Study of the intake system of automotive tractor internal combustion engines with variable parameters

. Increasing the effective performance of automotive tractor engines is primarily associated with the intensification of the working process parameters. One of the options for solving this problem is to improve the cylinder filling parameters, which will allow to increase the engine power and torque. In addition to mechanical and gas turbine supercharging, the little-studied resonant supercharging of the engine is of interest. In this case, by selecting the parameters of the inlet path of the engine, it is possible to achieve a significant increase in pressure in the zone of the inlet valve opening without expenditure of useful energy, using only the kinetic energy of the gases of the inlet path. The paper proposes a method to calculate the geometric parameters of the intake tract using a one-dimensional model of gas flow. The results obtained from the numerical investigations give good convergence. The article can be useful for masters, graduate students, and engineering and technical workers involved in the design of internal combustion engines.


Review of the status of the issue
Currently, more than 90 % of tractor engines are equipped with intake systems with constant parameters, the widespread use of which is due to the simplicity of design and the lack of a well-developed methodology for determining the parameters, taking into account the operating conditions of vehicles.
However, the problem of further improvement of mixing and cylinder filling, which is the main factor determining the fuel efficiency of modern engines, remains relevant.
Analysis of the processes occurring in the inlet channel of the engine has shown that the decisive influence on the quality of mixture formation has the value of air flow velocity.At partial speed and load modes, at which the engine in operating conditions operates 90...95 % of the time, the flow rate and cylinder filling is clearly insufficient.
It is possible to increase cylinder filling by means of supercharging, both gas turbine or mechanical and resonant.This will intensify the processes of heat and mass transfer in the channel and increase the level of turbulence of the charge in the cylinder.
The working process in the flow parts of the engine is characterised by a complex threedimensional, and in many cases non-stationary flow of the working body, associated both with the geometry of the flow part and with the peculiarities of the engine layout and operating process.
Design of inlet ducts is mainly based on general mechanical engineering methods of calculation and on the vast systematised experience of practical operation of these objects.In the traditional design methodology, a considerable place (up to 30-50% of the total costs) is occupied by the costs of experimental and final research and testing, as well as by the costs of rework on the defects revealed as a result of testing [1].Therefore, the task of automating the design process within the framework of the methodology of virtual development and maintenance of the product, as well as the task of in-depth calculationtheoretical and experimental studies of diverse and complex physical phenomena and interactions occurring in the inlet channel, using modern software and methods, is of particular relevance and is characterised by increased difficulty.
In this connection the task of creating effective methods of modelling and calculation of spatial gas flows remains in demand.
Physical processes characteristic for this particular segment dominate in the flow in each element of the flow path.Accordingly, it is necessary to select suitable models and set correct problems for them for adequate description of flows in these segments.On the one hand, the model should reflect the main features of the flow and, on the other hand, be efficient.
Modelling of flows in channels is based mainly on the solution of the Navier-Stokes and Reynolds equations.The development of new difference algorithms for numerical integration of these equations is stimulated, on the one hand, by the increasing requirements to the accuracy of numerical calculations and, on the other hand, by the need to carry out calculations in unsteady formulations in the entire flow path in an acceptable time.The use of non-uniform meshes with small spatial steps raises the problem of creating implicit difference schemes with a large stability margin and effective solvability comparable to explicit algorithms [2].The necessity of serial calculations dictates high requirements to the speed of algorithms and economical memory consumption of the computer system.An important aspect is the universality of the numerical method, i.e., its applicability to a wide class of problems.
In [3,4], the authors note that wave dynamics in the intake system strongly influence the performance of non-injected internal combustion engines.A sound wave with an appropriate phase in the intake port can maintain a pressure ratio at the closing intake valve that remains favourable to the intake into the cylinder until the valve finally closes.Such waves have been shown to be caused by the resonant response of the intake duct to the effects caused by unsteady volumetric flow through the intake valve.
Detailed measurements of wave dynamics are necessary to optimise engine performance, validate engine simulation results or to better understand the physics of the intake system.
The study of the intake tract of supercharged engines is the subject of [5].Today's downsized turbocharged engines are mainly focused on improving low speed torque and mass flow rate.This is done in order to improve the overall thermodynamic efficiency of the engine.An integral part of any internal combustion engine is the air intake duct, which has a first order effect on engine filling and cleaning.The wave action that takes place is usually modelled using one-dimensional codes.A new method based on the characterisation of the intake line in the frequency domain is presented in the papers.The relationship in a wide frequency spectrum between the instantaneous mass flow rate at the valve and the dynamic pressure response is found.This model is implemented in Simulink through a transfer function and linked to GT-Power for engine modelling.An experimental shock tube campaign has been carried out for a number of tubes of different lengths and diameters.The parameters of this transfer function are measured for each case and then combined with gas dynamic theory and frequency analysis to determine the law of behaviour as a function of tube geometry.The final model is validated on a single-cylinder engine in GT-Power mode for different tube geometries.
The air intake line of an internal combustion engine is an ideal application of unsteady hydrodynamics.The reciprocating motion of the intake valves causes the generation of pressure pulses that propagate through the pipework system.In the case of a multi-cylinder engine at constant speed, the pressure emissions from the different cylinders create a system of standing waves that affect the emptying, filling and purging processes of the engine.Thus, the volumetric efficiency and output torque of the engine are affected by this wave action, which in turn depends on two factors: the engine excitation (at the valve interface) and the inlet line geometry itself.
In [6], the modelling of pressure waves in the intake and exhaust manifolds of internal combustion engines is done without using a one-dimensional description of the system.It consists in studying the system using a frequency domain approach.A dynamic flow bench is used to create this model.The latter has been modified to generate waves in the gas, which may or may not be in motion.The inlet system is then characterised by its geometrical characteristics as well as the fluid characteristics.Indeed, the gas temperature and the gas velocity strongly influence the fluid behaviour.The new model is then used to simulate pressure waves in a 1 m pipe connected to a drive motor acting as a pulse generator.The experimental and numerical results are in good agreement.
The above requirements determine the relevance of the development of new stable and economical difference schemes of higher approximation order for modelling continuum mechanics problems.

Proposed solution
Usually resonance is achieved by properly changing the length of the intake manifold so that the resonance phenomenon occurs at nominal rpm.In this case, the length of the intake manifold has to be changed to obtain the effect over the entire operating frequency range.
It is also possible to use a method of tuning the intake channels in resonance, which is devoid of this inconvenience and allows to achieve resonance without changing the length of the manifold: the initial length is chosen with the condition of resonance for one speed mode of the engine, and further tuning of the system occurs by installing one or two resonators in the intake tract.For this purpose, resonators of variable volume are connected to several (often one or two) points of the intake pipe [7,8].
By varying the volume of the resonators, it is possible to achieve resonance in the intake manifold while keeping its length unchanged.
The use of unsteady gas-dynamic phenomena in the intake systems of internal combustion engines allows to obtain a certain effect on increasing their power and efficiency.
For example, the oscillatory process of the gas column (air-fuel mixture) in the intake pipelines is able to increase the power, in particular, of four-stroke engines, by 15-20%, and for two-stroke engines it is even possible to carry out their operation (at a fixed speed mode) with the purge pump switched off [9].
The principle of inertial resonance supercharging is based on the conversion of the kinetic energy of the working body stored in the suction pipes during the suction stroke into pressure energy, which contributes to the increase in cylinder filling and engine power.
It goes without saying that rational utilisation of oscillatory processes in the exhaust pipelines could further improve the quality of engine cylinder cleaning and, consequently, further improve the performance of reciprocating engine power plants.
Experimental search for the optimum geometry of the gas-dynamic path, providing the maximum energy reserve is difficult, because it requires large expenditures of time and material resources.
On the other hand, the search for the corresponding mathematical dependencies is also very difficult in terms of calculation, if only because both the length and diameter of pipelines in the case of inertial resonance supercharging almost directly affect the supercharging process itself [10,11].
Nevertheless, as the first stage of the mathematical solution of the problem of selecting a rational geometry of the gas-exhaust duct of engines, it seems reasonable to initially try to find a way to calculate and one indicator of the intake pipeline -its length.
In solving the problem, as an initial expression for the elementary increment of the weight charge of the working body dG (air, combustible mixture) in the engine cylinder (Fig. 1).
Fig. 1.Schematic diagram of the gas path of a four-stroke engine: LS -length of the intake pipe; fs and ds -cross-section and diameter; p -flow coefficient of the intake system, including the intake valve; P0, T0 and ρ0 -pressure, temperature and density of the external medium; T', ρ' -temperature and density of air (combustible mixture) at the valve outlet; f -variable valve cross-section; ω -gas flow velocity; P, T, ρ -pressure, temperature and density of gas in the cylinder; V -cylinder volume; G -cylinder air charge.dG = μρ'fωdt -which, taking into account the differential equation of the adiabatic process of gas compression, the formula for the speed of sound in gas and the relationship between the mass of gas and its volume G = ρv -, and we obtain: The second derivative of this expression According to Euler's differential equation for one-dimensional gas flow, the integral for relatively small pressure drops, taken over some length  ′ (3) Here  ′ =      -reduced length of suction pipe.
Substituting into the basic expression for the second derivative the last equality, as well as the equation of state of the gas in differential form and the equation of adiabatic flow of gas from the pipeline into the cylinder, after a number of transformations and rearrangement of terms, obtains (T=T') (aav -average value of sound velocity in gas for the whole period of cylinder filling, Va -total cylinder volume).
For the case under consideration, the obtained differential equation describes the process of damped harmonic oscillations of pressure in the engine cylinder with respect to some average pressure p0 depending on a number of operating factors, including the length of the inlet pipe.
At constant values of the coefficients m0, k0 and free member c0 (in the further calculations a correction factor will be introduced), integral of the second-degree differential equation:  =  0  − 0  sin (√ 0 2 −  0 2  +  0 ) +  0 (8) here e is a base of natural logarithms; a0 and b0 are integration constants; k0 and m0coefficients characterising the frequency of "free" oscillations of pressure in the cylinder and the intensity of decreasing amplitude and decreasing frequency of oscillations as a result of aerodynamic resistances in the filling system.
The term in the equation for p, the member √ 0 2 −  0 2 is particularly important; it represents the actual frequency of oscillation of the gas column in the pipeline; to maximise the effect of inertia-resonance supercharging, this term must numerically correspond to the frequency of engine operating cycles, i.e., it must be set in "resonance" [12,13].
For two-stroke engines with one piston stroke per crankshaft revolution (360° p.c.i. or 2π radian), the above square root must correspond to the angular frequency ω0 crankshaft rotation; for four-stroke engines -0.5ω0, as in this case the complete working cycle is 720° p.c.i. or two revolutions of the crankshaft.
Thus, for the circular frequency of the oscillating process of the pressure in the engine cylinder, the following expression is common: in which T is the period of a single oscillation, a m is the engine speed coefficient (for a two-stroke engine m= 1, for a four-stroke engine m= 1, for a four-stroke engine m= 1; T=2).
In order to clarify the obtained mathematical dependence, we introduce a correction factor ξ into the last equality, then  = 6 ) 2   (11) According to the obvious equation of continuity of the gas flow, the cross-section of the inlet pipe is: where Vh -working volume of the cylinder, ηv -filling factor of the working volume of the cylinder; ωav -average actual gas velocity). Thus, As preliminary experimental and computational studies show, with respect to inertiaresonant supercharging, the real velocities of the ωav gas flow in the intake pipelines, in order to avoid increased aerodynamic losses and deterioration of cylinder filling with fresh charge should not exceed 30-70 m/s.
Let us assume average velocity ls for calculation of lengths ωav ~ 70 m/s.
Further, since the speed of sound in gas (air) (k=1.4 -adiabatic index; R =0.287 kJ/(kg.deg)-gas constant of air, T = 273 + Δt-average gas temperature for the period of supercharging), and the approximate increase in air temperature in the cylinder due to "inertial" compression, heating from the cylinder walls and residual gases from the previous cycle can be up to Δt =40° C, then T=273+40=313°K.

Results and discussion
For carburettor engines with a sufficiently high hydraulic resistance of the carburettor diffuser (flow velocity greater than 200 m/s), energy loss coefficient ζ0 of the gas flow in the inlet system is 2.5-4.0,giving a flow coefficient (velocity) = 0.45 -0.55.For engines with direct injection of petrol, which do not have a carburettor, and diesels, it is possible to accept μ = 0.65 -0.70.The fill factor for four-stroke engines in general is 0.8-0.9, and for inertia resonance superchargers ηv = 0.9 -1.1; the active fill time of the engine cylinders α is 260-290 ° p.c.i.
For two-stroke engines, the full purge-fill "angle" is approximately 120-150° p.c.i., but a caveat is necessary here regarding the specificity of cylinder filling conditions in these engines.
In two-stroke engines, for example, a period of refuelling or supercharging (exhaust valves closed) is preceded by a joint purge-blowing period with the intake and exhaust valves open at the same time.
For this reason, the "resonance" length of the intake pipe calculated for the joint process must necessarily be adopted for the final stage of cylinder filling in engines; in this case, the efficiency of the supercharging or supercharging process must be determined by the choice of the angular phase of the end of the overall cylinder filling process.
A further caveat concerns the question of the influence on the frequency of pressure oscillation process not only of the length but also the diameter of the intake pipe, as mentioned above.
In fact, the above adopted average gas velocity in the inlet pipelines, determined by the diameter of the pipelines, should not in almost all calculation cases guarantee the best results and there is no doubt that, strictly speaking, the refinement of this diameter should affect the dynamic properties of the inlet pipelines.
This circumstance, in its turn, will affect the characteristics of the oscillatory process of the pressure in the cylinder, first of all, its oscillation period and, consequently, the balance of the corresponding frequencies will be disturbed.
Nevertheless, it seems that even under the accepted conditions of limiting the diameter of the inlet pipeline by setting the average flow velocity, the proposed method of calculating the length of pipelines really provides the necessary result.This is due to the relatively small numerical value of the value of  0 2 relative to the value of  0 2 , in connection with what on the known square root of the difference of these values, determining the period of forced pressure oscillations in the cylinder, the first value does not significantly affect (according to the authors' calculations of pressure in the cylinder of a two-stroke engine, the squares of these numbers differ in 16 times).
Such a difference is explained by the necessity to ensure in all cases a sufficiently small aerodynamic resistance of the inlet pipe (indicator  0 ) to avoid large pressure losses and deterioration of cylinder filling.
It should be noted that the mentioned correction of 1/16 of the value of  0 2 as a first approximation, can always be taken into account in any other computational case, and even some of its discrepancy to the true value of the amplitude multiplier  0 will not introduce a noticeable error in the calculation of the pipeline length [14,15].
The proposed method of calculating the effective length of the intake pipe for an engine with inertial resonance supercharging gives a very good convergence of calculated and experimental data.Although, as it was stipulated above, the length of the inlet pipe is not the only indicator of the piston engine boosting at inertia-resonance supercharging.

Conclusion
In conclusion, it should be noted that for boosting a multi-cylinder engine by the method under consideration, the supply of the working body to each cylinder must be individual, but the individual intake pipes can, of course, be assembled into a single manifold with a throttle valve at the inlet (for petrol engines).If it is desired to improve the tractive characteristics of the engine not only at its nominal operating mode, the pipework can also be tuned to resonance at maximum torque.
In this case, the inlet pipe must have a device for "switching" the lengths.