Apr 3, 2007 - AUTOMOTIVE RESEARCH CENTER W. E. LAY AUTOMOTIVE ... Engine Simulation for System Dynamics Studies , Mechanics of Structures .... it every crank-angle degree to form a nonlinear, transient, single-cylinder version.
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Mechanics of Structures and Machines: An International Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/lmbd19
A Flexible, Reconfigurable, Transient Multi-cylinder Diesel Engine Simulation for System Dynamics Studies a
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G. Zhang , Z. S. Filipi & D. N. Assanis
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a
NAVISTAR INTERNATIONAL TRANSPORTATION CORP. ENGINE ENGINEERING , 10400 W. NORTH AVE., MELROSE PARK, ILLINOIS, 60160, U.S.A b
AUTOMOTIVE RESEARCH CENTER W. E. LAY AUTOMOTIVE LABORATORY DEPARTMENT OF MECHANICAL ENGINEERING AND APPLIED MECHANICS , THE UNIVERSITY OF MICHIGAN , ANN ARBOR, MICHIGAN, 48109, U.S.A Published online: 03 Apr 2007.
To cite this article: G. Zhang , Z. S. Filipi & D. N. Assanis (1997) A Flexible, Reconfigurable, Transient Multi-cylinder Diesel Engine Simulation for System Dynamics Studies , Mechanics of Structures and Machines: An International Journal, 25:3, 357-378, DOI: 10.1080/08905459708905294 To link to this article: http://dx.doi.org/10.1080/08905459708905294
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MECH. STRUCT. & MACH., 25(3), 357-378 (1997)
A Flexible, Reconfigurable, Transient Multi-cylinder Diesel Engine Simulation for System Dynamics Studies* G. Zhang
2. S. Filipi and D. N. Assanis AUTOMOTIVE RESEARCH CENTER W.E. LAYAUTOMOTIVE LABORATORY DEPARTMENT OF MECIIANICAL ENGINEERING AND APPLIED MECHANICS OF MICHIGAN THEUNIVERSITY ANNARBOR. MICHIGAN 48109. U.S.A.
ABSTRACT
A new generation, transient, multi-cylinder, turbocharged diesel engine simulation is developed for predictions of dynamic response and performance of enginpowenrain systems, for assessment of alternative system configurations, and for integration studies in conjunction with the rest of the components of ground vehicles. The simulation is based on a comprehensive single-cylinder engine model with built-in physical submodels and transient capability to ensure high fidelity predictions. The single-cylinder model has been convened into a mod'Communicmed by E. J. Haug
357 Copyright O 1997 by Marcel Dekker. Inc.
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ule within the flexible and reconfigurabie MATLAB-SIMULINK environment to readily accommodate design changes, submodel upgrades, and interfacing with other vehicle models. It is shown that transient, multi-cylinder simulation of an arbitrarily-selected number of cylinders that are configured to form the engine can be readily accomplished. Illustrative studies are conducted to demonstrate the capability of the simulation to perform system dynamic studies and predict instantaneous torque and structural loads as a function of both driver demand and external load. The usefulness of the tool for powertrain design and optimization studies, and as a component of entire vehicle simulations, is apparent.
I. INTRODUCTION Advanced propulsion systems for military and civilian applications must be characterized by high power density, high fuel economy, and reliable performance under severe environmental conditions, while meeting increasingly more stringent emission standards. The turbocharged, direct-injection diesel engine has been widely adopted as the typical heavy-duty automotive powerplant, primarily because of its high energy conversion efficiency and reliability. The hean of the system shown in Fig. I is the multi-cylinder diesel engine; however, a number
COMPRESSOR
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1 INTERCOOLER
Fig. I.
I ? I
SYSTEM
---J
Schemalic of [he lurbochcarged. rnulwcylinder diesel engine system
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4
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DIESEL ENGINE SIMULATION of external components, primarily the turbocharger and the intercooler, have a profound impact on engine performance. Such ancillary components allow the designer flexibility to change engine rating by simply rematching the turbocharger with the engine, by introducing or eliminating intercooling, or by varying the efficiency of charge cooling. Furthermore, the system performance envelope can be enhanced if more complex configurations are considered; e.g., adding a wastegate valve to control boost pressure (also indicated in Fig. I), turbocompounding, adding two-stage or sequential turbocharging, and combining supercharging in series with turbocharging. Optimization of a turbocharged, diesel engine system typically requires extensive testing and hardware modifications. Development time and cost would be substantially reduced if engine and vehicle optimizat~oncould be conducted primarily on simulation models for the engine and its subsystems. Simulation of engine torque and vibration in response to changes in load and operator demand is also essential for the complete simulation of a ground vehicle. However, to be a viable alternative to testing, the simulation needs to be composed of high fidelity submodels to yield an acceptable level of predictiveness. At the same time, it needs to be highly flexible to allow easy reconfiguration of the engine system for changes in design and operating conditions. The simulation also needs to be highly modular to provide ease of integration with the rest of the powenrain (transmission, transfer case, differentials) and the vehicle itself, thus facilitating optimization of the complete vehicle mechanical system. Since automotive engines operate under constantly varying conditions in terms of both driver demand and external load. the engine simulation has to be transient in nature and able to run real-time to provide information to the other pans of the vehicle simulation. In the past, transient engine simulation models have been developed with the primary intention of analyzing various aspects of engine control and investigating some specific problems associated with dynamic system response, such as the turbocharger lag during rapid engine accelerations. Among the more flexible models. quasi-linear models link steady-state, experimentally-measured, thermal and gas flow data with dynamic models of the engine components [I ,2,3] and allow for easy configuration of the system, as well as addition of external components. For instance, the quasi-linear model proposed by Goyal [4] includes a linearized equation for the governor. The quasi-linear approach to modeling combined with the use of graphical, dynamic system simulation environmentsl such as MATLA BSIMULINK or MatrixX, provides flexibility in building subsystems, integrating them into the engine system. reconfiguring if necessary, and building even higher level of systems (i.e., powenrain systems and, eventually, vehicle systems) [:?I. However, the current generation of such flexible simulations still relies on very simplified "mean-torque" cycle models: i.e.. look-up tables that have to be gencrated from experimental data, thus severely limiting the predictive capabilities in terms of the process changes and effects resulting from truly unsteady, off-design engine operation.
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ZHANG, FILIPI, AND ASSANIS On the other hand, more comprehensive and accurate nonlinear, transient diesel engine simulations have been developed as extensions of quasi-steady thermodynamic engine models, following the lead work at UMIST [6] and Imperial College [7]. While Winterbone et al. [6] simplified the calculation of the closed part of the cycle somewhat in order to speed up calculations, they accounted for the "filling and emptying" of the different parts of the system and included a dynamic nibdel of the governor. However, a mean engine torque that ignored cyclic transients was used in the engine dynamics equation. The latter was integrated only at the end of an individual cycle's calculation. Watson and Marzouk [7] applied a set of differential equations based on the first law of thermodynamics to all cycle processes, and included the engine dynamics equation on acrank-angle basis. However, the instantaneous torque of the engine was tied to its mean indicated pressure to avoid modeling of the multi-cylinder aspect of the slider-crank mechanism dynamics. Validation of simulation predictions against experimental results for some simplified transients-e.g., step change of load or speed demand-produced encouraging results. Nevertheless, those older generation models have limited user friendliness and graphical capabilities, and changing system configuration or incorporating within hierarchical vehicle system simulations is cumbersome. Such . exercises typically involve reprogramming the code. The University of Michigan, in partnership with Howard University, the University of Iowa, Wayne State Univers~ty,and the University of Wisconsin, has established an Automotive Research Center for the development and validation of advanced models for ground vehicle simulation. In this context, the UM propulsion system group has undertaken the development of a new generation, transient, multi-cylinder, turbocharged diesel engine simulation that should be flexible and easily reconfigurable while ensuring high fidelity and predictiveness of results. The foundation of the model is the physically-based. phenomenological, steadystate, multi-cylinder diesel engine model introduced by Assanis and Heywood 18.91 and validated comprehensively for various engine designs. Recently, Filipi and Assanis 1101 added the engine dynamics equation to the model and integrated it every crank-angle degree to form a nonlinear, transient, single-cylinder version of the original simulation [a]. In this study, the nonlinear. single-cylinder model is converted into a module within the MATLAB-SIMULINK environment and used as the basic building block to form a flexible, reconfigurable. multi-cylinder engine sinlulation for system dynamic studies. This approach marries the accuracy features of filling and emptying types of codes with the symbolic capabilities of a graphical environment to achieve a high fidelity, flexible, transient diesel engine simulation. This paper is arranged as follows. First, the parent diesel engine model and its physical submodels are reviewed briefly. Next, the addition of full transient capability to the steady-state model is described, with emphasis on the technique to resolve instantaneous engine speed and torque on a crank-angle basis. The method-
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ology for the development of an "open" single-cylinder module, fully compatible with the MATLAB-SIMULINK environment, from the pre-existing FORTRAN code is explained next. Subsequently, the synthesis of the multi-cylinder engine model is presented using the single-cylinder module as the building block. Pinally, illustrative studies conducted using the MATLAB-SIMULINK version of the transient diesel engine simulation are presented; the latter include studies of the system dynamic response to changes of the fueling rate or the external load and predictions of the instantaneous engine torque values and structural loads during transients.
II. DIESEL ENGINE MODEL AND SUBMODELS O F PHYSICAL PHENOMENA The origins of the turbocharged and turbocompounded diesel engine computer simulation that laid the foundation for this study are described by Assanis and Heywood [9].The parent model is a thermodynamic, zero-dimensional simulation of the filling andemptying type. The cyclic processes in the cylinder are represented by a blend of more fundamental and phenomenological models of turbulence, combustion, and heat transfer. The parent simulation has been validated against k s t results from diesel engines of various sizes, ranging from highway truck engines (91 to large locomotive engines [I I]. This section briefly summarizes the main assumptions of the diesel engine model and its phenomenological submode:ls. Additional details on the parent code are given by Assanis [8]. The diesel four-stroke cycle is treated as a sequence of continuous processes; intake, compression, combustion (including expansion), and exhaust. The duration of the individual processes are as follows. The intake process begins when rhe intake valve opens and ends when it closes. The compression process begins at the closing of the intake valve and ends at the time of ignition. The combustion process begins when ignition occurs and ends when the exhaust valve opens. The exhaust process begins when the exhaust valve opens and ends when the intake valve opens (rather than when the exhaust valve closes). In the reciprocator simulation, the systemof interest is the instantaneouscontents of a cylinder; i.e., air, fuel, and combustion products. In general, this system is open to the transfer of mass, enthalpy, and energy in the form of work and heat (see Fig. I). Throughout the cycle, the cylinder is treated as a variable volume plenum, spatially uniform in pressure. Furthermore, the cylinder contents are represented as one continuous medium by defining an average equivalence ratio and temperature in the cylinder at all times. Gas properties are calculated assuming ideal gas behavior. At low temperatures (below IOOOK), the cylinder contents are treated as a homogeneous mixture of non-reacting ideal gases. At high temperatures (above 1000 K), the properties of
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the cylinder contents are calculated with allowance for chemical dissociation bv assuming that the bumedgases are in equilibrium, using an approximatecalculation method based on hydrocarbon-air combustion. Quasi-steady, adiabatic, one-dimensional flow equations are used to predict mass flows past the intake and exhaust valves. The intake manifold and the exhaust port are treated as plenums whose pressure and temperature history are specified as input. The compression process is defined so as to include the ignition delay period, i.e. the time interval between the start of the injection process (the point at which the injector needle starts to lift) and the ignition point (the start of positive heat release due to combustion). The total length of the ignition delay is related to the mean cylinder gas temperature and pressure during the delay period by an empirical Arrhenius expression. Combustion is modeled as a uniformly distributed heat release process. The rate of heat release is assumed to be proportional to the rate of fuel burning, which is modeled empirically. Since the diesel combustion process comprises a premixed and a diffusion-controlled combustion mechanism, Watson's fuel burning rate correlation [ 12)-which consists of the sum of two algebraic functions, one for each combustion mechanism-is used. The fraction of the total fuel that is injected and burnt by either mechanism depends on the length of the ignition delay period and the engine load and speed. Heat transfer is included in all the engine processes. Convective heat transfer is modeled using available engine correlations based on turbulent flow in pipes. The charxteristic velocity and length scales required to evaluate these correlations are obtained from a mean and turbulent kinetic energy model. Radiative heat transfer is added during combustion. The steady-state inside wall surface temperatures of the piston, cylinder head, and liner can be either specified or calculated from a specification of the component wall structure. A friction model based on the Millington's and Hartles' correlation [I31 is used. to convert indicated quantities predicted by the simulation to brake performance quantities. While the original model was based on a correlation which used the mean engine speed. our model currently uses the instantaneous engine speed based on engine system dynamics, as described in the next section.
Ill. ENGINE SYSTEM DYNAMICS The internal combustion engine as a mechanical system is characterized by the crank-slider mechanism and the reciprocating motion of the piston. The prospect of integrating the engine model with the transmission components so as to create a powertrain model that will be part of a ground vehicle simulation requires a code with inherently transient capability. The vehicle powertrain will constantly
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ENGINE CYCLE
n- Crank shafi speed T - torque
Fig. 2.
Block diagram for engine dynamics
experience varying driver demands and external loads as a function of terr:iin profile, vehicle speed, and wind velocity. Figure 2 shows the schematic of !he engine dynamic system with all the primary inputs coming from the humanlvehicle interface. the environmental conditions, and the vehicle model. The instantaneous engine speed and torque are the main outputs that need to be passed on to ihe transmission and vehicle model. In addition, the rotational speed of the crankshaft is unsteady during the individual cycles, due to rapid changes in cylinder pressure and the consequent varying forces acting on the crank during the cycle. Therefc're. the engine needs to be modeled as a dynamic mechanical system so the rotational speed can vary with crank-angle. according to the balance of the active and resistive torque and the combined enginelload inertia: i.e.
where we is the rotational velocity (radls); I< is the equivalent polar moment of inertia (kg-m') of the engine moving parts, including the flywheel; and 1, is the equivalent polar moment of inertia of the load (vehicle or dynamometer in the test cell). The active torque is the engine-indicated torque (T,). which is opposed by the engine friction torque (r,) and the external load (rL). Since the engine cycle simulation is using the angular position of the crank shaft in degrees-Cr.ank Angle (CA)-to time different events, the engine dynamics equation needs t c ~be
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transformed into
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This derivative becomes an additional equation in the simultaneous system of nonlinear first order differential equations that form the diesel engine simulation, and is thus integrated with the rest of the equations every time integrator is called. The instantaneous engine speed in rev/min is then
The engine torque is calculated from the instantaneous torques generated by each of the cylinders, as the result of the pressure and inertial forces acting on the reciprocating components. A detailed description of the instantaneous torque model for the single cylinder engine is given by Filipi and Assanis [lo]. The total engine torque (rengine) at any instant is the sum of the torque contributions from individual cylinders (ri) evaluated at the respective instantaneous value of crank angle for that cylinder (Oi). The latter is based on the crank angle O of the reference cylinder number I, the number of cylinders (icy/),and the firing order. Therefore,
For a six-cylinder, four-stroke engine, the phase shift between cylinders will be 120 degrees CA and the Oi values will be O 120•‹,O 240•‹,etc. If the model is intended to simulate an engine on the transient test bed, the polar moment of inertia of the load is equal to the dynamometer inertia. However, if the model is to be used to simulate engine transients in the vehicle, it is necessary to determine the equivalent polar moment of inertia that can represent the effect of vehicle inertia on engine acceleration or deceleration. The tire radius ( r , ) and the gear ratios in all mechanical subsystems of the drive-line are the key parameters that will allow such a transformation, according to the following formula 1141:
+
+
where M,, is the vehicle mass, G R is the current gear ratio in the transmission EP gear box, and G Rfc, is the gear ratio In the final drive (differential). If an additional component is added to the drive-line; e.g., the transfer case, the square of the transfer case gear ratio should be added as a factor in the denominator of Eq. 5. This implies that the equivalent polar moment of inertia of the load will change, not only with any change of vehicle mass, but even more dramatically with the change of the gear ratio in the transmission.
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IV. SELECTING THE SOFM'ARE ENVIRONMENTMATLAB INTERFACE A turbocharged diesel engine system can include any number of cylinders, manifolds, turbines, compressors, and various other external components, as illustrated in Fig. I . The objective of this work is to achieve the maximum degree of integration flexibility for the system simulation, so as to provide the user with the option to reconfigure the system graphically and enable its simulation without any additional programming. An additional objective is to allow interfacing of existing pieces of code in FORTRAN or C within the overall system shell implemented in the new simulation environment. After the evaluation of available options throu:gh the interaction with numerous ARC members, it was assessed that one of the most promising, graphical. user-friendly environments is the one provided by the MATLAB-SIMULINK package. Its structure is hierarchical and highly modularthese features are the prerequisite for the tasks of building subsystems suitable for integration with larger scale systems. The graphical programming interface is tailored for engineering applications, and once the necessary component blocks are generated, the development of the simulation becomes very similar to building the block diagram of the system. In addition. SIMULINK block libraries contain a large number of components categorized as sources, sinks, discrete, linear, nonlinear, connections, and extras, and these are very useful for building dynamic simulation systems. The implementation of the engine simulation in the MATLAB-SIMULINK emvimnment was approached in two phases. To take advantage of the existing body of routines written in FORTRAN, the diesel engine system simulation 181 was decomposed into a single-cylinder engine module and ancillary component mndules, including manifolds, turbocharger compressor and turbine, intercooler, and compounded turbine. Subsequently, the single-cylinder FORTRAN module was converted to a FORTRAN-MEX file, thus creating a single-cylinder block compatible with the SIMULINK environment. Next. various integrators available in MATLAB-SIMULINK were evaluated. Finally. the "open" single-cylinder block was used to build the multi-cylinder diesel engine simulation in SIMULINK. These two phases are described in the following subsections.
A. Creating a MATLAB-SIMULINK module based on a FORTRAN cycle simulation The basis for the development of the single cylinder engine block was a FORTRAN code [8] that essentially contains the system of simultaneous, nonlinear, ordinary differential equations (ODE) for the cycle processes. along with a set of "utility" routines providing values for various terms in the state equations; e.g., thermodynamic and transport properties. flow rates through valves,
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etc. The procedure to modify the FORTRAN source and make it fully compatible and "open" for communication links within SIMULINK required development of four standard MATLAB subroutines. The first subroutine is created from the former FORTRAN code; i.e., from the FORTRAN-MEX file, and contains all the necessary state derivatives. These derivatives are automatically passed to the SIMULINK built-in integrator at each time step, and new integrated values of the state variables are passed to the output block. The other three subroutines define the sizes of the state input and output vectors, provide initial conditions of the state vectors. and compute the output vectors of the system. The latter can then be passed to either the workspace-i.e., to the other blocks of the simulation requiring those values as inputs-or to the monitoring "scope" windows. After these steps were completed, the single cylinder engine simulation was ready to be incorporated into the SIMULINK shell and connected to the SIMULINK integrators to solve the system of ODES. An extensive series of test runs was conducted in order to assess which of the various integrators (RK-3, RK-5, ADAMS, and LINSIM) embedded in MATLABSIMULINK is the most suitable for engine cycle simulation. The basis of comparison were the results obtained from the stand-alone, parent FORTRAN code. The reference set of results is obtained by the standardized FORTRAN integrator code ODERT, which was developed by Shampine and Gordon [I51 and based on a predictor-corrector technique. The comparison of the cylinder pressure traces at full load obtained using the MATLAB-SIMULINK integrators and ODERT is presented in Fig. 3, while the numerical values for the primary, integrated engine
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performance variables are summarized in Table I . Agreement between all five pressure traces is generally very good, with minor discrepancies detected only when discrete numerical values are compared. The differences are a consequence of the fact that, although all integrators have the ability to adjust the step size, their techniques vary. Hence, the user does not have the same level of control over the integration process. Therefore, the actual step size at any particular instant can be different, depending on the integrator selected, and the differences can accumula.te over the 720 crank angle degree interval to produce the discrepancies observed in Table I . Since the RK-3 results are the closest in accuracy to the ODERT results that are used as the benchmark, RK-3 is the preferred package for cycle simulation work within the MATLAB-SIMULINK framework. The overall CPU time required by RK-3 is comparable to the FORTRAN-based ODERT code integrator.
B. Building the multi-cylinder transient engine simulation in SIMULINK The developed SlMULINK S-function representing the single-cylinder engine model can be used to build and quickly reconfigure a multi-cylinder engine with any number of cylinders. All of the external components, including the manifolds, the turbocharger, the intercooler, etc., can also be connected to this "engine" block to form a complete engine system block. This section focuses on building the multi-cylinder transient diesel engine simulation. Figure 4 shows the structure of the multi-cylinder engine SIMULINK model. Each of the blocks for the individual cylinders is actually a thermodynamic cycle simulation. as described in Section 11. Input design parameters are passed on to each of the blocks from the input file, but all of the operating parameters come from the blocks (functions) for the other components of the system, primarily the TABLE 1 Comparison of the results obtained with different integrators
Volumetric Efficiency Integrator
(-)
RK-3
93.2
RK-5
93.5 93.6 93.8 93.1
Adam LlNSlM ODERT (Fortran)
Peak Gas Temperature
(g/kWh)
Peak Cylinder Pressure (MW
196.6 197.0 197.4 197.8 196.3
14.846 14.828 14.812 14.809 15.024
1741.2 1739.6 1740.9 1740.4 1744.7
Brake Mean Eff. Pressure (pa)
Specific Fuel Cons.
196.6 197.0 197.4 197.8 196.3
Brake
(K)
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Fig. 4.
ZHANG, FILIPI; AND ASSANIS
Block diagram of the lransient multi-cylinder diesel engine simulation in SlMULlNK
manifold models and the engine dynamic submodel. A very imponant aspect of building a multi-cylinder simulation is phasing of individual cylinders, a function which is handled by the blocks Cylinder1 through Cylinder6 in Fig. 4. A reference cylinder (i.e., Cylinderl) is arbitrarily selected for phasing purposes, and used to define top dead center during the intake stroke as 0 degrees crank angle. Then, the rest of the cylinders are phase-shifted with respect to Cylinderl by adding an integral multiple of 120crank angle degrees to the reference crank angle, according to the firing order of the six-cylinder, four-stroke engine. Phasing requires that the in-cylinder model be able to handle partial cycles, whether the cylinder stans from intake, compression, combustion, or exhaust. The approach to modeling a partial cycle is to assume a "motoring"case; i.e., nocombustion takes place if a cycle starts after intake. Starting with the second cycle, all cylinders should execute a complete cycle. "Suml" (see Fig. 4) takes into account the number of cylinders, the engine block and crank-shaft configuration, and the firing order and sums up the various output parameters on a reference crank-angle basis. The instantaneous total brake torque value is passed on to the engine dynamics model, while the external load has to be supplied from the vehicle model or any other model capable of predicting the resistive torque (e.g., the dynamometer model). The integrator selected from the MATLAB-SIMULINK library simultaneously integrates the system of ODES supplied by all of the blocks and determines the instantaneous rotational speed of the crankshaft for the next calculation step.
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V. SIMULATING DYNAMIC ENGINE OPERATION In this section, some reference "elementary transients" are defined in order to predict multi-cylinder engine response in dynamic regimes under carefully controlled conditions and thus allow for comparative system studies. If the predictions are valid for the simple but extreme transients, it is reasonable to expect reliable behavior of the simulation during more complex dynamic cycles composed of a large number of "elementary transients." A typical heavy-duty automotive diesel engine, Detroit Diesel Corporation Series 60, is selected as the simulation object. Its primary specifications are listed in Table 2. The polar moment of inertia of the engine is estimated to be4.O kg-m2 (including the adapter plate on the flywheel), while the baseline value for the load moment of inertia is 21 kg-m2. The latter value is representative of the inertia of a large electrical dynamometer or the equivalent polar moment of inertia of an M916 military heavy-duty truck with a gross vehicle weight of 59,000kg in first gear. The database of steady-state test results obtained on the test stand at the University of Michigan W. E. Lay Automotive Laboratory was used to calibrate the constants in the engine cycle model prior to transient simulation runs. Unlike stationary engines, automotive diesel engines often undergo rapid changes of speed, and their response is crucial to vehicle behavior during sudd,en acceleration or deceleration. The dynamic engine operating regimes are associated with either sudden changes of the fueling rate or sudden changes of the external load. Two groups of results are presented. The first shows engine response after a rapid increase in the massof fuel injectedper cycle, and the secondexaminesengine response during a simultaneous gradual increase in the fuel injected and the external load. In both cases, additional runs were performed for a reduced value of the equlvalent polar moment of inertia of the load in order to assess how much the engine response changes if the overall gear ratio is changed because of the operator action. The first elementary engine transient is defined as follows. The engine is mnning at steady-state, 600rpm, with almost no external load for one second; the TABLE 2 DDC60 engine specifications Engine type Turbocharging system Bore Stroke Connecting rod length Compression ratio Rated powerlspeed
m m m
kW/rpm
4-stroke. 6-cylinder. [)I Turbocharged. intercoaled 0.13 0.16 0.2693 15 350/?100
-
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amount o f fuel injected per cylinder per cycle is just enough to overcome engine friction losses. A sudden change i n the fueling rate with nochange i n the external load causes the engine to accelerate until the rated speed is exceeded. As a result, the governor starts to cut off fuel to prevent the engine from overspeeding, thus keeping i t at a high idle speed. It may be argued that this transient regime is not the most common i n everyday engine use, but i t is suitable for validation o f the engine dynamics submodel because i t eliminates the effects o f the external load. Consequently. the calculated engine torque is the only influencing variable. assuming that moments o f inertia are physical properties that can be measured directly. Furthermore, to focus on predicting the behavior o f the multi-cylinder engine without requiring models o f ancillary components (e.g., turbocharger, intercooler). the intake nianifold pressure is supplied as input. A change i n the fueling rate, which is determined by the governor characteristics, is prescribed here. Hence. three hypothetical governor strategies are considered i n the tirst study: (A) a step change i n the mass o f fuel injected from a minimum to a maximum value. ( B ) a linear change between these two extreme values during the one-second interval. and (C) a polynomial profile representing the typical change i n the fueling rate con~rolled by the mechanical P I governor 114,161. Figure 5 illustrates the three fueling strategies used i n this study and compares the predicted engine responses: i.e.. engine speed as a function o f time. Differences are observed primarily during the first second o f the transient. The step change i n the fueling rate produces the fastest response, but the third case yields what is probably the most realistic speed protile. The slope o f the lines during the remainder o f the transient is very similar in all three cases. After the rated speed is reached, a simple governor model employing a linear function o f speed cuts o f f fuel and keeps the engine at high idle. Figure 6a illustrates how calculated cylinder pressures i n all six cylinders change during the observed period o f engine dynamic operation using fueling'strategy B. Cylinder pressure values start increasing as soon as the amount o f fuel injected is increased. However. the peak pressure characteristic is not linear because factors other than fuel affect the cycle, primarily the pressure i n the inlet manifold and the effect o f engine speed on volumetric efficiency. Although the amount o f fuel injected is maintained after i t reaches its maximum value, peak cylinder pressure does change somewhat with time, essentially following the volumetric efficiency variation with engine speed. Figure 6b shows the instantaneous engine torque calculated during the same time interval, emphasizing the fact that torque is affected not only by pressure i n the cylinder, but also by the inertial forces acting on the rcciprocating components. Initially, both the amplitude o f torque fluctuations and the mean torque value increase dramatically after the fueling rate increase between the one- and two-second intervals o f the transient. Subsequently, the amplitude o f torque fluctuations decreases steadily as the engine accelerates from approximately 800 rpm to 2160 rpm because the inertial force component reduces the peak value o f the instantaneous torque [lo]. The frequency o f both traces increases with time
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because the cycle duration in seconds decreases as the engine speed increases. Hence. the images in Fig. 6 become denser as the run progresses. Figure 7 shows a close-up of the cylinder pressure traces and the instantaneous torque characteristic during the sudden acceleration part of the transient for fueling schedule A.
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DIESEL ENGINE SIMULATION
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Next, the simulation predictions for strategy C are repeated for a reduced value o f the equivalent load inertia, i.e. IL = 4.2 kgm2. If the engine were used i n a heavy-duty truck, a change o f 2.23 i n the gear ratio o f the transfer case would effectively reduce the equivalent moment o f inertia by a factor of 5. thus yielding the selected value for I L . The instantaneous speed profiles o f the engine.for the baseline (high) and low load inertias are compared i n Fig. 8. With low load inertia, the profiles show that rated speed is reached after only two seconds, instead o f approximately five seconds with baseline inertia. I f i t is assumed that road load can be neglected at very low speeds after the truck moves from a standstill, this test case can provide a good illustration o f the effect that the addition o f the transfer casc could have on the ability o f the truck to accelerate. The engine dynamic operation under less extreme conditions is examined i n the sccond series o f simulation runs. The elementary transient for this series o f runs is defined as follows. The engine is running at steady-state, 600rpm, with almost no external load for one second. The fueling rate gradually changes as a linear function o f time from that point on, while the external load also starts to increase linearly. If the rated speed is exceeded, a simple governor model w i l l prevent overspeeding and reduce the amount of fuel injected per cycle. This fuel and load schedule is more representative o f an engine i n a vehicle moving up the grade while the driver reacts i n anticipation o f the external load change. Figure 9a shows the fueling schedule used as simulation input. The observed differences i n the fuel cut-off action correspond to the two strategies studied. One set o f calculations is performed for the baseline value o f the equivalent polar moment o f inertia o f the load. Another set o f the same parameters is obtained assuming that gear ratio has changed by a factor o f 2.23; therefore, the external load is also reduced by a factor of 2.23, as shown i n Fig. 9b. The equivalent polar moment o f inertia is 4.2 kg-m' instead o f 2 1 kg-n?'. When the engine response for the first run is compared to the profiles in Fig. 5 , it is clear that the instantaneous engine speed line exhibits a vcry different shape. Its gradient is much smaller initially and increases toward thc end o f the transient. The rated engine speed is reached after slightly more than eight seconds, and the fuel is cut o f f to maintain constant speed (see Fig. 9c). Note that i f the engine was operating i n the vehicle, the transmission gear ratio would have to be changed before that point. The consequences o f using a low gear ratio for the sccond.run are very dramatic. The engine rated speed is reached after only four seconds, which would be the time to change the gear ratio. The profile o f the engine speed line has also changed. Combining fueling characteristics identical to those used i n the first run with reduced external load and inertia produces an almost linear engine response. I n addition, the mechanical structure o f the engine experiences much lower loads because the peak cylinder pressures when the engine reaches its rated speed are much lower i n the second run (see Fig. 9d). Note that cylinder pressure traces i n Fig. 9d are plotted only for every sixth cycle. The rest o f the cycles are omitted for clarity.
DIESEL ENGINE SIMULATION
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VI. CONCLUSIONS In this study, a steady-state, zero-dimensional diesel engine model has been the basis for the development of a transient cycle simulation and itseventual integration in the flexible, reconfigurable MATLAB-SIMULINK simulation environment. Integrators embedded into MATLAB have been used successfully to solve the system of simultaneous, nonlinear, ordinary differential equations that govern the behavior of the system state variables. The new generation, multi-cylinder engine simulation includes an instantaneous torque model that accounts for engine dynamics on a crank-angle basis. Simulation predictions illustrate how different fueling strategies and e x t e n d load schedules affect the engine dynamic behavior. It is concluded that a predictive, transient, multi-cylinder diesel simulation is an extremely useful tool that can replace expensive prototype building and lengthy experimental testing programs. However, the simulation needs to be highly flexible and modular to integrate different components into the system easily and to make the subsequent reconfiguring of the system easy. Current and future activities include further decomposition of the diesel cycle simulation module to allow for refinement of its submodels, particularly by enhancing their predictiveness during transient operation and by concurrent validation of the submodels and the overall system model against experimental results.
VII. ACKNOWLEDGMENTS The diesel engine model that has formed the basis of the transient, multi-cylinder diesel engine simulation has been developed through the doctoral research of Dennis N. Assanis under the guidance of Professor John B. Heywood at the Massachusetts Institute of Technology. Funding for the extension of the parent model to simulate single-cylinder engine transients and for its reconfiguration in the MATLAB-SIMULINK environment has been provided in pan by the Automotive Research Center (ARC) under Contract No. DAAE07-94-C-R094. The contributions of Professor Panos Y. Papalambros, director of the ARC, and Dr. Waiter Bryzik, government technical director of the ARC, are gratefully acknowledged. The authors also wish to express their gratitude to the numerous colleagues and quad members of the Advanced Propulsion Simulation Thrust for many useful discussions, as well as for their on-going efforts to acquire experimental data for the validation and further improvement of flexible, multi-cylinder transient simulation.
REFERENCES I . J. D. Ledger. R. S . Benson, and N. D.Whitehouse. Dynamic modelling of a turbocharged diesel engine. Pmc. I Mech E. CP15. 1973.
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2. R. S. Benson. J. D. Ledger, N. D. Whitehouse, and N. D. Walmsley, Comparison of Experimental and Simulated Transient Responses of a Turbocharged Diesel Engine. SAE Paper 730666. 1973. 3. J. P. Jensen. A. F. Kristensen. S. C. Sorenson, N. Houbak. and E. Hendrics, Transient Simulation of a Snlall Turbocharged Diesel Engine. SAE Paper 904182, 1990. 4. M. R. Goyal. Simulation of a Turbocharged Diesel Engine lo Predict the Transient Response. ASME Paper 76-WAIDGP-I. 1976. 5. S. Berglund. A model of turbocharged engines as dynamic drivetrain members. SAE Paper 933050. SAE Trunsocrions 102. 1993. 6. D. E. Winterbone. C. Thimarooran, and P E. Wellstead. A Wholly Dynamic Model of a Turbocharged Diesel Engine lor Transfer Function Evaluation. SAE Paper 770124, 1977. 7. N. Watson and M. Marzouk. A Non-Linear Digital Simulation of Turbocharged Diesel Engines Under Transient Conditions. SAE Paper 770123. 1977. 8. D. N. Assanis. A Computer Simulation of the Turbocharged Turbocompounded Diesel Engine System for Studies of Low Heat Rejection Engine Performance. Ph.D. Thesis. M.I.T.. 1985. 9. D.N. Assanis and J. B. Heywood. Development and Use of a Computer Simulation of the Turbocompounded Diesel System for Engine Performance and Component Heat Transfer Studies. SAE Paper 860329. 1986. 10. 2. S. Filipi and D. N. Assanis, A nonlinear. transient. single-cylinder diesel engine simulation lor Technical predictions of instantaneousengine speed and torque, Proceedi~~gsofASME-ICESprifig Co~rfprence,1997. I I. R. R. Pooln. R. Sekar. D. N. Assanis. and G. R. Cataldi. Study of oxygen-enriched combustion air for locomotive diesel engines. Pmceedings of ASME-ICE Fall Technical Confereitce 27(4). 1996. 12. N. Watson. A. D. Pilley. and M . Marzouk. A Combustion Correlation for Diesel Engine Simulation. SAE Paper 800029. 1980. 13. B. W. Millington and E. R. Hanles, Frictional losses in diesel engines, SAE Paper 680590. SAE Truns. 77 (1968). and Gas Dwamics of 111renral 14. J. H. Horlock and D. E. Winterbone (eds). The Tl~er~~iod~nnrnics Corr~busrio~i Engines. Volume 11. Clarendon Press. Oxford. 1986. 15. L. F. Shampine and M. K. Gordon. Compurer Sdurion c ~ Ordinan. f Difleremiol Eqitrrrio,u: The lriiriol Itrlue P m h l e ~ r Freeman, ~, 1974. 16. C. D. Rakopoulos. E. G. Giakoumis, and D.T. Hountalas. A Simulation Analysis of the Governor Technical Characteristics and Type on the Transient Performance of a Naturally Aspirated ID1 Diesel Engine. SAE Paper 970633. 1997.
Received Februrrty 1997
