Function Of Crank Angle Research Articles

Effect of Spark Timing on Combustion Process of SI Engines using MATLAB

spark timing plays a significant role in the combustion process and in deciding the engine parameters of SI engine. This paper aims at demonstrating the effect of advanced and retarded spark timing on the burn fraction variation versus crank angle, cumulative heat release rate versus the crank angle and the pressure variation as a function of crank angle with the help of MATLAB programs. For this purpose, a basic finite heat release model is used for the combustion process in SI engines. This model can also be extended to evaluate effect of spark timing on engine work and thermal efficiency. In each section of the paper, the codes used for analysis are provided for future research work. Salient results, such as peak pressure crank angles for different spark timings , are derived from analysis. KeywordsHeat release model, SI engine, Combustion, MATLAB

Thermodynamic model for prediction of performance and emission characteristics of SI engine fuelled by gasoline and natural gas with experimental verification

In this study, a thermodynamic cycle simulation of a conventional four-stroke SI engine has been carried out to predict the engine performance and emissions. The first law of thermodynamics has been applied to determine in-cylinder temperature and pressure as a function of crank angle. The Newton-Raphson method was used for the numerical solution of the equations. The non-differential form of equations resulted in the simplicity and ease of the solution to predict the engine performance. Two-zone model for the combustion process simulation has been used and the mass burning rate was predicted by simulating spherical propagation of the flame front. Also, temperature dependence of specific heat capacity has been considered. The performance characteristics including power, indicated specific fuel consumption, and emissions concentration of SI engine using gasoline and CNG fuels have been determined by the model. The results of the present work have been evaluated using corresponding available experimental data of an existing SI engine running on both gasoline and CNG. It has been found that the simulated results show reasonable agreement with the experimental data. Finally, parametric studies have been carried out to evaluate the effects of equivalence ratio, compression ratio and spark timing on the engine performance characteristics in order to show the capability of the model to predict of engine operation.

Effect of cylinder pressure on engine valve-train friction under motored and fired conditions

In the last three decades, there has been a resurgence of interest in reducing friction in the engine valve-train for better fuel economy and improved emissions. Research studies and scientists have developed complex mathematical models and advanced test rigs to understand the interaction between cam and tappet. Most of the experimental valve-train work has been carried out on motored test rig assuming there is less difference in valve-train friction under motored and fired conditions. For complete understanding of the difference of camshaft friction under motored and fired conditions, experiments have been carried out on a real engine under both conditions allowing for the first time the detailed study of the effect of cylinder pressure on exhaust camshaft friction. A new method of directly measuring camshaft friction that offers excellent accuracy is described in this article. The technique uses strain gauges to measure the torque exerted upon the camshaft drive pulley sprocket. The advantage of this method over previous techniques is the instantaneous valve-train friction as a function of crank angle can be measured, simultaneously for both inlet and exhaust camshafts, under motored and fired conditions. Experiments have been carried out for both motored and fired conditions on a single-cylinder gasoline engine. Results are presented for instantaneous and mean valve-train friction as a function of engine speed and oil temperature, indicating a decrease in friction with increase in engine speed and an increase with increase in temperature. A significant difference in valve-train friction between motored and fired conditions was found, especially for the exhaust camshaft.

Modelling of the thermal cycle of a gas engine using AVL FIRE Software

Paper presents results of modelling gas engine thermal cycle using AVL FIRE and KIVA 3V software. There are described three combustion models used in software. KIVA and FIRE software are used in Institute of Internal Combustion Engines and Control Engineering for analysis of thermal cycle of IC engines. FIRE software gives many possibilities with many combustion models. All used combustion models are dependent on turbulence of flow field before ignition. Comparison of modelling results of thermal cycle of IC engine is presented in paper. Pressure, temperature, heat release and turbulence parameters variations in function of crank angle as well as spatial distribution of above mentioned quantities at selected crank angles were determined.

Towards a detailed soot model for internal combustion engines

At the University of Cambridge, the formation of soot was studied in an n-heptane fuelled Homogeneous Charge Compression Ignition (HCCI) engine, operated at a rich equivalence ratio of 1.93, by means of in-cylinder snatch sampling as well as by applying a new engine model which features a highly detailed description of soot. This new computationally efficient model is capable of providing not only averaged quantities as functions of crank angle like soot mass, number density, volume fraction, aggregate diameter, and the number of primary particles per aggregate for example, but also aggregate and primary particle size distribution functions and additionally can give detailed information on aggregate morphology and chemical composition.

Towards a detailed soot model for internal combustion engines

In this work, we present a detailed model for the formation of soot in internal combustion engines describing not only bulk quantities such as soot mass, number density, volume fraction, and surface area but also the morphology and chemical composition of soot aggregates. The new model is based on the Stochastic Reactor Model (SRM) engine code, which uses detailed chemistry and takes into account convective heat transfer and turbulent mixing, and the soot formation is accounted for by SWEEP, a population balance solver based on a Monte Carlo method. In order to couple the gas-phase to the particulate phase, a detailed chemical kinetic mechanism describing the combustion of Primary Reference Fuels (PRFs) is extended to include small Polycyclic Aromatic Hydrocarbons (PAHs) such as pyrene, which function as soot precursor species for particle inception in the soot model. Apart from providing averaged quantities as functions of crank angle like soot mass, volume fraction, aggregate diameter, and the number of primary particles per aggregate for example, the integrated model also gives detailed information such as aggregate and primary particle size distribution functions. In addition, specifics about aggregate structure and composition, including C/H ratio and PAH ring count distributions, and images similar to those produced with Transmission Electron Microscopes (TEMs), can be obtained. The new model is applied to simulate an n-heptane fuelled Homogeneous Charge Compression Ignition (HCCI) engine which is operated at an equivalence ratio of 1.93. In-cylinder pressure and heat release predictions show satisfactory agreement with measurements. Furthermore, simulated aggregate size distributions as well as their time evolution are found to qualitatively agree with those obtained experimentally through snatch sampling. It is also observed both in the experiment as well as in the simulation that aggregates in the trapped residual gases play a vital role in the soot formation process.

Analysis of the Interactions Between Indicated and Reciprocating Torques for the Development of a Torsional Behavior Model of the Powertrain

Torque-based engine control systems usually employ a produced torque estimation feedback in order to verify that the strategy target torque has been met. Torque estimation can be performed using static maps describing the engine behavior or using models describing the existing relationships between signals measured on the engine and the indicated torque produced. Signals containing information on the combustion development, suitable for this purpose, are, among others, the ion-current signal, the vibration signals obtained from accelerometers mounted on the engine block, or the instantaneous engine speed fluctuations. This paper presents the development and the identification process of an engine-driveline torsional behavior model that enables indicated torque estimation from instantaneous engine speed measurement. Particular attention has been devoted to the interactions between indicated and reciprocating torques, and their effects over instantaneous engine speed fluctuations. Indicated and reciprocating torques produce, in fact, opposite excitations on the driveline that show opposite effects on the engine speed wave form: For low engine speed, usually indicated torque prevails, while the opposite applies for higher engine speed. In order to correctly estimate indicated torque from engine speed measurement, it is therefore necessary to correctly evaluate the reciprocating torque contribution. Reciprocating torque is usually described using a wave form as a function of crank angle, while its amplitude depends on the value of the reciprocating masses. As mentioned before, knowledge of the reciprocating masses is fundamental in order to obtain correct estimation of the indicated torque. The identification process that has been set up for the engine-driveline torsional model enables to evaluate the relationship between torques applied to the engine and the corresponding engine speed wave form even without knowing the value of the reciprocating masses. In addition, once this model has been set up, it is possible to estimate with high precision the value of the reciprocating masses. Particular attention has also been devoted to the feasibility of the application of the identified model onboard for torque estimation; for this reason, the model has been developed in a very simple form. The approach proved to be effective both on gasoline and diesel engines, both for engine mounted on a test cell and onboard, with different engine configurations. Examples of application are given for some of the configurations investigated.

Numerical analysis of spark plugs number influence on selected parameters of combustion in piston engine

The results of numerical analysis of combustion in multi-spark plug SI engine are presented in the paper. The outcome of computational analysis of lean mixtures combustion in engine with one and two spark plugs are compared. The output data was presented in graphical form as screenshots (temperature distribution) and as pressure and temperature courses in function of crank angle. 3D numerical modelling of combustion in multi-spark plug engine proved that improvement in lean mixture combustion process can be obtained by increasing the number of active ignition points. As conclusion it can be stated that numerical modelling results confirmed the favourable influence of applying two active spark plugs in lean mixtures combustion.

The influence of engine speed and load on the heat transfer between gases and in-cylinder walls at fired and motored conditions of an IDI diesel engine

In this study, the heat transfer characteristics between gases and in-cylinder walls at fired and motored conditions in a diesel engine were investigated by using engine data obtained experimentally. For this investigation, a four-cylinder, indirect injection (IDI) diesel engine was tested under different engine speeds and loads. The heat transfer coefficient was calculated by using Woschni expression correlated for the IDI diesel engines, and also using Annand and Hohenberg expressions. The temperature of in-cylinder gases were determined from a basic model based on the first law of thermodynamics after measuring in-cylinder pressure experimentally. The results show that the heat transfer characteristics of the IDI diesel engine strongly depend on the engine speed and load as a function of crank angle at fired and motored conditions.

Effects of Piston Design Parameters on Piston Secondary Motion and Skirt - Liner Friction

In this article, a previously developed and experimentally validated piston secondary motion model has been improved further numerically and applied to understand the detailed interactions between the piston skirt and the cylinder liner for various piston design parameters. The model considers the roughness of the surfaces and the topography of the skirt in both the axial (barrel profile) and circumferential (ovality) directions. Three modes of lubrication: hydro-dynamic, mixed, and boundary lubrication regimes have been considered and the skirt is partially flooded in most cases. Elastic deformation of the skirt is an essential part of the model. In this model, the piston dynamic behaviour and frictional and impact forces are predicted as functions of crank angle and are examined in detail. Parameters investigated include piston skirt profile, piston-to-liner clearance, surface roughness, and oil availability. The results show that some of these parameters have profound effects on the frictional and impact forces at the piston skirt/liner interface, and therefore, they have the potential to optimize the piston frictional power loss. Correlations and non-dimensional scaling laws are developed to illustrate the basic governing phenomena. These results aim to provide a set of quantitative design guidelines.

The development of a semi-empirical model for rapid NOx concentration evaluation using measured in-cylinder pressure in diesel engines

Continued legislative pressure to reduce NO x emissions from diesel engine combustion systems generates a desire for cycle-by-cycle emissions data, with a view to their use in a feedback control strategy, perhaps in conjunction with an exhaust catalytic reactor. While NO x sensors that provide fast, robust, reliable, and continuous measurements in a diesel exhaust at a reasonable price are currently the subject of much development, the present work focuses on an indirect approach. This has led to the development of a semi-empirical model that can be used to estimate NO x emissions, based on more easily measured input data, primarily in the form of instantaneous in-cylinder pressure as a function of crank angle. The model computations are based on fundamental thermodynamic principles, but key empirical constants have been derived with the aid of statistical techniques. The approach taken relied on the availability of an extensive bank of experimental data from three different designs of direct injection diesel engine, each utilizing common rail type fuel injection systems and, in some cases, with the use of multiple injections per cycle.

NUMERICAL MODELING OF THE PROPAGATING FLAME AND KNOCK OCCURRENCE IN SPARK-IGNITION ENGINES

ABSTRACT The present paper reports multidimensional numerical simulations of knock occurrence in internal combustion engines. Knock occurrence in spark-ignition engines was examined within the context of a model of autoignition of hydrocarbon/air mixture, which has been extended by including chemical reactions for the propagating flames and an extended chemical model for the cool flames. Special attention was given to the influence of the propagating flame on the autoignition onset. Knocking occurrence is the self-ignition of the end gas as a result of combined effects of the end-gas compression by the moving piston in the compression stroke and by the accelerating propagating flame and expanding combustion products. It is recognized that the autoignition onset is accompanied by an acceleration of the propagating flame that acts as an accelerating piston emanating pressure waves in the end gas. Given the initial fuel/air mixture concentration, temperature, and pressure, the developed model was used to calculate temperature, pressure, species concentration as a function of crank angle, combustion mixture, exhaust gas recycled and engine speed, and the time of the autoignition onset. The model was validated using the experimental data obtained with a Ricardo test engine and excellent agreement was achieved between the modeling predictions and the observed experimental data. In particular it was shown that the increase of the engine speed results in the decrease of the knock onset tendency, allowing the engine to operate with higher compression ratio without knocking.

Laser-Induced Fluorescence Measurements of Formaldehyde in Homogeneous Charge Compression Ignition (HCCI) of Dimethyl Ether

Crank angle resolved monitoring of formaldehyde using laser-induced fluorescence (LIF) has been conducted at homogeneous charge compression of dimethyl ether (DME) -air mixture in an externally motored single cylinder piston engine. In order to correct the raw LIF intensity profiles, which are significantly influenced by collisional quenching and pressure broadening, fluorescence lifetime and spectral linewidth of the observing transition were evaluated as a function of crank angle. It is clearly demonstrated that formaldehyde is promptly generated at the cool flame and disappears at the thermal flame in the two-stage autoignition, as expected by the simulation using the detailed DME oxidation mechanism of Curran et. al.

Experimental and Theoretical Study of Instantaneous Engine Valve Train Friction

A new method has been developed to directly measure valve train friction as a function of crank angle using specially designed timing belt pulley torque transducers fitted to the inlet and exhaust camshafts of a single-cylinder gasoline engine. Simultaneous and instantaneous friction torque of both the inlet and exhaust camshafts at any engine speed can be measured, with no apparent detrimental effect of timing belt loading on the output reading. Experiments are reported for valve train friction at a range of motored engine operating conditions with different lubricant formulations, with and without a friction modifier. These are compared with the predictions of an existing valve train friction model based upon elastohydrodynamic lubrication theory. Measured friction decreased with increasing engine speed but increased with increasing oil temperature and the fuel economy benefit of friction modifiers was observed. The model yielded similar magnitudes of friction at medium engine speeds and above but predicted much lower friction with high oil temperatures at low speed. Comparison of theory and experiments also suggests that some oil may leak from hydraulic lash adjusters during the cam event with a consequent reduction in geometric torque.

Numerical analysis of the piston secondary dynamics in reciprocating compressors

In this study, a numerical analysis for the piston secondary dynamics of small refrigeration reciprocating compressors is performed. In general, the length of cylinder in this class of compressors is shortened to diminish the frictional losses of the piston-cylinder system. So, the contacting length between piston and cylinder wall is in variable with the rotating crank angle around the BDC of the reciprocating piston. In the problem formulation of the piston dynamics, the variation in bearing length of the piston and all corresponding forces and moments are considered in order to determine the piston trajectory, velocity and acceleration at each step. A Newton-Raphson procedure was employed in solving the secondary dynamic equations of the piston. The developed computer program can be used to calculate the entire piston trajectory and the lubrication characteristics as functions of crank angle under compressor running conditions. The results explored the effects of some design parameters and operating conditions on the stability of the piston, the oil leakage, and friction losses.

Development and validation of a comprehensive two-zone model for combustion and emissions formation in a DI diesel engine

A two-zone model for the calculation of the closed cycle of a direct injection (DI) diesel engine is presented. The cylinder contents are taken to comprise a non-burning zone of air and another homogeneous zone in which fuel is continuously supplied from the injector holes during injection and burned with entrained air from the air zone. The growth of the fuel spray zone, consisting of a number of fuel–air conical jets equal to the injector nozzle holes, is carefully modelled by incorporating jet mixing to determine the amount of oxygen available for combustion. Application of the mass, energy and state equations in each one of the two zones yields local temperatures and cylinder pressure histories. For calculating the concentration of constituents in the exhaust gases, a chemical equilibrium scheme is adopted for the C–H–O system of the 11 species considered, together with chemical rate equations for the calculation of nitric oxide (NO). A model for the evaluation of soot formation and oxidation rates is incorporated. A comparison is made between the theoretical results from the computer program implementing the analysis, with experimental results from a vast experimental investigation conducted on a fully automated test bed, direct injection, standard ‘Hydra’, diesel engine located at the authors' laboratory, with very good results, following a multi-parametric study of the constants incorporated in the various sub-models. Pressure indicator diagrams and plots of temperature, NO, soot density and of other interesting quantities are presented as a function of crank angle, for various loads and injection timings, elucidating the physical mechanisms governing combustion and pollutants formation. Copyright © 2003 John Wiley & Sons, Ltd.

Cycle analysis for fuel-inducted internal combustion engine configurations

A quasi-one-dimensional computer code based on a fuel-air cycle analysis was developed to predict the performance of two- and four-stroke fuel-inducted engines. The analysis was developed to provide boundary conditions for a finite element analysis to predict thermal and mechanical loading of carbon-carbon pistons for use in advanced internal combustion engine concepts. The computer code can predict the required boundary conditions, which are gas pressure and temperature and heat transfer coefficients as a function of crank angle, along with engine indicated and brake power output, thermal efficiency and mean effective pressure. The code utilizes a variable specific heat calculation throughout the cycle. The compression of an air-fuel-residual gas mixture is calculated followed by a finite rate burn, where the burn duration is calculated on the basis of the turbulent flame speed and cylinder geometry. The residual gas content is calculated by an iterative technique. During combustion and expansion, ten equilibrium combustion product constituents are tracked. Engine friction, instantaneous heat transfer and blowby past the rings are calculated on the basis of empirical correlations. The tendency for engine knock or autoignition of the fuel is also calculated. Good agreement is obtained when compared with actual engine operation for power output, thermal efficiency and exhaust gas temperature.

Stochastic prediction of cycle-by-cycle cylinder pressure fluctuations in a spark ignition engine

The generality of recent stochastic models for cylinder pressure development is exploited, both to recreate or simulate cyclic datasets with similar statistical properties to real engine data, and to derive many of the more traditional statistics (e.g. standard deviations of maximum pressure, mean effective pressure, burn angle, etc.) directly from the parameters of the more general model form. The same approach also provides insight into the phasing of the cyclic process, since a number of statistics (such as the standard deviation of pressure or burn rate variations) can be computed directly as a function of crank angle. It is also straightforward to evaluate the contribution to such quantities from each of the physically meaningful model parameters, and thereby obtain some insight into the mechanisms involved.

Stirling's air engine—a thermodynamic appreciation

Stirling's original engine is remarkable for having been the first application of the thermal regenerator—and an instant technological success. While the patents and their intriguing history are the normal focus of study, this paper shifts attention to the insights afforded by reconstructing the thermodynamic personality of the engine itself. The kinematics of the drive mechanism are recovered, and volume variations determined as a function of crank angle. Recently developed thermodynamic tools are introduced and applied to the construction of the fluid particle trajectory map. The map forms the integration grid for calculation of the temperature response of the regenerator. The claim for 2 bhp from the original engine is explored. Potential is identified for an up-to-date version of Stirling's elegant concept in the form of cheap quiet power units of attractive specific output.

Dynamics of mountain bicycles with rear suspensions: modelling and simulation

A dynamic model of a rider on a rear-suspension mountain bicycle is presented. By combining the rider, main frame and crank into a single rigid body, the need for determining interface loads between the rider, seat, handlebars and pedals is eliminated. The only excitation to this relatively simple model is the chain tension force as a function of crank angle. The equations of motion are obtained in symbolic form using Maple algorithms and a linear graph representation of the system. The resulting equations are solved numerically in order to simulate the bicycle being ridden up a smooth 6% grade. The simulation results are in good agreement with those obtained from a more complex model, and clearly show the pedal-induced oscillations of the rear suspension.