity.

z
-conditional duration of the combustion process; z x -the proportion of fuel burning by the time of the practical end of the reaction.


-the average coefficient of excess air in the combustion zone; v  -the average coefficient of excess air throughout the cylinder.The function ) (  can be satisfactorily approximated by the dependency:


-coordinates of the minimum of the function ) (  . , the initial and current diameter of the drop; K -evaporation constant; e  -the time from the beginning of evaporation of this drop (the moment it enters the considered zone) to the current moment.
parameter determined by the nozzle design and injection features; b W -the value of the Weber criterion at the average injection rate av U ; c d -diameter of nozzle holes;  -density; M - criterion characterizing the ratio of surface tension, inertia and viscosity forces.The Weber criterion is determined from the expression: the value of the surface tension of the fuel, N/m.The average injection rate is calculated by the formula: flow rate, depending on the design features of the sprayer; f -total area of nozzle holes, m 2 ; in t -duration of injection, with.The criterion M can be determined from the equation: dynamic viscosity of fuel, Pa•s.The evaporation constant of the atomized fuel torch in the first approximation can be determined by the evaporation characteristics of a single drop: Nusselt criterion; р D -diffusion coefficient; s p -saturated vapor pressure; g - acceleration of gravity, m/s 2 .The Nusselt criterion is the dependence of the mass evaporation rate of a drop on the intensity of convection.The criterion can take different values depending on the evaporation zone.The saturated vapor pressure can be determined by the Antoine formula: B -coefficients determined by reference data.The vapor diffusion coefficient is expressed by the formula: diffusion temperature; T -diffusion temperature; a v , b v -molar volumes of diffusing gases A and B; a M , b M -molecular weights of gases.


-ignition delay period, degree of rotation of the crankshaft; in  -injection duration, degree; f  -fuel density, g/cm 3 ; in  , R in  -the fuel injection advance angle in degrees and radians, respectively; e  -dimensionless temperature at the start of injection; А, f К -factors taking into account the physical properties of fuel;  -the ratio of heat release and runoff characteristics; a, a1 - coefficients depending on the design parameters of the diesel engine and fuel supply parameters.

Figure 1 .
Figure 1.Results of combined computational and experimental studies of the ignition delay period of a dual-fuel engine.