Manifold Pressure Research Articles

An implementable zone NMPC applied to an ESP-lifted oil well system: Handling the lack of measurements with nonlinear state estimator coupling

This paper addresses the first application of a nonlinear model predictive control (NMPC) scheme, coupled with an extended Kalman filter (EKF), for oil production processes with electric submersible pump (ESP) installations. The resulting nonlinear program of the proposed NMPC is most computationally tractable by the use of zone control scheme to deal with the downthrust and upthrust operational envelope-type ESP time-varying constraints, making it implementable in practice. The coupling of EKF seeks to solve the challenger problem of lack of measurements in ESP-lifted oil wells, besides is strategically used to compute downthrust and upthrust ESP head bounds from the estimated average flow rate in the production column. The implementable zone NMPC+EKF scheme is also flexible to incorporate optimizing targets in its formulation aiming at economic performance improvements. The effectiveness of the proposal is carried out in noisy plant-model mismatch scenarios for fairly different operating condition tracking, including cases of rejection of significant disturbances on manifold pressure. Analysis on the inclusion (or not) of optimizing target on the choke valve opening also demonstrates the economic gains in terms of ESP power savings, in addition, the computational effort evaluation corroborates with the feasibility of the controller in real-time implementation purposes.

Improve Supply Manifold Pressure of Proton Exchange Membrane Fuel Cell by using of Reset Control

Proton Exchange Membrane as one of the most advanced types of fuel cells plays an effective role in renewable energy generation and supply manifold is one of its main subsystems. Aiming to cover nonlinear behaviour, this study presents a new robust method for controlling the supply manifold pressure at the cathode side. To consider the uncertainty effects as well as the nonlinear behaviour of the supply manifold, a delayed transfer function model is considered. The proposed reset control approach improves the transient response in regulating the supply manifold pressure at the cathode side. The simulation and comparison results in MATLAB environment show the capabilities of the proposed method to improve the transient response of the system from different perspectives and stability despite of uncertainty effects.

Modeling Transient Control of a Turbogenerator on a Drive Cycle

<div class="section abstract"><div class="htmlview paragraph">GTDI engines are becoming more efficient, whether individually or part of a HEV (Hybrid Electric Vehicle) powertrain. For the latter, this efficiency manifests itself as increase in zero emissions vehicle mileage. An ideal device for energy recovery is a turbogenerator (TG), and, when placed downstream the conventional turbine, it has minimal impact on catalyst light-off and can be used as a bolt-on aftermarket device. A Ricardo WAVE model of a representative GTDI engine was adapted to include a TG (Turbogenerator) and TBV (Turbine Bypass Valve) with the TG in a mechanical turbocompounding configuration, calibrated using steady state mapping data. This was integrated into a co-simulation environment with a SISO (Single-Input, Single-Output) dynamic controller developed in SIMULINK for the actuator control (with BMEP, manifold air pressure and TG pressure ratio as the controlled variables). Transient verification with WAVE-RT was conducted on WLTP and NEDC drive cycles, estimating dynamic energy recovery and fuel consumption improvement. Hints are given for a more advanced MIMO (Multiple-Input, Multiple-Output) control system architecture and calibration.</div></div>

Validation and Enhancement of a Supermesh Strategy for the CFD Simulation of Four-Stroke Internal Combustion Engines

The present paper describes and validates an efficient CFD implementation to replicate the working fluid-dynamics of a real four-stroke internal combustion engine. To do this, experimental data obtained on a single-cylinder engine are used to validate the proposed computational approach. The engine domain is divided into regions according to each moving zone, and these are coupled using a pseudo-supermesh interface presented in a previous work by the authors. In this work, the original pseudo-supermesh strategy is enhanced by introducing the dual-boundary concept to model the valve opening/closing events to increase the accuracy and simplicity of the simulation procedure. The results produced by the proposed software tool show a good correlation to the experimental measurements of the complete engine cycle. Macroscopic quantities of the in-cylinder flow are accurately replicated as well as the instantaneous evolution of the in-cylinder and intake manifold pressure. Furthermore, the present work shows that the computational efficiency and scalability of the enhanced pseudo-supermesh approach are preserved even when applied to more complex real problems. In this sense, this work contributes to a new engineering tool promoting the enhanced pseudo-supermeshes as an effective tool for the design, development, and optimization of internal combustion engines.

Neural network-based air handling control for modern diesel engines

Complex air handling systems, featuring technologies such as exhaust gas recirculation (EGR) and variable geometry turbochargers (VGTs), are commonly used in modern diesel engines to meet stringent emissions and fuel economy requirements. The control of diesel air handling systems with EGR and VGTs is challenging because of their nonlinearity and coupled dynamics. In this paper, artificial neural networks (ANNs) and recurrent neural networks (RNNs) are applied to control the low pressure (LP) EGR valve position and VGT vane position simultaneously on a light-duty multi-cylinder diesel engine. Intake manifold pressure (IMP) and air-fuel equivalence ratio, or [Formula: see text], are selected as the control objectives since they directly impact engine emissions and cylinder power output. Meanwhile both signals are available on production engines, so no additional hardware costs for measurement systems will be introduced. Both transient and steady state experimental data are separately used to train the two categories of neural networks (NNs). The NNs with minimum mean square error (MSE) for the training data sets are compared to conventional proportional-integral (PI) control and model predictive control (MPC). The most accurate NN controller has almost no overshoot during the transient process while the steady state error [Formula: see text] and IMP are at most 7.0% and 3.8%, respectively, under a wide range of engine speeds from 2500 to 4000 rpm, thus showing the potential of this approach.

Investigation of the Effects of Intake Manifold Pressure on Performance and Combustion Characteristics in an HCCI Engine

Homojen dolgulu sıkıştırma ile ateşlemeli (HCCI) motorların yüksek termik verimleri ve düşük NOx emisyonları sebebiyle buji ile ateşlemeli (SI) ve sıkıştırma ile ateşlemeli (CI) motorlara göre önemli üstünlükleri bulunmaktadır. Ancak HCCI motorlarda yanma başlangıcının kontrol edilmesi oldukça zordur. Bu çalışmada, dört silindirli SI motordan dönüştürülmüş olan bir HCCI motoru kullanılmıştır. 373 K hava giriş sıcaklığı için, emme manifold basıncının HCCI yanma üzerine etkileri deneysel olarak incelenmiştir. Deney yakıtı olarak RON0, RON20 ve RON40 kullanılmıştır. Manifold basıncının artmasıyla yanma başlangıcının avansa alındığı gözlenmiştir. Ayrıca oktan sayısının değişiminin de yanma başlangıcı üzerine önemli etkileri olduğu gözlenmiştir. En yüksek indike termik verim RON40 yakıtı kullanımında, 120 kPa manifold basıncında %46,38 olarak kaydedilmiştir. Manifold basıncının artırılmasına bağlı olarak volümetrik verimin de artması maksimum silindir içi basınç ve ısı yayılımında artış sağlamıştır.

Design of PSO-tuned FOPI & Smith predictor controller for nonlinear polymer electrolyte membrane fuel cell

ABSTRACT The polymer electrolyte membrane (PEM) fuel cell or proton exchange membrane fuel cell (PEMFC) has sparked a lot of interest in renewable electricity generation due to high efficiency, quick start up time, and low operating temperature. However, they exhibit highly nonlinear behavior with degraded power quality under uncertain input conditions. The hydrogen, oxygen, and air feed determine the PEMFC system’s performance. Controlling the manifold pressure at the cathode side is essential in preventing the problem of oxygen starvation. In this paper, a nonlinear dynamic model of the PEMFC is considered to control the supply manifold pressure. The performance of the nonlinear PEMFC with various classical controllers (PI, PD, PID, and PID with filter derivative), Smithpredictor, and Fractional Order PI (FOPI) controllers are compared. The optimization of classical controllers is performed by PID tuner. On the other hand, Smith predictor and FOPI controller are tuned by artificial intelligence technique, namely, Particle Swarm Optimization (PSO). The FOPI controller is also tuned with Genetic Algorithm (GA). The PEMFC output is compared in terms of performance evaluation parameters, i.e. settling time, overshoot, and steady state error. The computer simulations suggest that in comparison with GA-FOPI [settling time (ts) = 1.374 s, overshoot (Mp) = 18.452%, steady state error (ess) = 0.1%] and PSO-Smith predictor (ts = 1.262 s, Mp = 5.581%, ess = 0%), the PSO-FOPI controller results in much better settling time (ts = 1.008 s), overshoot (Mp = 2.577%), and steady state error (ess = 0%). Thus, PSO-optimized FOPI controller with nonlinear PEMFC outperforms the classical, PSO-Smith predictor, and GA-FOPI control schemes.

Experimental Studies of Low-Load Limit in a Stoichiometric Micro-Pilot Diesel Natural Gas Engine

While operating at light loads, diesel pilot-ignited natural gas engines with lean premixed natural gas suffer from poor combustion efficiency and high methane emissions. This work investigates the limits of low-load operation for a micro-pilot diesel natural gas engine that uses a stoichiometric mixture to enable methane and nitrogen oxide emission control. By optimizing engine hardware, operating conditions, and injection strategies, this study focused on defining the lowest achievable load while maintaining a stoichiometric equivalence ratio and with acceptable combustion stability. A multi-cylinder diesel 6.7 L engine was converted to run natural gas premix with a maximum diesel micro-pilot contribution of 10%. With a base diesel compression ratio of 17.3:1, the intake manifold pressure limit was 80 kPa(absolute). At a reduced compression ratio of 15:1, this limit increased to 85 kPa, raising the minimum stable load. Retarding the combustion phasing, typically used in spark-ignition engines to achieve lower loads, was also tested but found to be limited by degraded diesel ignition at later timings. Reducing the pilot injection pressure improved combustion stability, as did increasing pilot quantity at the cost of lower substitution ratios. The lean operation further reduced load but increased NOx and hydrocarbon emissions. At loads below the practical dual-fuel limit, a transition to lean diesel operation will likely be required with corresponding implications for the aftertreatment system.

Numerical investigations of low load diesel-methane dual fuel combustion at early diesel injection timings

The present work focuses on the development and validation of a CFD simulation setup of diesel-methane dual fuel combustion in a single-cylinder research engine (SCRE). The validated setup is used to provide insight about dual fuel combustion at low-load operation. The computational campaign consisted of evaluating three different diesel injection timings of 310, 320, and 330 CAD at a methane percent energy substitution (PES) of 80%, 5.1 bar gross IMEP, 500 bar diesel injection pressure, and 1.5 bar manifold air pressure where 360 CAD corresponds to firing top dead center. The computational setup ability to capture combustion, performance, and emissions trends accurately is demonstrated by good agreement with experimental data. The validated setup is further utilized to provide insights into the nature of dual fuel combustion, particularly, the effect of methane on diesel autoignition. Analysis of the computational results showed that the onset of both low-temperature heat release and high-temperature heat release of n-dodecane (the chemical surrogate used for diesel) is delayed by the presence of methane in the system. For early diesel injection in a dual-fuel engine at low-load, initial high-temperature combustion arises from the burning of n-dodecane followed by methane combustion. Most of the methane present in the piston compression ring crevices, areas near the piston top and the liner, remained unreacted after combustion is done. The effect of diesel and methane fuel amount on engine performance at low-load was also explored.

Combined effects of electric supercharger and LP-EGR on performance of turbocharged engine

LP-EGR and turbocharging can improve thermal efficiency, but its specific mechanism needs to be further studied from the energy conversion. The fast response characteristic of electric supercharger can make up for turbine lag. The effect of electric supercharger on the steady state and transient characteristics of a LP-EGR turbocharged engine are investigated. Under the condition of 1500 r·min−1 and 14 bar, the electric supercharger can increase the EGR rate from 5% to 30%. The introduction of exhaust gas can increase the intake volume and reduce the pumping losses. The increase of turbocharger power indicates the reduction of exhaust energy losses. The decrease of combustion temperature optimizes the combustion phase, increases the constant volume degree of combustion and reduces the heat transfer losses. The application of EGR improves the fuel economy by 5%. For emission, low temperature combustion and low oxygen content reduce NOx emission by 80%. Incomplete combustion losses increase THC emission. CO emission is related to excess-air coefficient, so it is basically unchanged. The electric supercharger can speed up the establishment of the intake manifold pressure. The power transient response time is shortened by 72%. The advance of torque platform improves the power performance of engine at low speed.

Optimization of plunger pump suction manifold parameters

Hydraulic fracturing plays an important role in increasing oil and gas reserves. In hydraulic fracturing, fluid is injected until the fluid pressure overcomes the stresses inherent in the rock or exceeds the forces holding the rock together. The fracturing fluid is a cohesive-dispersed system characterized by a continuous spatial structure. It is assumed that the configuration of the suction manifold, velocity and pressure pulsations lead to changes in the volumetric characteristics of the system phases at the pump outlet. The purpose of the study, is to analyze the movement of liquid with proppant through three suction manifolds of different design, to identify the design with the lowest volume of proppant sedimentation. The paper considers three design variants of suction manifold of high-pressure plunger pump. The hydrodynamic analysis of fluid motion with proppant has been carried out, data on distribution of velocities, pressures and proppant concentration in the manifold have been obtained. A series of numerical experiments carried out for different designs of three-plunger pump suction lines confirms the hypothesis about influence of manifold design, velocity and pressure pulsation on change of volume characteristics of system phases.

Benefits of Feedforward for Model Predictive Airpath Control of Diesel Engines

This paper investigates options to complement a diesel engine airpath feedback controller with a feedforward. The control objective is to track the intake manifold pressure and exhaust gas recirculation (EGR) rate targets by manipulating the EGR valve and variable geometry turbine (VGT) while satisfying state and input constraints. The feedback controller is based on rate-based Model Predictive Control (MPC) that provides integral action for tracking. Two options for the feedforward are considered one based on a look-up table that specifies the feedforward as a function of engine speed and fuel injection rate, and another one based on a (non-rate-based) MPC that generates dynamic feedforward trajectories. The controllers are designed and verified using a high-fidelity engine model in GT-Power and exploit a low-order rate-based linear parameter-varying (LPV) model for prediction which is identified from transient response data generated by the GT-Power model. It is shown that the combination of feedforward and feedback MPC has the potential to improve the performance and robustness of the control design. In particular, the feedback MPC without feedforward can lose stability at low engine speeds, while MPC-based feedforward results in the best transient response. Mechanisms by which feedforward is able to assist in stabilization and improve performance are discussed.

Extreme Miller cycle with high intake boost for improved efficiency and emissions in heavy-duty diesel engines

This study experimentally investigates the impact of extreme Miller cycle strategies paired with high intake manifold pressures on the combustion process, emissions, and thermal efficiency of heavy-duty diesel engines. Well-controlled experiments isolating the effect of Miller cycle strategies on the combustion process were conducted at constant engine speed and load (1160 rpm, 1.76 MPa net IMEP) on a single cylinder research engine equipped with a fully-flexible hydraulic valve train system. Late intake valve closing (LIVC) timing strategies were compared to a conventional intake valve profile under either constant cylinder composition, constant engine-out NOx emission, or constant overall turbocharger efficiency ([Formula: see text]) to investigate the operating constraints that favor Miller cycle operation over the baseline strategy. Utilizing high boost with conventional intake valve closing timing resulted in improved fuel consumption at the expense of sharp increases in peak cylinder pressures, engine-out NOx emissions, and reduced exhaust temperatures. Miller cycle without EGR at constant [Formula: see text] demonstrated LIVC strategies effectively reduce engine-out NOx emissions by up to 35%. However, Miller cycle associated with very aggressive LIVC timings led to fuel consumption penalties due to increased pumping work and exhaust enthalpy. LIVC strategies allowed for increased charge dilution at the baseline NOx constraint of 3.2 g/kWh, resulting in significant fuel consumption benefits over the baseline case without compromising exhaust temperatures or peak cylinder pressures. As Miller cycle implementation was shown to affect the boundary conditions dictating [Formula: see text], the LIVC and conventional IVC cases were studied at an equivalent [Formula: see text] point representative of high boost operation. With high boost, LIVC yielded reduced NOx emissions, reduced peak cylinder pressures, and elevated exhaust temperatures compared to the conventional IVC case without compromising fuel consumption.

Exhaust Gas Recirculation (EGR) valve, design and computational fluid dynamic analysis

All EGR systems used on contemporary cars operate on the principle of “external” exhaust gas recirculation. A certain proportion of the engine exhaust gases is extracted and transmitted back into the fresh air-gasoline mixture by means of a control valve. Exhaust gas recirculation valve is generally controlled by a pneumatic or mechanical system designed to dose the exhaust gases in accordance with certain factors such as: engine speed; intake manifold pressure; engine temperature. This paper presents the design steps of the EGR valve using NX SIEMENS. After making the 3D model, it was imported into ANSYS where a study of the flow of fluids (flue gases CO2 and liquid coolant) was made. In this study it was considered that the valve was actuated and the exhaust gases enter the engine while they are also cooled by the liquid coolant. From the fluid flow modeling process it can be seen that the coolant does not take much of the flue gas temperature, its role being more to maintain a proper temperature of the body valve.

Experimental Study on the Unsteady Spray Combustion Process of a Liquid Oxygen/Methane Swirl Coaxial Injector.

The present study experimentally investigated the dynamic spray combustion process of a liquid-centered swirl coaxial injector using liquid oxygen/methane in an optically accessible liquid rocket engine. Data were obtained at combustor pressures from 0.4 to 1.8 MPa and the ratio of the oxidizer mass flow rate to the fuel rate between 1.32 and 1.55. Liquid oxygen was injected at 120 K, and the injection temperature of gaseous methane was about 285 K. Based on the obtained spatial distribution and oscillation characteristics of liquid oxygen/methane flame, the combustion process was described by four subprocesses: ignition, low-frequency oscillation combustion, quasi-steady state combustion, and shutdown. In the quasi-steady state combustion subprocess, both the flame length and the normalized flame area are the largest, and the flame expansion angle is the smallest. At the initial stage of combustion, the instability of the liquid oxygen phase state leads to flame instability, which generates low-frequency unstable combustion with a dominant frequency of 93.74 Hz. In addition, the high-frequency (2500–3000 Hz) oscillation of the flame appeared in the whole combustion process. It has been confirmed to be caused by the self-pulsation of spray. Furthermore, with the increase in liquid oxygen manifold pressure, the liquid oxygen phase state changes from a two-phase mixture of liquid and gaseous oxygen to a liquid phase, which increases the mass flow rate of liquid oxygen entering into the combustor, thus generating the increase in the high oscillation frequency of the flame through the whole combustion process.

Analysis of operating parameters of the aircraft piston engine in real operating conditions

The article presents the results of analysis of operational parameters of piston engine CA 912 ULT which is a propulsion system of ultralight gyroplane Tercel produced by Aviation Artur Trendak. Research was conducted under normal operating conditions of the autogyro and data was collected from 20 independent tests including a total of 28 flight hours, divided into training flights and competition flights.Engine speed, manifold air pressure and temperature, fuel pressure, injection time, and head temperature were recorded at 9 Hz during each flight. Collective results were presented to show the statistical analyses of the individual parameters by determining the mean values, standard deviations and histograms of the distribution of these parameters. Histograms of operating points defined by both engine speed and manifold air pressure were also determined. Analyses of the engine dynamics as a distribution of the rate of change of the engine rotational speed were also carried out. It was shown that the engine operating points are concentrated mainly in the range of idle and power above 50% of nominal power. The most frequent range is 70-80% of nominal power. It was also shown that the dynamics of engine work in real operating conditions is small. It was also shown that the way of use significantly influences the distribution of operating points. During training flights, an increase in the number of take-offs and landings causes an increase in the amount of engine work at take-off and nominal power and at idle.

Exhaust valve profile modulation for improved diesel engine curb idle aftertreatment thermal management

Rapid warm-up of a diesel engine aftertreatment system (ATS) is a challenge at low loads. Modulating exhaust manifold pressure (EMP) to increase engine pumping work, fuel consumption, and as a result, engine-outlet temperature, is a commonly used technique for ATS thermal management at low loads. This paper introduces exhaust valve profile modulation as a technique to increase engine-outlet temperature for ATS thermal management, without requiring modulation of exhaust manifold pressure. Experimental steady state results at 800 RPM/1.3 bar BMEP (curb idle) demonstrate that early exhaust valve opening with negative valve overlap (EEVO+NVO) can achieve engine-outlet temperature in excess of 255°C with 5.7% lower fuel consumption, 12% lower engine out NOx and 20% lower engine-out soot than the conventional thermal management strategy. Late exhaust valve opening with internal EGR via reinduction (LEVO+Reinduction) resulted in engine-outlet temperature in excess of 280°C, while meeting emission constraints at no fuel consumption penalty. This work also demonstrates that LEVO in conjunction with modulation of exhaust manifold pressure results in engine-outlet temperature in excess of 340°C while satisfying desired emission constraints. Aggressive use of LEVO can result in engine-outlet temperatures of 460°C, capable of active regeneration of DPF at curb idle, without the significant increase in engine-out soot emissions seen in previously studied strategies.

Combining machine learning with 3D-CFD modeling for optimizing a DISI engine performance during cold-start

This work presents a methodology for using machine learning (ML) techniques in combination with 3D computational fluid dynamics (CFD) modeling to optimize the cold-start fast-idle phase of a gasoline direct injection spark ignition (DISI) engine. The optimization process implies the identification of the range of operating parameters, that will ensure the following criteria under cold-start conditions: (1) a fixed IMEP of 2 bar (BMEP of 0 bar), (2) a stoichiometric exhaust equivalence ratio (based on carbon-to-oxygen atoms) to ensure the efficient operation of the after-treatment system, (3) enough exhaust heat flux to ensure a rapid light-off of the after-treatment system, and (4) reduced NOx and HC emissions. A total of six operating parameters will be identified as having a significant influence on cold-start engine performance. These parameters are associated with the fuel injection strategy (end of the second injection, injection pressure, and fuel mass); combustion strategy (spark timing, spark energy); and intake airflow (intake manifold pressure). Performing an optimization study exclusively using multi-cycle (at least 3 cycles) 3D CFD simulations would be an arduous task. For example, to achieve an exhaust equivalence ratio of 1 and an IMEP of 2 bar, multiple iterations would be required for fuel mass (to account for film formation), intake manifold pressure (to ensure enough air in-cylinder), and spark timing (to ensure the fixed load). This process would be more convoluted and expensive with the addition of constraints for exhaust heat flux and emissions. A promising approach to tackling such a complicated optimization process is to employ the concept of machine learning, which demands a database formed by the six operating parameters mentioned above. The current work will demonstrate a strategy of combining CFD modeling with advanced Gaussian Process Regression (GPR)-based ML models to make predictions about DISI cold-start behavior with acceptable accuracy and a substantially reduced computational time.

Engine Speed Regulation During Gear Shift Process of Torque Decoupled HEV Using Triple-Step Nonlinear Method

For the torque decoupled hybrid electric vehicles (HEVs) equipped with automated manual transmission (AMT), the motor torque can be used to compensate for traction loss during gear shift. Thus, engine speed regulation can be used to achieve speed synchronization, and the clutch can be removed, which simplifies the overall structure of AMT. A triple-step nonlinear method is proposed in this paper to improve the engine speed tracking accuracy, which utilizes the steady-state, reference trajectory dynamics, and the tracking error information comprehensively. By the expense of the intake manifold pressure tracking performance, the developed controller can guarantee the asymptotic convergence of the engine speed tracking error. After the triple-step controller is deduced, it is verified through co-simulation between AMT HEV plant model in AMESim and controller model in Simulink. The simulation results demonstrate that the proposed controller can exert the advantages of the two control inputs: throttle opening α and spark advance deviation Δθ, and certificate the overall gear shift quality, including shift time and vehicle jerk.

Validated Analytical Modeling of Diesel Engines Intake Manifold with a Flexible Crankshaft

The flexibility of a crankshaft exhibits significant nonlinearities in the analysis of diesel engines performance, particularly at rotational speeds of around 2000 rpm. Given the explainable mathematical trends of the analytical model and the lack of available analytical modeling of the diesel engines intake manifold with a flexible crankshaft, the present study develops and validates such a model. In the present paper, the mass flow rate of air that goes from intake manifold into all the cylinders of the engine with a flexible crankshaft has been analytically modeled. The analytical models of the mass flow rate of air and gas speed dynamics have been validated using case studies and the ORNL and EPA Freeway standard drive cycles showing a relative error of 7.5% and 11%, respectively. Such values of relative error are on average less than those of widely recognized models in this field, such as the GT-Power and the CMEM, respectively. A simplified version for control applications of the developed models has been developed based on a sensitivity analysis. It has been found that the flexibility of a crankshaft decreases the mass flow rate of air that goes into cylinders, resulting in an unfavorable higher rate of exhaust emissions like CO. It has also been found that the pressure of the gas inside the cylinder during the intake stroke has four elements: a driving element (intake manifold pressure) and draining elements (vacuum pressure and flow losses and inertial effect of rotating mass). The element of the least effect amongst these four elements is the vacuum pressure that results from the piston’s inertia and acceleration. The element of the largest effect is the pressure drop that takes place in the cylinder because of the air/gas flow losses. These developed models are explainable and widely valid so that they can help in better analyzing the performance of diesel engines.