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Reporte Técnico RT-ID- 012/2003

Intake and exhaust system optimization of internal combustion engines Juan Pablo Alianak y Norberto Nigro Departamento de Ingeniería Escuela de Ingeniería Mecánica Facultad de Ciencias Exactas, Ingeniería y Agrimensura Universidad Nacional de Rosario

Disciplina: Ingeniería Mecánica

Enviado 10 de Octubre de 2003 Revisado

Secretaría de Ciencia y Técnica Facultad de Ciencias Exactas, Ingeniería y Agrimensura Universidad Nacional de Rosario Av. Pellegrini 250 - 2000 Rosario – Argentina http://www.fceia.unr.edu.ar/secyt

Este documento es publicado por la FCEIA para su consulta externa. El mismo se publica como Reporte de Investigación para divulgación de las tareas científicas que se desarrollan en la FCEIA, Universidad Nacional de Rosario. Los autores conservan los derechos de autoría y copia de la totalidad de su trabajo aquí publicado. Luego de su posterior eventual publicación externa a la FCEIA, los requerimientos deberán dirigirse a los autores respectivos. El contenido de este reporte refleja la visión de los autores, quienes se responsabilizan por los datos presentados, los cuales no necesariamente reflejan la visión de la SeCyT-FCEIA. Tanto la SeCyT-FCEIA como los autores del presente reporte no se responsabilizan por el uso que pudiera hacerse de la información y/o metodologías publicadas. Cualquier sugerencia dirigirla a: [email protected]

Un trabajo basado en este pero resumido ha sido enviado recientemente a la Revista International Journal of Engine Research y hasta el momento no hemos recibido respuesta de parte de ellos acerca de su recepción

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Optimización del sistema de admisión y escape de un motor de combustión interna Juan Pablo Alianak* y Norberto Nigro** Departamento de Ingeniería Escuela de Ingeniería Mecánica Facultad de Ciencias Exactas, Ingeniería y Agrimensura Universidad Nacional de Rosario El diseño de motores es uno de los proyectos mas desafiantes de la Ingeniería Mecánica. Esto es principalmente debido a la gran cantidad de variables involucradas. Mas aún, los motores de alta performance aplicados a vehículos de competición necesitan un estudio detallado y una muy profunda tarea de optimización con el fin de alcanzar los más altos índices de potencia específica. Entre los diferentes factores que influencia el rendimiento de un motor la eficiencia volumétrica parece ser uno de los mas importantes. Este índice mide la capacidad de aspirar de un motor asociado a las carreras de carga de mezcla fresca y barrido de gases quemados a través de los sistemas de admisión y escape. Siguiendo los últimos avances científicos en cuanto a las capacidades computacionales, los métodos numéricos basados en la teoría de a dinámica de gases aparecen como muy atractivos para resolver este tipo de problemas. En general estas ecuaciones son acopladas con otras de índole termodinámica aplicadas a los principales componentes del motor tal como cilindros, tomas de aire, tanques o recipientes de volumen fijo, silenciadores, etc. Debido a los simples modelos fenomenológicos incluidos en el sistema del motor, un gran número de coeficientes empíricos necesitan ser estimados. Esta tarea involucra mediciones experimentales combinadas con una buena estrategia para vincularlos con los principales parámetros incógnitas. No obstante, no solo la dinámica de fluidos y la termodinámica juegan un rol crucial sino también la respuesta mecánica del tren de válvulas completo es muy importante para optimizar la eficiencia volumétrica de un motor. En este sentido la teoría de sistemas multi cuerpos puede asistir en el entendimiento de cómo las no linealidades influencian el comportamiento dinámico del tren de válvulas completo. Este trabajo presenta una nueva estrategia para calibrar el software de un motor y una metodología de diseño óptimo de levas para trenes de válvulas de motores de combustión interna basada en un análisis combinado de la termodinámica, la dinámica de gases y la mecánica. Palabras claves: : Dinámica de gases, motores de combustión interna, admisión y escape, tren de válvulas

Intake and exhaust system optimization of internal combustion engines Engine design is one of the most challenging mechanical engineering projects. This is mainly due to the huge amount of variables involved. Moreover, high performance engines applied to a racing car need a detailed study and a very good optimization task in order to achieve the highest indices of specific power. Among the different factors that influence the engine performance, volumetric efficiency seems to be one of the most important ones. This index measures the breathing capacity of an engine associated with the gas charge process through the intake and exhaust systems. following Following the latest advances in computers capability, numerical methods whose principal equations come from the gas-dynamic theory have been applied to solve this problem. In general, these equations are coupled with thermodynamic equations applied to the principal devices of an engine, such as cylinders, air intake, tanks, mufflers, etc. Due to the very simple phenomenological models included in the engine system, a number of empirical coefficients need to be estimated. This task involves experimental measurements combined with a good strategy to link them with the main numerical unknown parameters. However, not only fluid dynamics and thermodynamics play a crucial role, but also the mechanical response of the whole valve train is very important to optimize the volumetric efficiency of an engine. In this sense, the multibody system theory can be of assistance in order to understand how the nonlinearities influence the dynamic behavior of the whole valve train. This paper presents a new strategy to calibrate an engine system software, plus a methodology to design optimal cams for valve trains of internal combustion engines based on thermodynamics, gas dynamics and mechanical analysis. Keywords: Gas dynamics, internal combustion engines, optimization, intake and exhaust, valve train. * [email protected] **[email protected] 3

Introduction Today, the fast advances in computer hardware make it possible to reproduce an engine test virtually and with high accuracy before going to the laboratory for fine-tuning. In this way, an important amount of development lead-time in trials and errors is saved. The strong influence of the intake and exhaust system dynamics on the volumetric efficiency and eventually on the engine performance is well known. A strong effort was developed since the publication of two of the pioneer papers in this area [1, 2] written with an analytical and graphical point of view.Earlier contributions were based on characteristic method [3, 4]. In the last decade a great number of robust and accurate algorithms was developed for the gas dynamics and wave propagation in multi-dimensional configurations. One of the main research lines has got robust and fast algorithms for unstructured grids in very complex and variable geometries. On the other hand, numerous scientific papers have been published with the aim of attaining high resolution schemes in very simple geometries like a one dimensional domain. The results obtained by the CFD community along this research line have been very fruitful and they can be used in the simulation of more complex dynamic systems in which the assumption of one dimensional flow is valid. This is just the case in an internal combustion engine where the flow in manifolds can be approximated through this assumption without losing much accuracy, the main goal of the analysis being the tuning effects. Joining CFD schemes for the manifolds with some thermodynamic models for cylinders, tanks, junctions and valves, it is possible to build a computational tool for the whole engine system that is able to predict its performance before going through more expensive laboratory experiments. Finally, the actual observation in the laboratory determines the degree of accuracy in the simulation, which allows us to do finer adjustments to reach the target. This project began some years ago with the development of a singlecylinder four stroke spark ignition engine simulator. The mathematical model is based on a thermodynamic and a one dimensional gas dynamics description of the intake and exhaust system published earlier [5]. Later, multi cylinder configurations were added to this development in order to enhance this predictive tool. The Euler equations arising from the gas dynamics model were solved using two different numerical approximations, a streamline upwind Petrov-Galerkin finite element method (SUPG-FEM) [6, 7], and also a high resolution finite volume scheme called total variation diminishing (TVD) [8], with no significant differences in the results obtained with them. For the coupling of tanks and cylinders with pipes, a model based on a nozzle analogy is used [9], allowing for the possibility of subsonic or sonic flow condition through the intake and the exhaust valves. The coupling of pipes and the junctions is solved using a model based on a pressure equalizer coupled with mass and energy balance equations, characteristic propagation equations, and an entropy equalizer for the outgoing branches at the junction [10]. Much work is currently being done along this research line since the code validation is a very intricate subject. The inherent difficulties in getting detailed measurements in engine configurations compel us to take indirect and global measures in order to estimate some engine operation parameters. The selection of this strategy is crucial for the software reliability, and good predictions are necessary for design improvements. Nowadays this open problem is subject of debate; how to combine in an optimal way the theory and the available measurements to get good software calibration is the question to be answered. This is one of the main topics that this papers covers, and a novel strategy is proposed as an answer to the scientific community. Besides, there is a real need to combine gas dynamics, thermodynamics and mechanical analysis in order to optimize the volumetric efficiency of an internal combustion engine. While thermodynamics is mainly necessary to solve the power cycle of the engine operation, 4

the flow pattern is crucial to understand how the pressure waves interact with the valves timings, drastically influencing the pumping work in the engine cycle. But these two phenomena are not enough to predict the engine performance. The mechanical behavior of the involved mechanism is also responsible for the normal operation of the engine. The valves timings, the mechanical reliability and the durability will be warranted only if the mechanical response is under control. This kind of analysis is not frequently reported in the literature, probably because there is a standard division between fluid dynamics and solid mechanics for researchers on computational mechanics. This paper also presents an optimization task linking these three great areas in order to improve the valve train design. This methodology can easily supplement our daily work so as to get better control on the whole engine behavior. The first section of this paper is a brief description of the mathematical and numerical modeling of the gas dynamics and thermodynamics equations used for the engine system. The following section presents the code calibration with a few new available basic measurements in order to link them with the main unknown parameters in the model in order to reproduce accurately the engine power recorded in the laboratory. The next sections deal with the intake and exhaust timings optimization task, the optimal cam profile generation and finally the mechanical response verification. The final section is for conclusions.

Numerical models for the gas dynamics and thermodynamics in an internal combustion engine Historically, researchers and engine designers following Heywood [11] and Ramos [12] have been using four different categories of internal combustion engine models: 1. 2. 3. 4.

air standard cycle simulation, zero and quasi-dimensional thermodynamic models, a combination of zero dimensional and one dimensional models, multidimensional models

The first approach was used in the past when only human work was available and there were no computer capabilities. The limitation of this kind of model was in the prediction of the pumping cycle, when the influence of the gas dynamics in the manifolds is crucial. Following in complexity, the zero dimensional thermodynamic models offer the possibility of including the unsteady behavior of the system and the variable thermo physical properties along the whole cycle. Because of its simplicity, the emptying and filling models [13] may result an attractive technique for the intake and the exhaust system. It consists of assuming a fixed volume for each manifold and follow their time evolution with a spatial average for the thermodynamic variables. In this sense, this strategy represents a significant improvement in relation to the earlier models because the gas charging process can be added to the whole computation and tuning may be predicted. However, the traveling waves in the manifolds are not represented at all because of the spatial averaging. In order to include this effect that has a significant influence on the volumetric efficiency, the following model includes a one dimensional representation of the gas flow inside the manifolds solving the mass, momentum and energy balance in each tube of the whole engine network [5, 9, 14, 15, 16, 17]. A simple spatial discretization is adopted using a robust numerical scheme to solve it. It is possible to solve the entire engine configuration including a number of devices like cylinders, mufflers, manifolds, tanks,

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junctions, carburetors, air cleaners, catalytic converters, and so on, with an accuracy level that depends strongly on experimental measurements to calibrate the whole model. The last kind of model deals with multidimensional or CFD models that includes the whole three dimensional domain with the added complexity of treating moving boundaries, turbulent flows, and reactive flows. This kind of model requires powerful computer resources like parallel processing on cluster of personal computers or workstations and they are only used for special purposes. As mentioned above, the goal of the engine simulator is to predict the engine performance allowing for some modifications in order to improve it. Generally, the engine software of thermodynamic based models solving the flow in the manifolds by a one dimensional CFD scheme is composed by: a set of cylinders, the intake and exhaust ports and valves, the intake and exhaust manifolds air intake or tanks junctions A brief description the devices mentioned above is included below; readers interested in these topics can refer to the papers published in the related literature [5, 9, 14, 15, 16, 17, 18, 19]

Cylinder model This model assumes the cylinder to be a variable volume reactor. In general, it is an open thermodynamic system with the inlet and outlet represented by the intake and exhaust valves. The model is composed by the mass and energy conservation equations and the ideal gas law assumption. dm = ∑mj dt j dE = ∑ h j − pV + Q dt j p

= R gas T ρ where m is the cylinder trapped mass, E is the internal energy of the cylinder contents, h is for the entalphy, ρ ,p and T are the density, pressure and temperature inside the cylinder, V is the cylinder volume, Q the heat flux through the system and R is the gas constant employed in the ideal law. To close this model the following models are added: the crank rod mechanism model a combustion heat release model a heat transfer model a model for the flow through ports and valves The first model establishes the piston position at each time step solving the motion of the crank rod mechanism analitically. Using the expression for the piston position in time,

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the heat transfer surface area, the combustion chamber volume and its time variation are computed straightforwardly using one of the following expressions:

s = a cos(θ ) + l 2 − a 2 sin(θ ) 2 A = Ach + A p + πDc (l + a − s ) V = Vc +

πDc2 (l + a − s ) 4

where θ is the crank angle, Vc is the clearance volume, Dc is the cylinder bore, l is the connecting rod length, a is the crankshaft radius, Ach is the head cylinder surface area and Ap is the crown piston surface area. The combustion is solved using a single zone model in which the burned fraction of fuel is computed by the Wiebe function [11], an empirical based formula that expresses the burning rate as a function of the combustion duration. The well known Woschni or Annand heat release models may be used for the heat losses estimation from the hot gases inside the cylinder through the combustion chamber walls to the cooling system [20, 21]. Mathematically these models are written as: Qht = A h (T − Twall ) This model consists of a simple analogy with flow over a flat plate [22] adjusted by experimental measurements to estimate the heat losses to the engine cooling system. The main feature of this model is the correlation between the Nusselt, the Reynolds number and the Prandtl number, which allows us to compute a convective film coefficient (h in the above expression). A and Twall are the heat transfer surface area and the cylinder wall temperature respectively. For the flow through poppet valves, the treatment is split according to the flow direction following a model extracted from the earlier Benson papers[9]. In both cases a simple analogy with flow through nozzles is done, and sonic condition is only possible for the exhaust valve. For inflow condition the process is treated as subsonic and isentropic. This condition is generally found for normal intake or for exhaust with backflow at the end of its stroke. For outflow from cylinder to the pipe through the exhaust valve, a simple analogy with a convergent nozzle that may be chocked or not depending on the pressure jump between the cylinder and the exhaust manifold is used [9]. The same model is also used for backflow at the intake valve where normally chocked condition is not established.

Manifolds Manifolds are three dimensional curved ducts with variable cross section in which the flow inside has a very complex behavior. Because performance prediction of an internal combustion engine is the main target and due to the computer resources available a one dimensional approach is adopted for such a device. This approximation allows us to represent the pressure waves developed inside the manifolds, which makes it possible to 7

gain an insight into the gas dynamics inside the engine. The gas motion affects the tuning and therefore the global performance through the volumetric efficiency. In order to include effects like variable cross section, viscous friction, and wall heat transfer in a one dimensional description, some source terms are defined. Then, an inviscid gas dynamic model represented by the Euler equations enhanced with extra sources terms to account for these effects is used to predict the gas motion during the charge and discharge processes. The numerical computations are carried out by an upwinding finite element scheme using the well known SUPG method [6, 7] or a finite volume high resolution scheme like a second order accurate TVD scheme [8] with similar results. For more details see [5, 11, 15, 17, 19].

Tanks It is a particular case of a cylinder (chamber) with a fixed volume. Therefore, its model is similar to the cylinder model with neither piston work nor combustion heat generation. In this work the tank is also considered as adiabatic. The links between each tank and the set of manifolds connected to them is solved using the same valve model used for the cylinders but now considering the flow area to be the same as the cross section of each tube connected to the tank.

Junctions Branch junctions are frequently found in the intake and exhaust systems of multi-cylinder internal combustion engines. They are one of the most complex boundary conditions for wave action models. The one employed in this work [10] is based on the following equations: mass balance at the junction energy balance at the junction the conservation of the incoming Mach lines characteristic corresponding to each pipe end the conservation of the incoming path lines characteristic the pressure is uniform in all the N branch junctions the equalizing of the outgoing entropy or enthalpy Let the junction be defined as the intersection of p incoming tubes and q outgoing tubes, with p + q = N the total number of tubes at the junction. Mathematically this model can be written as: 1. mass conservation N

•

∑m j =1

j

•

m j =ρ jFju j ⋅ n j

= 0 with

2. energy conservation N

•

∑ h j = 0 with j =1

•

•

hj= mj(

c 2j

1 + u 2j ) (γ − 1) 2

3. conservation of the incoming Mach lines dp du ( ) j + α j ρ j ,in c j ,in ( ) j dx dx 4. conservation of the incoming path lines 8

∀j

dp dp ) j − c 2j ,in ( ) j ∀j ∈ p dx dx 5. equal pressure at all branches pi = p j ∀i ≠ j (

6. equal entropy at all the outgoing branches c 2j ci2 1 2 1 + ui ) = ( + u 2j ) ∀i ∈ q , i ≠ j , j ∈ q ( (γ − 1) 2 (γ − 1) 2 All the models above are solved in a time marching procedure using an explicit scheme; the nonlinearities are solved by a Newton method that proves to be very robust.

Code calibration This section starts with a preliminary numerical example in which the results achieved with the 1D engine simulator serve as rough calibration of the code for future design purposes. Other numerical results and also experimental measurements are available for this example [19]. This example is a good starting point to detect differences in the code implementation prior to moving to real engine tests in which the differences in the results come from several factors very difficult to identify, specially those concerning data uncertainties. Many other academic examples not included in this paper have been tested showing in general a good agreement.

An academic example The table below shows the main parameters of the engine used for this preliminary example. The rest of the data set is described in the related literature [19]. Engine Model Displacement volume Bore x Stroke Rod connected length Compression ratio IVO IVC (lift = 0.0001 m) EVO EVC (lift = 0.0001 m)

FIAT, 4 cylinder GDI 1.60E-03 m3 0.08051 x 0.0784 m 0.1285 m 11.5 7° BTDC 47° ABDC 45° BBDC 5° ATDC

Table 1: Engine data – Example 1 The engine configuration is sketched in figure, 1 which shows an EGR valve recycling burned gases from the exhaust to the admission. The main goal of this example is the tuning of the EGR and throttle valve openings for a preset value of the residual gases trapped in the cylinder charge to have an idea about the control of this kind of system. One of the main changes relative to the original problem definition is the usage of a different valve lift profile where only the maximum lift and the timings were kept. Another difference

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is the absence of a swirl valve placed at the intake port. In this example, only a straight tube was placed with only one valve having the same geometric area as the two valves of the original configuration. The original work includes simulation with and without EGR system and for three engine speeds. In this work we only include results with the EGR system. Figures 2 to 4 show the pressure at the intake plenum for 1000 rpm, 2000 rpm and 4000 rpm respectively. Increasing the engine speed produces an increment in the amplitude of the pressure waves located at the intake plenum and also a change in the shape of the pressure wave. Figures 5 to 7 show the intake plenum temperature where the mean value ncreases drastically with the engine speed, as well as the amplitude of the temperature variation inside this tank. Throttle Air valve Cleaner Intake Plenum Intake manifolds

EGR valve

Cylinders Exhaust manifolds

Catalytic converter Muffler

Figure 1: Engine configuration – Example 1

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Figure 2 Plenum pressure– 1000 rpm with EGR

Figure 3 Plenum pressure– 2000 rpm with EGR Figures 8 to 10 show the cylinder trapped mass. There is more trapped mass for 2000 rpm than for 1000 rpm, but increasing to 4000 rpm produces a drop of the mass trapped probably due to a lack of intake and exhaust tuning.

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Figure 4 Plenum pressure– 4000 rpm with EGR

Figure 5 Plenum temperature– 1000 rpm with EGR

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Figure 6 Plenum temperature– 2000 rpm with EGR

Figure 7 Plenum temperature– 4000 rpm with EGR

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Figure 8 cylinder trapped mass 1000 rpm with EGR

Figure 9 cylinder trapped mass – 2000 rpm with EGR

14

Figure 10 cylinder trapped mass 4000 rpm with EGR

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Experimental data and results The following tables show some experimental data and results. Regime (rpm)

Plenum pressure (Pa) 8.38E+04 9.01E+04 6.75E+04

1008 2005 3999

Plenum temperature (Kelvin) 335 334 355

Exhaust temperature (Kelvin) 493 657 998

Table 2(a): Experimental results – Example 1 Regime (rpm)

Trapped Mass (Kg)

% EGR

1008 2005 3999

0.302E-03 0.330 E-03 0.259 E-03

29.2 18.5 11.2

Table 2(b): Experimental results – Example 1 The diameters of the throttle and EGR valves are included in the following table: 1000 rpm EGR 2000 rpm EGR 4000 rpm EGR

Throttle valve 0.010 m

EGR valve 0.006 m

0.014 m

0.0073 m

0.016 m

0.007 m

Table 2(c): Experimental data – Example 1 In this example the strategy was based on fixing the throttle and EGR valve diameters according to table 2 (c), and the trend of the results obtained was in agreement with a similar analysis over the available measurements, specially with EGR, trapped mass and the average values of pressure and temperature at the intake plenum.

Real engine test This methodology was used on two types of engines: a Mitsubishi Lancer with a direct acting overhead cam-valve gear configuration and an overhead valve cam in block valve gear Chevrolet engine. For the sake of brevity, only results on the latter are included here.

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As mentioned above, the ultimate goal of this test is the manufacturing of a new and more promising camshaft that will improve engine power performance. The numerical strategy adopted for this task is below: 1. Finding a new valve timing capable of enhancing the power curve in a wide range of engine speeds using the engine simulator. No fuel consumption and emissions were taken into account. 2. An optimal valve profile [23] based on kinematics arguments is obtained with this new valve timing. 3. With this valve profile the corresponding cam profile is generated by an inverse method using Mecano software. 4. A computational prediction of the new cam profile dynamic response inserted in the valve train is done using Mecano software. Geometric interferences, mechanical stresses and valve floating are the main topics to be analyzed. The first step is purely a thermodynamics and gas dynamics analysis, the second and the third are based on geometric arguments and the last is a mechanical verification of the design.

Six cylinder engine test – Stage 1 The first item above consists in optimizing the engine performance mainly by changing the valve timings. Changes in the maximum valve lift were avoided because the piston and the valve are closely mounted to allow for changes in this value in the current operation of this engine. This first task was performed using the engine simulator presented in this paper. The engine configuration of the six cylinder Chevrolet engine is shown in figure 11, and details about it are included in the next paragraphs.

Sensor 2

Sensor 3

Sensor 4

Sensor 1

Intake manifold

Exhaust manifold

Cylinder

Figure 11: six cylinder engine configuration

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Intake manifolds: formed by ten tubes and four junctions connecting them. The carburetor is considered to be at wide open throttle, and due to this operation condition the pressure drop through it is neglected. The wall temperature of these tubes is considered uniform at a value of 293 Kelvin degrees. Cylinder head: formed by a piece of manifold modeled as a tube and a valve modeled as a nozzle for each side, the intake and the exhaust ports. Cylinder: with 0.097m of bore, 0.0675m of stroke, connecting rod length of 0.163m and a compression ratio of 9.5:1. The wall temperature was taken in relation to data available from the experimental data set, mainly the oil and water temperature. Exhaust manifold: formed by nine tubes and three junctions

Calibration of six cylinder engine In order to make the predictions more accurate, a calibration of the engine simulator with experimental measurements obtained from a real engine test is needed. After this process, it is possible to propose some modifications in order to improve the engine design. The mathematical model of the engine contains some uncertain parameters that introduce errors in the computation. Supplementing the model with information from the real test minimized those errors. The following data coming from the real test were used: a) Flowmeter: The flow rate of air through the cylinder head as a function of the lift of the valve is measured. This test is performed in a static way, modifying the position of the valve step by step and forcing the air through the gap between the valve and the seat through a vacuum of ten inches water column. Thus it is possible to get an idea of the influence of the three dimensional effects present in the cylinder head, which was not considered with the engine simulator. On the other hand, the dynamic behavior coupled with the three dimensional flow pattern is not reproduced by this type of test. However, this kind of information is useful in order to adjust the flow rate of fresh mixture through the cylinder head. By comparing these measurements with those obtained doing the same test in a virtual way it is possible to compute the discharge coefficient, which is one of the parameters to be adjusted. b) Air consumption : the information of the air consumed by the engine in the real test is also available. It is very useful information when it comes to doing extra adjustment of the discharge coefficient with the engine speed.

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DISCHARGE COEFFICIENT 0,35 0,30

CD

0,25 0,20 0,15 0,10 0,05 0,00 0

5

10

15

20

Valve lift [mm]

Figure 12: Discharge coefficient from flowmeter measurments

Figure 12 shows a typical discharge flow coefficient curve obtained through a port flowmeter test c) Exhaust temperature: One of the main drawbacks of most engine simulators oriented to race applications is the need to introduce estimations of the combustion duration. As the combustion is modeled with a single zone model, it is one of the main unknown parameters that should be input in the computation. As far as the authors know, the novel methodology proposed in this paper, which is able to estimate the combustion duration through measurements of the exhaust temperature, has never been published before in the related bibliography. In the real test some thermocouples were placed at a distance of 0.300 m from the cylinder head. By working out averages with these temperature values over the six cylinders and repeating these measurements for the whole range of engine speeds used in its normal operation, it is possible to get an idea of how long the combustion lasts as a function of the engine speed. When plotting the temperature curve versus. rpm and approximating this behavior with a curve, the following two features should be remarked: 1-

The slope of the approximate curve represents the sensitivity of the combustion duration with the engine speed, i.e. the ratio between the time consumed for the combustion of the whole fresh mixture at high engine speed in relation to that at low engine speed. This argument is based on the assumption that the increasing in the exhaust temperature may be caused by a delayed quenching of the flame front.

2-

The value of the exhaust temperature represents how long the combustion takes for an specific engine speed.

This assumption was checked on the engine simulator using different combustion durations and keeping the ignition angle fixed until the exhaust temperature away from the cylinder agrees with the experimental measurement. These computational results allow us to quantify this lack of information about the combustion duration. On the other hand, looking at the

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torque and fuel consumption plots of the real engine it is possible to enforce the combustion duration results obtained with the above mentioned procedure. d) Torque and power curve: This information is used to scale the convective heat transfer film coefficient in the Woschni or Anand model. This parameter mainly change the level of engine power keeping the curve shape unaltered.

270 250 230 210 190 170 150 5500

6500

7500

8500

Curve 1

9500

10500

Curve 2

Figure 13: Power for different convective film coefficient Curve number two in figure 13 was obtained using a convective film coefficient smaller than that of curve number one producing a larger power. e) Fuel and air consumption. Fuel and air flow rate allows us to adjust the equivalence ratio of the fresh mixture going into the engine. This information is necessary due to the fact that the engine tested uses carburetor for fuel metering. The table below summarizes the strategy adopted : Real Data Head cylinder flowmeter Exhaust temperature Torque and power Fuel and air consumption

Adjusted variable Discharge coefficient Combustion duration approximated by a straight line Convective heat transfer coefficient Equivalence ratio of fresh mixture

Table 3: Real data and adjusted variables used for calibration Results after calibration In the pictures below both the simulation results and the experimental ones obtained in the laboratory can be plotted. Figure 14 shows the torque and power curve, figures 15,16 and 17 show the temperature of the exhaust gases, the air flow rate and the fuel consumption respectively.

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The difference between the simulated and the real fuel consumption is mainly related to the fuel metering of the engine; the carburetor in the real engine does not keep the equivalence ratio fixed with the engine speed (rpm), and the engine simulator was used with a fixed value obtained by an average of the real ones. After the calibration the curves achieved by the engine simulator agree quite well with the real ones. Remarks 1. the simulator has the necessary calibration to be used as a good diagnostic tool for this engine, 2. after the calibration, improvement of the engine is feasible. In order to achieve this, one of the main variables to optimize are the valve timings. 3. Regarding the assumption of the variable combustion duration in relation to the engine speed, the fuel consumption (figure 17) does not show a significant variation at different engine speeds while the torque (figure 14) drops drastically at high rpms. Assuming that the fuel is completely burned, the fact that the combustion duration at high rpm is longer than that at low rpm can be inferred.

290 270

[HP] [Nm]

250 230 210 190 170 150 5500

6500

7500

8500

9500

rpm Torque_Sim

Power_Sim

Torque_exp

Power_exp

Figure 14: Experimental versus simulation torque and power

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1500 1400

[ºF]

1300 1200 1100 1000 900 800 5500

6500

7500

8500

9500

10500

rpm Temp_Sim

Temp_exp

Figure 15: Exhaust temperature

1500

[Lbs/Hr]

1400 1300 1200 1100 1000 900 800 5500

6500

7500

8500

9500

rpm Mass air sim

Mass air exp

Figure 16: Air mass flow rate

22

10500

115

[Lbs/hr]

110 105 100 95 90 85 80 75 70 5500

6500

7500

8500

9500

rpm Mass fuel sim

Mass fuel exp

Figure 17: Fuel mass flow rate

Intake and exhaust optimization The optimization of the engine is defined in terms of the description of the objective function, the constraints and the variables to be modified. With regard to the objective function, the main goal is the improvement of the power curve at a specified engine speed range. At first sight there is no constraint in this problem; only lower and upper bound for the variables are desirable. The variables chosen for the optimization task are the angles where the intake and the exhaust valves open and close. The modification of the valve timings achieved during the engine optimization may require changes in the camshaft design depending on how this changes are selected. Before making the decision of building a new camshaft, some simple modifications were explored. The computational analysis was divided in three stages: 1. keeping the original camshaft, only the position of both cams in relation to the crankshaft were modified. 2. modifying the position of the two cams independently 3. building a new cam profile Stage 1: Figure 18 shows the original configuration and two modifications, one with an advance of three degrees and the other with a retard of three degrees in relation to the original one. These curves show that while the engine power is improved at high engine speeds, with a retarded timing at low engine speeds the timings needs to be advanced.

23

Stage 2: This stage was divided in two parts, the first with the exhaust valve timing being fixed in the original position and moving the intake valve timing, and the second with the intake valve fixed and changing the exhaust valve timing forward and backward from the original position. Both results can be seen in figures 19 and 20. Gains and losses should be seen as a percentage relative to the original configuration. Stage 3: Finally, a completely new profile was adopted in which the timings were moved separately. Figure 21 shows the behavior when modifying the intake valve and keeping the exhaust valve fixed to the original timings and figure 22 shows the behavior when the exhaust valve is modified keeping the intake timings fixed to the original values. For example, AAA+5° means an advance of 5 degrees in the intake valve opening in relation to the original value, the intake valve close and the two exhaust timing being fixed to the original values.

102,5

3º delay

Original

3º advance

102,0 101,5

[%]

101,0 100,5 100,0 99,5 99,0 98,5

5800

6800

7800

8800

RPM

Figure 18: Stage 1- comparison of curves with different camshaft positions

24

101,5 101,0 100,5

%

100,0 99,5 99,0 98,5 5800

6800

7800

8800

RPM Adv 6°

Adv 3º

Delay 3°

Delay 6°

Figure 19: Stage 2- comparison of curves with different intake camshaft positions

103,0 102,0

[%]

101,0 100,0 99,0 98,0 97,0 5800

6300

6800

7300

7800

8300

8800

9300

RPM Adv 6° Delay 3° Delay 12°

Adv 3 Delay 6° Delay 15°

Orig Delay 9°

Figure 20: Stage 2- comparison of curves with different exhaust camshaft positions.

25

102,5 102,0 101,5

[%]

101,0 100,5 100,0 99,5 99,0 98,5 5500

6000

6500

7000

7500

8000

8500

9000

9500

10000

RPM IVC+5°

IVC+10°

IVO-5°

IVO-10°

Figure 21: Stage 3- comparison of curves with different intake camshaft positions

107,0 106,0 105,0

[%]

104,0 103,0 102,0 101,0 100,0 99,0 5500

6000

6500

7000

7500

8000

8500

9000

9500

10000

RPM EVO-5°

EVO-10°

EVC+5°

EVC+10°

Serie3

IVO-10 and EVC+10°

Figure 22: Stage 3- comparison of curves with different exhaust camshaft positions

26

The most relevant conclusion about this optimization task is shown in figure 22, where the power improvement at almost all engine speeds is obtained modifying only the exhaust valve close timing. Figures 23, 24 and 25 help clarify the reason of this behavior. The higher the gas flow rate at the overlapping angles, the lower the pressure inside the cylinder, which helps get more fresh mixture during the intake stroke. These figures were obtained at 8500 rpm close to the rated speed. VELOCITIES THROUGH VALVES 250

[m/s]

200

150

100

50

0

-300

-200

-100

0

100

200

300

Figure 23: original configuration (blue) and EVC+10° (red)

MASS FLOW RATE THROUGH VALVES 0.2 0.15

[Kg/s]

0.1 0.05 0 -0.05 -0.1

-300

-200

-100

0

100

200

300

Figure 24: Original configuration (blue) and EVC+10° (red)

27

CYLINDER PRESSURE 2

[atm]

1.8 1.6 1.4 1.2 1 0.8 0.6 -300

-200

-100

0

100

200

300

Figure: 25: Original configuration (blue) EVC+10° (red)

Further remarks From the optimization point of view, it can be concluded that the power improvement of this engine is exhaust valve timings- sensitive, specially at the closing phase, while the intake timings do not produce significant changes.

An introduction to mechanical analysis A number of factors should be considered in the design of motor engine valve trains and cams, which may be briefly classified into thermodynamics, gas dynamics and mechanical ones. The maximum valve lift and the valve timings are determined according to thermodynamics and gas dynamics considerations as presented in the above sections. After finding the best valve timings from the engine power optimization point of view, the mechanical analysis is used to build a feasible camshaft whose computed timings and optimal valve lift profile warrant a safe mechanical behavior. The main goal is to find a way to reproduce the above defined timings in an optimal way from the mechanical point of view. This task is split in the following three parts: 1. an ad-hoc novel software is employed to produce an optimal valve lift profile with several constraints. [23] 2. the next step transforms the valve profile in a cam profile through an inverse kinematics synthesis. 3. Finally this cam profile is placed inside the whole valve train mechanisms and it is verified through a dynamical analysis.

28

For the last two steps Mecano multibody software was used [24]. Structural considerations are taken into account both to satisfy thermodynamics, gas dynamics and mechanical factors, and to keep the structural integrity of the mechanism and optimize its performance. To this aim, efforts should be minimized to work within the allowable stress levels, and jumping between cam and follower should be avoided. Further complexity appears because of nonlinearities introduced by the kinematical chain usually interposed between cam and valve. Last but not least, the feasible solution space is restricted to avoid mechanical interferences. In [23] a systematic procedure for optimal cam design was presented and this code is applied in the first step of this work. After properly defining an optimization problem and solving it, a valve lift profile is computed as input data to a mechanical synthesis phase of analysis in which the cam profile required to reach the desired valve motion is the output result, i.e. the second step. Finally, in the third step, the whole mechanical system is dynamically analyzed in order to validate the operation conditions.

Optimal Cam profile Among the various mechanical design factors that influence the design of cams for motor engine valve trains, we take into consideration geometrical interferences and dynamic forces. Even though the considerations below were used for overhead cam end pivot rocker arm valve train configuration, their applications to pushroad type are similar. Interferences The intake valve opening and exhaust valve closing are carried out in the area of the piston top dead centre (TDC). Since the distances between valves-piston and also between valves themselves are very small, it is necessary to detect and avoid any possible geometrical interference during the design of valve motion. This factor is very critical especially in engines with large valves overlapping. Dynamical forces In order to reach the maximum valve lift L in the time interval when the valve remains open, it is necessary to specify a motion profile that satisfies not only the above mentioned interference constraints but also the following dynamic restrictions [25]: no jumping between cam and follower, no impact in the valve seating, maximum stresses bounded for reliability and minimal wear. Spring dynamics also plays a fundamental role in high speed cam follower systems. At highspeeds, springs may lose force due to an internal resonance. This resonance may be excited by high-order harmonics of the cam lift at any speed. Distributed-parameter models of the spring have been proposed to simulate the spring dynamics [26, 27, 28, 29, 30, 31]. Modelling of coil clash phenomena has been taken into account using a moving boundary technique [32]. Furthermore, spring designs with variable cross section have also been proposed to minimize amplitude of spring resonance [33]. Nested springs are used to introduce dissipation by Coulomb friction between inner and outer spring coils and damp 29

internal resonance. The estimation of friction values is a difficult task, so various forms of predicting them have been proposed [27, 34].

Constrained Optimization Strategy In this section we present some brief details about the optimization problem fully explained in the original paper [23] Motion in time of motor valves may follow the general description in figure 26.

u

dwell rise

return

ahigh

a

θ

θ alow Figure 26: Valve acceleration profile shape function Five zones can be distinguished: initial ramp, acceleration, spring-control, deceleration, and final ramp. Ramps are designed to strike the cam-follower at a given velocity and to allow some amount of clearance between cam and follower at the closed position. At the end of the ramp, the valve is accelerated by a curve of increasing slope. The curve should be such that transmitted load does not suffer sudden changes and the valve effectively follows the cam. While moving under spring control, the valve decelerates up to reaching zero velocity and then accelerates downward until closing, passing through a deceleration zone and final ramp [25]. The maximum values of positive acceleration are limited by the maximum efforts the system can sustain. On the other hand, in the spring-controlled zone, the negative acceleration imposed by the cam profile should be lower than a given limit in order to make the inertia load a fraction of the available spring force and avoid jumping. As mentioned before,

30

thermodynamics and gas dynamics factors are used to select both the maximum valve lift L and the valve timings θVO (valve opening angle) and θVc (valve closing angle) are assumed as input data for the mechanical analysis.θ represents the crank angle. Valve motion is induced through an imposed smooth profile of acceleration as follows: N

a (θ ) = ∑ a j (θ ) j =1

where 0  − λ (θ −θ j − 1 ) a j 1 − e a j (θ ) =  − λ (θ −θ ) a j 1 − e j  0

[ [

]

θ < θ j −1

]

θ j −1 ≤ θ ≤ θ 0.5 θ 0.5 ≤ θ ≤ θ j θ >θj

with

λ=

λ αj

θ 0.5 =

[

θ j −1 + θ j 2

]

where α j is the length of the interval θ j −1 ,θ j Function a j (θ ) can be seen as a smoothed

[

]

rectangular profile, with support θ j −1 ,θ j and height a j . Parameter λ controls smoothness (and thus, jerk): for large values of λ accelerations are closer to a rectangular profile. In practice a value of λ = 7 is generally adopted, which gives a smooth enough accelerations profile. Velocities and displacements can be obtained by time integration. Looking at figure 26 three zones can be distinguished in the valve motion: rise, upper dwell and return. Moreover, the valve motion is parameterized in terms of the set of angles θ j , , = 1, …11 . These parameters are not independent, and it is possible to extract a subset of only six free parameters using the following considerations: The initial and final angular displacements θ 0 and θ 11 are equal to the valve opening and closing angles θ VO and θ VC . During the rise phase, the motion profile should verify the conditions~: u (θ 0 ) = hramp

v(θ 0 ) = vramp

u (θ 5 ) = L

v(θ 5 ) = 0

During the return phase, the motion profile should verify the conditions: u (θ 6 ) = L

u (θ 11 ) = hramp

v(θ 6 ) = 0

v(θ 11 ) = −vramp

Here, hramp and vramp are the height and velocity of the quietening ramps (at the design speed). Ramps are added to ensure that the valve contacts the valve seat at a maximum speed equal to vramp , low enough to minimize impact forces and avoid jumps, regardless of the actual value of clearance [35]. Typical values of valve velocity are approximately 0.4 to 31

0.6 m/sec, and clearance of about 0.0001 to 0.0002 m is used between cam and follower. From the conditions mentioned for the rise phase some angles can be eliminated from the set of independent parameters. Doing the same for the return phase and after some algebra we finally get the selected values for parameterization of motion that are the three first intervals lengths plus the last three intervals lengths, i.e.:

α * = {α1 α 2 α 3 α 9 α10 α11 }

Optimization The objective of the design is to maximize the area below the lift curve in order to maximize the net flow income. Defining the flow area as: θVC

∫ u(θ ) dθ

θVO 11

This integral can be evaluated as A = ∑ A j with j =1

θj

Aj =

∫ u (θ ) dθ j

θ j −1

The definition of the optimization problem is completed with the set of constraints: No interference between valve and piston: the piston displacement in relation to the closed position of the valve, projected along the valve axis, can be written as: 2 2 x(θ ) = ∆ +  ac (1 − cos(θ )) + lb − lb − ac sin 2 (θ )  cos(β )  

where ac is the crank radius, lb is the connecting-rod length, ∆ is the free displacement of the valve when the piston is at the TDC θ 0 , and β is the angle between the valve axis and the piston axis. Then, the condition of non-interference can be expressed in the form: u (θ ) − x(θ ) ≤ 0 No interference between the valves: in order to avoid interference between valves, the valves displacements uint , uexh for which each valve touches the other are first determined. Then the intake valve displacement profile without this particular constraint is computed. Afterwards, the exhaust valve displacement profile is calculated which verifies u (θ ) < uexh

∀θ > θ int

where θ int is the crank angular displacement from which u (θ ) > uint at the intake valve.

32

Positive interval lengths: the interval lengths should be greater than or equal to zero

α j ≥ 0 , ∀j = 1, 11

Positive valve displacement: the computed valve displacement should be greater than zero, i.e. u (θ ) ≥ 0 The objective function and restrictions are scaled so that the optimization problem is well defined. An optimization problem is therefore defined, whose solution * α opt = arg max (A(α * ))

is computed using standard routines for constrained optimization. Remarks: As mentioned before, the valve train configuration used for this development was an overhead cam end pivot rocker arm. As in this work the engine has a pushroad type configuration, two minor modifications are implemented: there is no interference between valves and the acceleration shape functions normally have not a dwell zone. For the latter an overlapping between points 5 and 6 in figure 26 is imposed with a negative acceleration, a zero velocity condition and maximum lift.

Mechanisms analysis The valve train configuration is shown in figure 27. It is composed by several mechanical elements modeled by a multibody system approach and solved by finite elements. The main elements are described in the following paragraphs. This model is fully parametric and the configuration is mounted from a set of geometric data.

Figure 27: Valve train configuration 33

Cam and follower : In the kinematics synthesis or inverse problem we input the valve movement and we replace the unknown cam profile and its follower by a distance captor that measures the distance between the end of the hydraulic valve lifter and the center of the camshaft. The result is the temporal variation of this distance that allows us to draw the cam profile. In the dynamic or direct analysis, the cam and follower pair are linked by contact forces, the cam profile input from the inverse synthesis being the medium by which the whole valve train movement is entered. The follower may be plane or curved with a user specified radius. In order to avoid numerical drawbacks associated with the contact between cam and follower, the cam profile is smoothed through a spline curve approximation and its profile is composed by approximately 180 points written in polar coordinates. Hydraulic valve lifter: in the multibody system this mechanical element is modeled as a rigid body and its mass is the main parameter to be input. Hydraulic valve lifter and pushrod coupling: this is solved using a spring which works only in compression with a stiffness coefficient similar to that of steel. Pushrod: the flexibility was considered only for this mechanical element, and the pushrod was split in N parts. In this work N=4 was used, but this value can be modified by the user. Rocker arm: this was modeled as a rigid body with a specified mass and mass moment of inertia about its pivot. The coupling between the rocker arm and the pushrod is solved by another spring that works only in compression load with no reaction in traction load. This gross representation of the real linkage is enough for our goals because the latter is evidence of a mechanical failure in the valve train in which case the simulation should not continue. On the other hand, the coupling between the rocker arm and the valve stem is modeled by another cam and follower element solving the contact forces in detail for the verification of a valve floating condition. Valve spring: The force exerted by the valve spring in a running engine deviates substantially from its static values. The reason for these deviations is that the spring has internal oscillation modes, the so called spring surge modes. The lowest surge eigenfrequency lies below the first valve train eigenfrequency, and both are strongly excited at high engine speeds. The valve spring is a very elastic medium compared to the other valve train components in which disturbances are transmitted longitudinally and relatively slowly in the form of waves. The motion of individual elements is governed by the wave equation, and one way of obtaining the spring force under dynamic conditions is to discretize the spring into a large number of small spring elements. The external spring and internal springs are split in N parts choosing N as the number of spring coils, eight in this work. Valve: This element is considered as a rigid body The interaction between the valve and the port seat has not been taken into account.

Mechanical simulation results Taking into account the dynamical behavior at different engine speeds and considering that the more interesting regime is above 8000 rpm, the engine speed has been swept between 8000 to 10000 each 150 rpm. Five cycles are done at each speed in order to stabilize the

34

engine operation which leads to a clear understanding of how the cam profile and the spring dynamics interact with the rest of the valve train. A comparison between the operation of the original configuration in relation to the modified one allows us to check if the behavior of the new valve train configuration satisfies mechanical criteria. Some interesting results with this model are shown in the figures below. They are obtained for one of the most representative engine speeds. Figure 28 shows the contact force acting at the linkage between the main cam and its follower Here the force never crosses through the horizontal axis and it is always of the same sign. Therefore, it is never at a critical situation of valve floating. Next, figure 29 shows the external spring force evidencing the dynamic behavior of the spring. Even though the valve is closed and remains at rest, the spring continues moving, and when the valve starts to open at the next cycle the spring is not generally at rest. In this way, it is possible to include the residual vibration caused by the spring internal modes in the analysis. Figure 30 plots the lateral displacement of the pushrod, which shows the flexural behavior of this element and its own dynamic response caused by the inclusion of the flexibility component. Finally, figure 31 shows the contact force acting at the linkage between the rocker arm and the valve stem where once more the curve does not cross over the horizontal axis, evidencing that contact is always warranted. SAMCEF

APR

2 2003 08:52:00

Stress (ORD.) Time (ABS.) Str.(EL=401 C=1) 100.

0.6500

0.6550

0.6600

0.6650

0.6700

0.6750

0.6800

0.6850

-100. -200. -300. -400. -500. -600. -700. -800. -900. -1000.

Figure 28: Cam follower contact force

35

0.6900 Time

SAMCEF

APR

2 2003 08:56:16

Stress (ORD.) Time (ABS.) Str.(EL=1005 C=1) Time 0.7300 0.7350 0.7400 0.7450 0.7500 0.7550 0.7600 0.7650 0.7700 0.7750 0.7800 0.7850

-60. -80. -100. -120. -140. -160. -180. -200. -220. -240. -260.

Figure 29: external spring forces

SAMCEF

APR

Displacement Time (ABS.)

2 2003 08:54:14

(ORD.)

Displ.(N=605 C=1) 0.2000

0.6850 0.6900 0.6950 0.7000 0.7050 0.7100 0.7150 0.7200 0.7250 0.7300 0.7350 0.7400 Time -0.2000

-0.4000

-0.6000

-0.8000

-1.

-1.2000

Figure 30: Lateral displacement of the pushrod

36

SAMCEF

APR

2 2003 08:52:58

Stress (ORD.) Time (ABS.) Str.(EL=301 C=1) Time 0.7600 0.7650 0.7700 0.7750 0.7800 0.7850 0.7900 0.7950 0.8000 0.8050 0.8100 0.8150 0.8200

-50.

-100.

-150.

-200.

-250.

-300.

-350.

Figure31: contact forces at the rocker arm and valve stem coupling

Conclusions A valve train optimization procedure was presented in which gas dynamics, thermodynamics and mechanical effects are included. This strategy allows us to have better control of some design variables that prove to have a great influence over the volumetric efficiency of an internal combustion engine. Besides, a new calibration methodology is proposed, which is based on the linking of some uncertain critical parameters in the engine simulator data set and some basic laboratory measurements. This procedure proves to be very efficient, showing high agreement between numerical predictions and real observations. The whole procedure finishes with the design description of the cam profile to be manufactured.

Acknowledgements To Juan Tofoni for his work in part of this project, to Professor Alberto Cardona for his guidance in topics related with multibody systems, to CONICET and UNR for their financial support.

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