CI Engine Modeling Techniques

Trends in Mechanical Engineering and Technology ISSN: 2231-1793 www.stmjournals.com CI Engine Modeling Techniques Sowmya Thyagarajan* Amity Institute of Space Science and Technology, Noida, India Abstract The internal combustion engine is a heat engine that converts chemical energy in a fuel into mechanical energy, usually made available on a rotating output shaft. Internal combustion engines can be classified in many ways primarily by the type of ignition system they use, spark ignition (SI) and compression ignition (CI). An SI engine starts the combustion process in each cycle by use of a spark plug. The spark plug gives a highvoltage electrical discharge between two electrodes which ignites the air-fuel mixture in the combustion chamber surrounding the plug. The combustion process in a CI engine starts when the air-fuel mixture self-ignites due to high temperature in the combustion chamber caused by high compression. The turbocharged compression ignition (diesel) engine is nowadays the most preferred prime mover in medium-large applications like automobiles, trucks, locomotives, marine vessels, or airplanes. Moreover, it continuously increases its share in the highly competitive automotive market, owing to its reliability that is combined with excellent fuel efficiency. The major goal of this paper is to provide a comprehensive reference source for the researchers in understanding the CI engine, and describes the different types of engine models available. Keywords: internal combustion engine, spark ignition, compression ignition, turbocharger *Author for Correspondence E-mail: sowmicatty@gmail.com INTRODUCTION Today’s engines are designed to meet the demands of the automobile-buying public and many government-mandated emissions and fuel economy regulations. The internal combustion engine used in automotive applications utilizes several laws of physics and chemistry to operate. Although engine sizes, designs, and construction vary greatly, they all operate on the same basic principles. One of the many laws of physics utilized within the automotive engine is thermodynamics. The driving force of the engine is the expansion of gases. The internal combustion engine (ICE) is an engine in which the combustion of a fuel (normally a fossil fuel) occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an ICE, the expansion of the high-temperature and highpressure gases produced by combustion apply direct force to some components of the engine. The force is applied typically to pistons, turbine blades, or a nozzle. This force moves the components over a distance, transforming chemical energy into useful mechanical energy. The term ICE usually refers to an engine in which combustion is intermittent, such as the more familiar four-stroke and twostroke piston engines. A second class of ICEs use continuous combustion – gas turbines, jet engines and most rocket engines, each of which is an ICE on the same principle as previously described. Basically, this paper deals with compression-ignition (CI) engines, their characteristics and modeling. For heavyduty applications, i.e., road-going transport vehicles, the diesel engine is today the only realistic option due to its high efficiency as compared to other alternatives. The purpose of turbocharging has in the past been to increase the power-to-weight ratio of the engine. By increasing the amount of air available for the combustion process, more fuel can be burned effectively. Various techniques have been carried out to model the CI engines, where turbocharger modeling has been of special importance. The sections in this paper have been divided depending on the various primary TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 7 CI Engine Modeling Techniques Thyagarajan Sowmya __________________________________________________________________________________________ engine elements for which different modeling techniques have been carried out by various researchers. Section 1 gives an overall view of diesel engines and a brief description of their characteristics. Section 2 describes various modeling techniques carried out on torque generation of the engine. Section 3 describes various models that are used in manifold modeling. Section 4 describes the methods that are carried out in turbocharger modeling. This review does not contemplate to go into details of particular models or describe results of comparative experiments; rather a summary of more approaches and interesting parts is presented in this paper. SECTION 1 Internal Combustion Engine Ignition Spark Ignition (SI): High-voltage electrical discharge between two electrodes ignites airfuel mixture in a combustion chamber surrounding a spark plug. In SI engines [1], the burning of fuel occurs by a spark generated by the spark plug located in the cylinder head of the engine. Due to this fact, they are called spark ignition engines. Compression Ignition (CI): Air-fuel mixture self-ignites due to high temperature in combustion chamber caused by the highcompression diesel engine Strokes Four-Stroke [2]: Four piston movements over two engine revolutions for each engine cycle. Two-stroke: Two piston movements over one revolution for each engine cycle. A four-stroke engine (also known as fourcycle) is an ICE, in which the piston completes four separate strokes. These are  Intake stroke  Compression Stroke  Power Stroke  Exhaust Stroke Basic CI Engine Components [3] Basic components of a CI engine are block, bearing, camshaft, carburetor, catalytic converter, combustion chamber, connecting rod, crankcase, crankshaft, exhaust manifold, fan, flywheel, fuel injector, fuel pump, head, head gasket, intake manifold, oil pan, oil pump, oil sump, piston rings, push rods, radiator, rod bearing, speed control-cruise control, starter, supercharger throttle, turbocharger, water jacket, water pump. Compression Ignition (Diesel) Engine Diesel and gasoline engines have many similar components. However, the diesel engine does not use an ignition system consisting of spark plugs and coils. Instead of using a spark delivered by the ignition system, the diesel engine uses the heat produced by compressing air in the combustion chamber to ignite the fuel. Fuel injectors are used to supply fuel directly into the combustion chamber. The fuel is sprayed, under pressure, from the injector [4] as the piston completes its compression stroke. The temperature increase generated by compressing the air (approximately 1000 °F) is sufficient to ignite the fuel as it is injected into the cylinder. This begins the power stroke. Since starting the diesel engine is dependent on heating the intake air to a high enough level to ignite the fuel, a method of preheating the intake air is required to start a cold engine. Some manufacturers use glow plugs to accomplish this. Another method includes using a heater grid in the air intake system. Diesel engines can be either four-stroke or two-stroke designs though, like gas engines, production automotive applications currently use four-stroke engines. Two-stroke engines complete all cycles in two strokes of the piston, much like a gasoline two-stroke engine Turbocharged Diesel Engine Diesel engines, also known as CI engines, have been turbocharged for many decades. It is the operating principle of the CI engine that enables them to be turbocharged without some of the problems occurring when turbocharging spark ignition (SI) engines. The basic idea of turbocharging is to increase the amount of air inducted into the cylinders. The more air you induct, the more fuel you can inject, and the more power output you get. A turbocharged engine can then be made smaller than a naturally aspirated engine which has the same power output, i.e., a turbocharged engine has a higher power-to-weight ratio. Other advantages are that pumping losses and friction decrease Exhaust Gas Recirculation The concept of exhaust gas recirculation (EGR) has been introduced as a way to TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 8 Trends in Mechanical Engineering and Technology Volume 3, Issue 3, ISSN: 2231-1793 __________________________________________________________________________________________ decrease NOx production. Since NOx is mainly produced under high pressures and high temperatures, it is possible to control its formation by either reducing the compression or the temperature in the combustion chamber. When using EGR, it is the temperature that is affected. EGR mixes cooled exhaust gas into the intake air stream, helping to lower combustion temperatures as less air and fuel are burned in each cycle. One of the drawbacks with EGR is that it decreases the combustion stability. Because you do not want to lose drivability, i.e., power output, EGR is only active during low load conditions. The amount of EGR diesel engines can tolerate before misfire is up to 40%. The use of EGR reduces the formation of NOx up to 30%. Variable Geometry Turbocharger A conventional turbocharger has a limited optimal working area. At low engine speeds, there is not enough flow through the turbine to drive the turbocharger, and at high engine speeds some of the flow must bypass the turbine by a waste gate not to exceed the maximum rotational speed of the turbine. In order to widen the optimal working area, especially in the lower engine speeds, variable geometry turbocharging is applied. The basic idea is to have variable inlet geometry to the turbine. This is managed by a set of vanes arranged in the path of the flow, by changing the angle of the vanes the inlet area to the turbine changes. During low engine speeds, when the flow through the engine is small, one can increase the velocity of the flow by partially closing the vanes, thus gaining turbine speed. With this setup, there is also no more need for a waste gate. In some literature, the term variable nozzle turbocharger (VNT) is used. Air Path System The intake manifold is a small but important part of this system. Engine models are often based on the mass flow through the engine. After entering the engine through the air filter, the air is compressed by the turbo charger (compressor). In the turbo charger, the temperature of air is also increased. This is an unwanted effect, so the air is then cooled in the charge air cooler (intercooler). Since there is no throttle, the flow of air then directly enters the intake manifold where it can be mixed with recirculated exhaust gases. Then the air is inducted into the cylinders where combustion takes place. On the outlet side of the cylinders, the exhaust gases enter the exhaust manifold, from where a portion of the gases can be recirculated through the EGR cooler back to the inlet manifold. The rest is led through the turbine (VGT) that drives the compressor and then through catalysts and the silencer. SECTION 2 In this section, various modeling techniques carried out on torque generation have been described. Method 1 In order to model the engine accurately, the thermal efficiency of the engine should be available. Engine torque generation depends on some of the engine’s operational parameters. It is shown that a diesel engine’s thermal efficiency is mainly a function of three major parameters. Here, least square methods [5] have been used. ( ) The effect of injection timing ζ on torque generation is modeled as a second-order function ξ = 1-k ( ) in which ξ0 (N, P1) is the maximum brake torque (MBT) conditions in every operational state. The result torque is calculated using energy equations. The generated torque, external load and internal friction torque together accelerate or decelerate the crankshaft. ̇ In the above formula represents the internal friction torque of engine’s moving parts and also pumping losses of the engine. √ in which “k”s are fixed coefficients that are typical data for small diesel engines, “S” is engine speed and e, max is the maximum ratio of exhaust pressure to inlet pressure in low speeds. k1 (Ten) takes into account the temperature of engine while the other “k” factors are constant. TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 9 CI Engine Modeling Techniques Thyagarajan Sowmya __________________________________________________________________________________________ Method 2 Under transient operating conditions [6], has been modeled here. The updated values of crankshaft rotational speed and angular acceleration during transients are derived from the conservation of energy principle applied on the total system (engine-load). For quasi-linear models, this procedure is applied once per cycle or per firing interval using the respective mean torque values. When a filling and emptying modeling is involved, it can be applied at each degree crank angle: Te(ϕ)–Tfr(ϕ)–Ts(ϕ)– Td(ϕ) = Ge * dω/dt + 0.5 * ∂Ge/∂ϕ * ω ^ 2 Ts(ϕ) + Td(ϕ)–Tl(ϕl) = Gl * dωl/dt Ge = Ge(φ) and Gl are the engine and load mass movements of inertia respectively and Te is the engine torque including gas, inertia and (the usually negligible) gravitational forces contribution. Load Torque is calculated by Tl(ϕl) = k1 + k2 * (ωl ^ s) In most cases, the crankshaft can be assumed as sufficiently rigid (φ = φl) and the engine inertia constant. Hence, the energy balance equation reads Te(ϕ)−Tfr(ϕ)−Tl(ϕ) = (Ge + Gl)dω/dt Method 3 The multi-order nonlinear model of diesel engine is formulated based on quasi-steadystate method [7], which allows simulating the dynamics of diesel engines with a relatively simple model. The engine torque equation is expressed as π/30(Ie + Il)dn/dt = Me−Ml 2 where Ie (Nms ) and Il are the equivalent moment of inertia of engine and load respectively, Me (Nm) and Ml are brake torque of engine and load torque on engine respectively. The indicated torque of engine, Mi is given by Mi = Hugc i/(2π) = f1(gc, i) where H (kJ/kg) is the low calorific value of u fuel and gc (kg) is the amount of fuel injected into cylinder per cycle. i is the engine’s indicated efficiency and it can be simplified as a function of engine speed ω (rad/s) and excess air coefficient α. According to the experimental data, it is expressed as 2 i 2 2 = f2[(ω−ω0) + d (α−α0) ] The engine’s mechanical efficiency m mainly depends upon the engine speed, load (indicated power Ni) and cooling water temperature t w (ºC). From the regression analysis of experimental data, = (75.347−0.010n + 0.000477N + 0.0872t ) m i w /1 SECTION 3 In this section, various techniques used in manifold modeling are described. Model 1 These models are so-called mean value engine models (MVEMs). To generate the models, filling and emptying (F&E) modeling [8] is used. This method assumes a number of assumptions. Intake manifold temperature is constant. The pressure, temperature and composition inside the manifold are assumed to be homogeneous. Also instant and perfect mixing of incoming flow with matter inside the manifold is assumed. Modeling the intake manifold in a correct way is important because this system governs the flow into the engine’s cylinders. This flow is crucial to engine performance since the amount of air inducted into the cylinders to a large extent governs the amount of fuel that can be burned and, therefore, the power output. The amount of air in the intake manifold depends mainly on three factors – the flow into the manifold (from intercooler and EGR valve), the flow into the cylinders, and the inlet manifold pressure. The intake manifold can be viewed as a reservoir. Flows from both the intercooler (WInter) and the EGR valve (WEGR) are entering the reservoir and the flow into the cylinders (WInlet) is leaving the reservoir. p & m State Model An adiabatic assumption is made, i.e., heat transfer in the manifold is neglected. Two gases will be mixed inside the volume, the fresh air from the intercooler and the exhaust gas re-circulated (egr). Two gas components are treated when deriving state equations. The two gas components separately we assume that each of them has, in the intake manifold, the partial pressure pi, the mass mi TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 10 Trends in Mechanical Engineering and Technology Volume 3, Issue 3, ISSN: 2231-1793 __________________________________________________________________________________________ ̇= ̇ + ̇ = R1cp1/V cv1(W1,inT1,in−W1,outT) + R2cp2/V cv2(W2,inT2,in−W2,outT) By letting subscript 1 denote the air, and subscript 2 denote the re-circulated exhaust gas in the manifold and the assumption that W1,out = (m1/m1 + m2)Wout,tot W2,out = (m2/m1 + m2)Wout,tot We can rewrite the pressure state equation in the following way: ̇ Intake = 1/Vintake((Rair * cpair/cpair–Rair) Winter Tinter + (Rexh * cpexh/cpexh– Rexh)Wegr Tegr−((1−Zegr) (Rair cpair/(cpair–Rair))+Zegr * Rexh cpexh/cpexh– Rexh)Winlet Tintake) where Zegr = (megr/mair) + megr ̇ air = WInter − (1−Zegr)WInlet ̇ egr = Wegr–Zegr * WInlet Tinter = (pintake * Vintake/mair * Rair) + meg r * Regr p & T State Model In this model, we will use pressure and temperature in the intake manifold as states. Heat transfer in the manifold is neglected, i.e., we have an adiabatic assumption. We also assume perfect mixing of the air and egr flow in the manifold and that air and exhaust gas properties are equal. ̇ = WInter + Wegr–Winlet ̇ intake = (R(T ^ 2intake)/pintake * Vintake)[ Winter((γTinter/Tintake)−1) + Wegr((γTegr/Ti nter)−1)−Winlet(γ−1)] The inlet manifold pressure state equation can now be deduced. To do this, we use the differentiation of the ideal gas law applied to the mass of gas in the intake manifold. ̇ * Iintake = R/Vintake(mintake * Tintake + mintake * ̇ intake) ̇ intake = (γ * R * Tintake/Vintake)(Winter(Ti nter/Tintake) + Wegr(Tegr/Tintake)−Winlet) Model 2 A state space representation of a turbocharged diesel engine is provided based on off-line least square method [9]. This nonlinear mean value model predicts engine speed as a function mass of fuel injected per cycle, injection timing (ξ), ambient pressure and temperature, and external loads. Fig. 1: Manifold Setup Inside an Engine. In turbocharged engines, the manifolds are intermediate volumes placed between compressor and inlet ports or turbine and exhaust ports. The airflow of turbine and compressor has been calculated before. The engine airflow rate is calculated using the volumetric efficiency as follows: TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 11 CI Engine Modeling Techniques Thyagarajan Sowmya __________________________________________________________________________________________ ̇ Volumetric efficiency is a function of inlet manifold pressure and engine RPM. = The inlet manifold pressure plays an important role on volumetric efficiency; there are many models which predict the volumetric efficiency as a function of inlet pressure. ( ) Inlet manifold pressure is calculated as follows: ̇ +( ̇ Using thermodynamic relations, ̇ ̇ = ̇ ( ) ( ) Model 3 The exhaust manifold pressure is a crucial variable for turbocharged diesel engines, affecting the torque production and the emissions through variations in the EGR mass flow and in the residual mass fraction in the cylinder. This variable is, therefore, considered very relevant for closed-loop EGR and turbocharger control. This model describes the development of an estimator [10] for the exhaust manifold pressure in a turbocharged diesel engine. The approach proposed relies on a feed-forward scheme based on the inversion of a two-stage turbocharger model, which includes the radial turbines, nozzles and valves. The estimator accounts for the various operating modes of the turbocharger, namely, the effects of the high-pressure turbine VGT and bypass, and the low-pressure waste-gate valve. Results of the estimator are presented in both steady state and transient operating conditions. The estimation scheme for the exhaust manifold pressure of a turbocharged engine is based on the inversion of a grey box, quasistatic model that is generally adopted to characterize the flow in a radial turbine. The turbine flow is generally specified in terms of corrected mass flow rate, which is related to the (dimensional) mass flow rate as: ̇ corr = ̇ TB(√Tin/Pin) where, pin and Tin are the inlet conditions. The flow model of radial turbine generally assumes the device as a quasi-steady nozzle; hence, applying the equations for compressible flow: ̇ corr = Ωeq * (Pref/√RTref) * f1(ɛ) Ε = pin/pout is the pressure ratio across the turbine and γ is the specific heat ratio for air treated as ideal gas. ̇ TB = ̇ corr * (Pout/√Tout) * ɛ ^ ((1 + m)/2 m) ̇ = ln(ɛ)/(ln(ɛ) + ln[1− lp(ɛ)(1−ɛ ^ (1−γ/γ))]) TB = Ωeq * (Pref/√RTref) * Pout/√Tout) *ɛ ^ ((1 + m)/2m) * f1(ɛ) The above expression can be used to scale the dimensional mass flow rate into a corrected mass flow rate, with respect to the thermodynamic conditions downstream the turbine: ̇ corr,down = ̇ TB * √Tout/Pout = ̇ corr * ɛ ^ ((1 + m)/2m) Ultimately, the upstream pressure is the output. Parameters a0, a1, a2 can be identified [10] on engine data. Pin = (( ̇ corr,down−a0 * a2)/a0) ^ (1/a1) * Po ut This equation is used as a feed-forward estimator of the exhaust manifold pressure for a single-stage, fixed geometry turbine. Model 4 A multi-order nonlinear model [7] diesel engine is formulated based on quasi-steady state method, which allows simulating the dynamics of diesel engines with a relatively simple model Exhaust gas temperature in manifold Tm is determined by dTm/dt = ke/Mm[Ge * Te−(Gt + (1/ke) * (dM m/dt))Tm] where, Ge is the gas flow rate from cylinder to manifold, Gt is the gas flow rate of turbine and Mm (kg) is the amount of gas in the exhaust manifold. The gas pressure in manifold Pm is represented by: dPm/dt = (ke.Re/Vm)(Ge * Te–Gt * Tti) TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 12 Trends in Mechanical Engineering and Technology Volume 3, Issue 3, ISSN: 2231-1793 __________________________________________________________________________________________ where, Vm is the volume of exhaust manifold and Tti is the inlet gas temperature of the turbine 0.325 Te = 165.415gc + 41.878n + 305.4. SECTION 4 This section deals with various methods that are used in turbocharger modeling which is considered to be the primary component of diesel engines these days. The typical turbocharger in an automotive application is a simple device, which is mechanically separated from the reciprocating internal combustion engine. The turbocharger consists of a centrifugal compressor which is mechanically connected to and driven by a single radial turbine. The turbine extracts energy from the otherwise wasted exhaust gases. The role of the compressor is to increase the air density entering the combustion chamber, thus a higher available mass of air is achieved for the combustion process. Fig. 2: Air Path inside an Engine. Method 1 This model [11] is based on steady-flow rig measurement of the turbine and compressor used under the assumption that the flow within the turbo machine is quasi-steady, i.e., behaves at any instant in time as under steady flow conditions. The turbine and compressor performance parameters needed to define steady operation of the turbo machine are usually specified as quasi-nondimensional parameters to take the inlet conditions into account. For the turbine, i.e., reduced speed (Nred), reduced mass flow (mred) and pressure ratio (PR) Nred = N/√To ̇ red = ( ̇ √To)/Po PR = Po,in/Pexit where (Po) denotes inlet pressure and (To) inlet temperature. The power produced/consumed by the turbine/compressor is derived from the Euler equation via the isentropic relation including losses PT = T * ̇ cp * To,in(1–(Po,out/Po,in) ^ γ– 1/γ)–Pc = 1/ c * ̇ * cp * To,in(1– (Po,out/Po,in) ^ γ–1/γ) The turbocharger speed is derived from the torque imbalance associated with the compressor and turbine power between the turbine, compressor and frictional losses in the shaft assembly according to dωTC/dt = ( mechPT–PC)/I TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 13 CI Engine Modeling Techniques Thyagarajan Sowmya __________________________________________________________________________________________ Fig. 3: Schematic Diagram of a Turbocharged Diesel Engine with EGR. Method 2 In this method, a mean-value model of the AIR path of a turbocharged diesel engine with EGR is described. A third-order nonlinear model can be derived using the conservation of mass and energy, the ideal gas law for modeling the intake and exhaust manifold pressure dynamics, and a first order differential equation with time constant τ for modeling the power transfer dynamics of the VGT. Under the assumption that the intake and exhaust manifold temperatures, the compressor and turbine efficiencies, the volumetric efficiency and the time constant τ of the turbocharger are constant, this modeling approach results in the nonlinear model ̇ ̇ ̇ Wci describes the relationship between the flow through the compressor and the power Wxi is the flow through the EGR Valve = ( √ ) √ Wie is the flow from the intake manifold into the cylinders Wxt is the turbine flow ( )* * ( ( ) )( ) where, pi is the intake manifold pressure px is the exhaust manifold pressure Pc is power transferred by the compressor √ √ Pressure in the turbine ( ) Wxi describes the flow through the EGR valve. Aegr(Xegr) is the effective area of the EGR valve. TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 14 Trends in Mechanical Engineering and Technology Volume 3, Issue 3, ISSN: 2231-1793 __________________________________________________________________________________________ Multi-model Approach A multi-model approach [12] is considered for controlling the air path of a turbocharged diesel engine. The multi-model controller is a well suited control approach to regulate a diesel engine due to the nonlinear multivariable structure of the process and the present constraints on inputs and states =1+ B( With nA < = nB, we imply an RST algorithm S( And the polynoms are A Method 3 The variable geometry turbocharger is modeled [13] using turbine and compressor maps provided by the turbocharger manufacturer to determine the flow and efficiency of both the turbine and the compressor. This model describes a simple, low order model of the air-handling system for a multi-cylinder turbocharged diesel engine with cooled exhaust recirculation. The turbine flow and the turbine efficiency are found with the turbine maps given the turbine inlet temperature, the pressure ratio across the turbine, the turbocharger shaft speed, and the nozzle position. [Wturb, turb] = f(Tem, PRturb, Nturb, Xvgt) The turbine efficiency is represented by hturb, PRturb is the pressure ratio across the turbine, Nturb is the turbocharger shaft speed, and Xvgt is the turbine nozzle position. Pt = Wturb * cp,exh * turb * Tem[1Pamb/Pe m] ^ γexh−1/γexh [Wcomp, comp] = f(Nturb,Tamb,PRcomp) Pcomp = Wcomp * cp,amb * Tamb/ comp[((P cac/Pamb) ^ γamb−1/γamb)−1] dNturb/dt = ( mPturb−Pcomp)/(Iturb * Nturb) Iturb is the moment of inertia of the turbocharger, m is the mechanical efficiency of the turbocharger and is a function of the turbocharger shaft speed, m = m(Nturb). Method 4 This is a new dynamic model [14] of a turbocharged diesel generator. The purpose of this model is to study the impact of dispersed generation on distribution systems. The model is based on the mean torque method which presents the advantages to be simple and representative and to have a modular structure. The developed model takes into account only the mechanical dynamics of the process. It is defined by steady-state data and geometrical characteristics. The various polynomial functions are obtained by curve fitting. Compressor Model The modeling of the compressor relies on the basic thermodynamic laws. The compressor torque and the outlet temperature are expressed by Cc = (γ/γ−1) * (R * Tat/ c * Ωct)[((Pad/Pat) ^ (γ−1/γ))−1]qmac Tad = Tat[1 + 1/ c{(Pad/Pat) ^ γ−1/γ−1}] Turbine Model Ct = (γ1/γ1– 1) * (R * T3/Ωct)[1−(Pat/P3) ^ (γ1−1/γ1)]qma t* t The speed of the turbocharger R is determined from Newton’s second law. Jct * (dΩct/dt) = Ct−Cc Base Model The base model given below has been formulated by my own attempt keeping Guzella and Onder’s [5] book as a basic reference for the equations and concepts given below. Any diesel engine can be modeled in the following manner. Here we have carried out the 1. Air intake 2. Inlet manifold 3. Gas exchange 4. Torque generation 5. Thermal model 6. Exhaust manifold 7. Exhaust outlet Model Equations These equations [15] are mostly nonlinear differential equations, which may require alteration to suit the requirements of the paper. As the resulting equations will be continuoustime differential equations they will require discretization for use in a simulation. For the TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 15 CI Engine Modeling Techniques Thyagarajan Sowmya __________________________________________________________________________________________ development of this simulation, the Euler method for discretization is used as it is simple to implement and can cope with nonlinear equations. The resulting equations are nonlinear differential equations which can be directly implemented in a real-time numerical simulation. Air Intake Flow control or restriction elements for gases are modeled as an isothermal throttle, for which the mass flow rate depends on the temperature and the pressure drop across the orifice volumetric flow is driven by the pressure difference; however, the density of the output gas is influenced by both the pressure and the temperature. This means that the resulting mass flow varies strongly with both temperature and pressure in a strongly nonlinear manner. This behavior could result in interactions with the receiver models with which these will be coupled. The inputs to these models are the inlet and outlet pressures and the input temperature Ψ(Pin(k)/Pout(k)) = 0.707, Pout(k) < 0.5 Pin(k)1 Ψ(Pin(k)/Pout(k)) = (2(Pout(k)/Pin(k))(1– Pout(k)/Pin(k))) ^ 0.52 Pout(k) < = 0.5 Pin(k) If Pout(k) < 0.5 Pin (k) put 1 here, else put 2 here. ̇ (k) = Cd.A.(Pin(k)/(R * in(k)) ^ 0.5) * Ψ(Pi n(k)/Pout(k)) Manifold Inlet and exhaust manifolds are constant volume gas receivers which can be defined by mass- and energy-balances with temperature, pressure, internal energy and mass as state variables. These variables are linked both by the mass- and energy-balance equations and by fundamental equations of thermodynamics. This allows the entire system to be reduced to two coupled differential equations; these output the temperature and pressure of the gas within the reservoir. The inputs to these models are the input and output mass flow rates and the input temperature. The mass flow rates are defined by subsequent models, to which this model is coupled. These models interact with this model, and as this model is an accumulator of mass and energy, the level of these quantities within this element influences the inflow and outflow of mass differently. a) Inlet Manifold ̇ in(k) = Cd.A.(Pin(k)/(R * in(k)) ^ 0.5) * 0. 707, if Pout(k) < 0.5 Pin(k) ̇ in(k) = Cd.A.(Pin(k)/(R * in(k)) ^ 0.5) * (2( Pout(k)/Pin(k))(1−Pout(k)/Pin(k))) ^ 0.5, if Pout(k) > = 0.5 Pin(k) ̇ out(k) = ρin((k) * (Pm, ωe) * (Vd/N) * (ωe(k)/2π) (k) = a[[1 + (delt * a * R/P(k) * V * Cv)[C p( ̇ in(k)− ̇ out(k)] Cv[ ̇ in(k)− ̇ out(k)]]] P(k) = Pa + (delt * Cp * R/Cv * V) * [ ̇ in(k) * in(k)− ̇ out(k) * a] b) Exhaust Manifold ̇ inexh(k) = ̇ air(k) + ̇ fuel(k) ̇ outexh(k) = Cd.A.(Pin(k)/(R * in(k)) ^ 0.5) * 0.707, if Pout(k) < 0.5 Pin(k) ̇ outexh(k) = Cd.A.(Pin(k)/(R * in(k)) ^ 0.5) * (2(Pout(k)/Pin(k))(1−Pout(k)/Pin(k))) ^ 0.5, if Pout(k) > = 0.5 Pin(k) (k) = a[[1 + (delt * a * R/P(k) * V * Cv)[C p( ̇ in(k)− ̇ out(k)]−Cv[ ̇ in(k)− ̇ out(k)]]] P(k) = Pa + (delt * Cp * R/Cv * V) * [ ̇ in(k) * in(k)− ̇ out(k) * a] c) Gas Exchange TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 16 Trends in Mechanical Engineering and Technology Volume 3, Issue 3, ISSN: 2231-1793 __________________________________________________________________________________________ The transfer of air through the engine is modeled as a volumetric pump, for which the volumetric efficiency and resulting mass flow rate depends on the temperature and the pressure difference between the inlet and exhaust manifolds. Volumetric efficiency is reduced due to an increase in either the pressure difference or the speed. The density of the air is influenced by both the inlet pressure and the inlet temperature. The air mass flow consequently varies with temperature, pressure and speed in a nonlinear manner. This behavior results in observed interactions with the receiver models and flow restrictions to which these will be coupled. The inputs to this model are the inlet and outlet pressures, the inlet temperature and the engine speed Pvol,p(Pm) = (CR/CR−1)−((Pexh/Pm) ^ (cv/c p)) * (1/CR−1)Pressure efficiency vol,ω(ωe) = 1−(0.3(ωe–ωmin/ωmax−ωmin)) Density of intake air, ρin((k) = Pin(k)/Rair * in(k) vol(Pm, ωe) = (CR/CR−1)−((Pexh/Pm) ^ (cv/cp)) * (1/ CR−1) * 1−(0.3(ωe−ωmin/ωmax−ωmin)) ̇ (k) = ρin((k) * vol(Pm, ωe) * (Vd/N) * (ωe(k)/2π balance within this model as various efficiency losses. The non-frictional losses are modeled as a heat flow which is split between the exhaust gas and the cylinder wall, whilst the frictional losses are modeled as a heat flow into the oil and cylinder block. Step 1:Torque calculated= Pme(K)* Vd/ 4π  1 Pme(K) = (K) Pm, fuel(K)−Pme, 0(K) where, Pm, fuel(K) = H1 mfuel(K)/Vd and Pme, 0(k) = assumed as zero Step 2: Now, Pme(K) = (K) Pm, fuel(K) 2 Step 3: T = Pme(K) * Vd/4π, using 2 in 1 Step 4: Q ^ exh(K) = K exh. (Pm fuel(K)−Pme(K)) Assuming Pme, 0 f(K).ωe(K−1)Vd/4π = 0 Step 5: exh(K) = m(K) + Qexh(K) ----> 3 Step6: Calculate by adding 3 here in Pme0, f(K) = K1( exh(K−1)). (K2 + K3S ^ 2(ωe(K−1)) ^ 2)√K4/B --4 Step7: Calculate by adding 4 here in Pme, 0(K) = Pme, 0f(K) + Pme, 0g(K) 5 Pme, 0g(K) = Rexh(K−1)−Pm(K) Step8: Calculate by adding 5 here Pme(K) = (K)Pm, fuel(K)−Pme, 0(K) 6 where, Pm, fuel(K) = H1mfuel(K)/Vd Step9: Calculate Te(K) = Pme(K).Vd/4π ,by adding 6 here. Thermal Model d) Torque Generation Torque production is modeled as a fuel mass flow rate-dependent mean cylinder pressure, which acts upon the piston area with a variable thermodynamic efficiency which depends on several parameters. Input energy is directly proportional to the fuel flow as air is always present in excess; consequently the input energy is determined by the fuel mass flow and the calorific value. The thermodynamic efficiency is reduced by the pressure difference between the manifolds and as the speed increases (due to reduced time for gas transfer). Exhaust gas temperature and other heat losses are calculated from an energy Temperatures within the engine are modeled by a set of three thermal reservoirs linked by thermal resistances and with heat flows into and out of the reservoirs. These reservoirs model the temperatures of the cylinder wall, the volume of coolant within the engine and a reservoir that combines the engine block and the engine oil. The heat flows into the reservoir system are generated within the torque-generation model as both the remaining waste heat that does not escape with the exhaust gas is transferred to the cylinder wall and the frictional energy losses are transferred to the oil and the block. Heat flows from the wall to the coolant and between the coolant TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 17 CI Engine Modeling Techniques Thyagarajan Sowmya __________________________________________________________________________________________ and the block/oil system. Removal of heat occurs via radiation and convection from the block to ambient and via the temperature change of the coolant flow. Cylinder Wall Temperature ̇ oil = Pmeof * ωe * (Vd/4π) ̇ exh = Kexh. (Pmfuel−Pme−Pmeof) * ωe * Vd/4π ̇ wall = (Pmfuel * ωe * Vd/4π)− ̇ oil− ̇ exh Θexh = m + ( ̇ exh/Cpexh * ̇ exh) d wall/dt = (1/Cblock * mwall) * ( ̇ wall−( w all− c,out/Rwc) ) Coolant Temperature d c,out/dt = (1/Cc * mc) * (Cc * ̇ c * ( c,in− c, out) + ( wall− c,out/Rwc)−( c,out− oil/Rco)) Oil Temperature d oil/dt = (1/Cblock * mblock + Coil * moil) * ( ̇ oil + ( c,out− oil/Rco)−( oil− a/Rba)) Proportion of relief valve open A = 0.5−Kp * (Poild−Poil) Oil Pressure Oil flow is provided via an engine-driven positive displacement pump discharging into oil galleries, which are treated as a reservoir containing an incompressible fluid. The discharge from the galleries is modeled using two valves with temperature-dependent discharge coefficients to model the effect of temperature on viscosity. One of these valves is constantly open and models oil flow into bearing journals and discharge from oil sprayers, the other behaves as the control element for a reverse-acting proportional pressure controller, which is used to model the pressure relief valve. The result is that this model displays the type of behavior observed, with oil pressure increasing with engine speed and decreasing with temperature. Poil = Poild * [Kωp * ωe– A * (Cd1 * oil/μoil) * (Poil) ^ 0.5 + (Cd2 * oil/μoil) * (Poil) ^ 0.5] Exhaust Outlet Flow control or restriction elements for gases are modeled as an isothermal throttle, for which the mass flow rate depends on the temperature and the pressure drop across the orifice volumetric flow which is driven by the pressure difference; however, the density of the output gas is influenced by both the pressure and the temperature. This means that the resulting mass flow varies strongly with both temperature and pressure in a strongly nonlinear manner. This behavior could result in interactions with the receiver models with which these will be coupled. The inputs to these models are the inlet and outlet pressures and the input temperature. Ψ(exh_press_pa/exh_mani_pa) = 0.707, exh_mani_pa < 0.5 exh_press_pa 1 Ψ(exh_press_pa/exh_mani_pa) = (2(exh_mani _pa/exh_press_pa) * (1– exh_mani_pa/exh_press_pa)) ^ 0.5  2 exh_mani_pa < = 0.5 exh_press_pa If exh_mani_pa < 0.5 exh_press_pa, put 1 here, else put 2 here… ̇ (k) = Cd.A.(exh_press_pa/(R * in(k) ) ^ 0.5) * Ψ(exh_press_pa/exh_mani_pa) CONCLUSIONS This paper gives a broad idea about the techniques used for modeling different elements of compression ignition engines. This paper can be used while modeling any diesel engine mathematically. Further simulations can also be done depending on the engine model. Basic idea behind this paper is to provide a clear idea about the techniques that are recently being used in modeling CI engines. ACKNOWLEDGMENTS Setting an endeavor may not always be an easy task, obstacles are bound to come in its way and when this happens, help is welcome and needless to say without help of those people whom I am mentioning here, this endeavor would not have been successful. I am thankful from the core of my heart for the precious contribution of Mr. Manickam (Scientist ‘B,’ FSIM Department, ADE, DRDO) for guiding me in this paper. I would like to convey my special thanks to Mrs. Cynthia Surya (Technical officer) for helping me to work in one of the India’s best TMET (2013) 7-19 © STM Journals 2013. All Rights Reserved Page 18 Trends in Mechanical Engineering and Technology Volume 3, Issue 3, ISSN: 2231-1793 __________________________________________________________________________________________ labs. I would also like to thank my friend Vshyam Prasada Rao for the moral support he provided me in completing this paper. Last but not the least; I would like to convey my special thanks to my parents for their moral support and ethical values they imposed on me without whom I could not have reached this height. 8. 9. REFERENCES 1. Kota Sridhar, R. B. V. Murali, Sk. Mohammad Younus, et al. Computerized simulation of spark ignition internal combustion engine. IOSR J. Mech. Civil Eng. 2013;05–14p. 2. Air cadets the next generation. ACP 33Flight, Vol. 3. Air Cadet Publications: UK. 3. Willard W. Pulkrabek. Engineering Fundamentals of the Internal Combustion Engine, 2nd edn. Pearson Prentice Hall; 1997. 4. Mihir Sen. Internal Combustion Engine. University of Notre Dame; 2009. 5. Lino Guzzella, Christopher H. Onder. Introduction to Modeling and Control of Internal Combustion Engine Systems. Springer: Berlin, Germany; 2004. 6. C. D. Rakopoulos, E. G. Giakoumis. Review of Thermodynamic Diesel Engine Simulations under Transient Operating Conditions. SAE International 2006. 7. Jianyuan Zhu. 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