An Analytical Model of Diesel Engine Intake System for Performance Prediction

AN ANALYTICAL MODEL OF DIESEL ENGINE INTAKE SYSTEM FOR PERFORMANCE PREDICTION

Rohith Kamath, Dr. Vivek Venkobarao – System Engineering, Continental India, Powertrain Division.

Prof. Subramaniam C K – VIT, Vellore.

Abstract: With increased complexity of engine, stringent emission constraints, fuel economy and enhanced power demand from OEM’s it becomes necessary for the ECU suppliers to have an engine model which represents as close representation as a practical engine in-order to design a robust controller. With this regards there are numerous developments happening in the area of engine model design from decades.

In this paper two possible approaches namely equilibrium/reversible and non-equilibrium irreversible thermodynamics for designing mathematical model of an IC engine are presented, also requisite for better model is discussed and a dynamic simulation of classical thermodynamic model of diesel engine is performed and results show that the modeled behavior is in close approximation with ideal engine, and results are analyzed for future work.

Key words: Finite Time Thermodynamics, Non-Equilibrium Thermodynamics, Irreversibility.

I. INTRODUCTION

There are legion work done with conventional thermodynamic approaches and some of which are highlighted by Aguilera-Gonza [6], developed a pressure model for diesel engine and proposed a Parallel Distributed Compensation Fuzzy controller is applied to regulate the intake and exhaust manifold pressures in a four-cylinder diesel engine air-path system accompanied with EGR and VGT. Junmin Wang [7], Describes a hybrid robust nonlinear control approach for modern diesel engines operating multiple combustion modes; in particular, low temperature combustion and conventional diesel combustion modes. An innovative control system is designed to track different key engine air-path operating variables at different combustion modes as well as to avoid singularity which is inherent for turbocharged diesel engine running multiple combustion modes.

Since FTT was first introduced in the year 1983, researchers are trying to come up with new way of defining irreversible thermodynamic processes. Omprakash [4] presented irreversible Otto cycle model for net power generation and efficiency calculation by including bypass heat leakage, frictional losses and internal irreversibility factors associated with compression and expansion process. It is shown that the power is independent of heat leakage term but depends only on irreversibility’s and frictional losses. However the efficiency reduces drastically by inclusion of heat loss via cylinder walls. Curto-Risso, Medina, and Hernandez [5], presented and validated quasi-dimensional thermodynamic model of piston-cylinder system for 4 cylinder engine including chemical reactions undergoing Otto cycle. A theoretical model based on FTT is presented and computer simulated: considering internal irreversibility, heat losses and frictional losses as function of crank angular velocity, it is shown that for more realistic model, how power and efficiency deteriorates with irreversibility and unavoidable losses.

This article is organised as follows, in section II two possible approaches of modelling IC engines are discussed. Section III a dynamic simulation of air-path system of diesel engine is shown. Section IV contains results of simulation and section V contains conclusion and results.

II. POSSIBLE APPROACHES

1. Classical Equilibrium (Reversible) thermodynamic approach

The thermodynamic process for an equilibrium standard Otto and Diesel cycles is represented on a P-V diagram as shown in Fig 1. The standard Otto cycle comprises of following process [1][2].

Fig 1: The ideal air standard Otto cycle

1-2 Adiabatic compression of the working gas. 2-3 Isochoric (constant volume) heat addition to the working gas from external source. 3-1 Adiabatic expansion of working gas. 4-1 Isochoric heat rejection from the gas to the external sink.

The standard Diesel cycle shown in Fig 2 comprises of following process [1][2], it can be seen the difference between full load cycle and part load cycle by a dashed line.

Fig 2: p-V diagram of the Diesel cycle

1-2 Adiabatic compression of the working gas. 2-3 Isobaric (constant pressure) heat addition to the working gas from external source. 3-1 Adiabatic expansion of working gas. 4-1 Isochoric heat rejection from the gas to the external sink.

Generally pressure models are derived considering constant temperature of working fluid and having calculated the volume of working fluid it is possible to estimate the pressure formation for the future time instant subsequently available mass of air and hence amount of fuel to injected so as maintain stoichiometric ratio for proper combustion process.

Pressure = f(maf, mff) ,

The state equation for the ideal gases is given by

Where p is the pressure in the volume, V is the volume, m is the mass of gas in the volume, R is the gas constant and T is the temperature of the gas in the volume [9].

Differentiating above equation

Internal energy of the gas inside a piston is given by

==>

Differentiating above equation

An alternative equation for rate of change of internal energy in the volume:

Where Cp is the specific heat at constant pressure, the Wn are the mass flows into the volume, the Tn are the temperatures of hose gas flows and Q is the heat transfer from the volume to the environment. If heat loss from the volume is neglected,

Where γ is the ratio of specific heats. Conservation of mass is used to give:

Law of conservation of mass and energy is used for analyzing the Otto and Diesel cycles. Hence model becomes relatively simpler. Models are based on first principles of equilibrium thermodynamics following the basic 4 laws of thermodynamics.

(Law of Energy Conservation)

Assumptions:

1)The specific heat of working gas is considered to be constant.

2)The dynamics of the temperature variation are ignored. = 0

Advantages:

• Mathematical models are linear/or with limited non-linearity.
• The controlling of such systems need simpler controller (Linear or very basic non-linear controller).

Disadvantages: The disadvantage of these models is that they are not close approximation of practical Engine processes. The practical engine (Otto/Diesel) cycles are never in equilibrium thermodynamics. There are lots of irreversibilities involved in the process and these unavoidable losses are not recoverable which must be included in the mathematical model.

Need for better Models:

Because of the drawbacks and OEM requiring better power with straight exhaust more robust models need to be developed. According literature study it is found that FTT is one of the approaches to satisfy both the objectives mentioned above.

2. Modern Non-Equilibrium Thermodynamics (Finite Time Thermodynamics FTT)

What is Finite Time Thermodynamics?

In practical engines the thermodynamic processes are never in equilibrium. So in order to deal with non-equilibrium thermodynamics a new domain in physics called Finite Time thermodynamics is introduced in the year 1983, which deals with extension of traditional equilibrium thermodynamics [3].

FTT problem formulation is to have generalized thermodynamic properties for the thermodynamic processes and finding out finite time pathway to optimize these generalized properties that will yield extremal work.

The Temperature v/s entropy generation graph is shown in Fig 3.

Fig 3: Temperature-Entropy (T-S) diagram of an irreversible Otto cycle [4]

Process ‘1 - 2S’ is a reversible adiabatic compression, while process ‘1 – 2’ is an irreversible adiabatic process that takes into account the internal irreversibility in the real compression process. The heat addition is an isochoric process ‘2 – 3’. Process ‘3 - 4S’ is a reversible adiabatic expansion, while ‘3 – 4’ is an irreversible adiabatic process that takes into account the internal irreversibility in the real expansion process. The heat rejection is an isochoric process ‘4 – 1’.

How FTT is better??

Following are some of the parameters and constraints which are considered in modeling the mathematical model which is as close representation of practical Otto/Diesel cycle engine.

Some of the Irreversibilities:

Irreversibility involved in process: Internal irreversibility factors associated with compression and expansion process which are represented as compression and expansion efficiencies [3].

Engine friction irreversibilities: To evaluate the friction work associated with the piston motion inside the cylinder, a friction force proportional to the instantaneous velocity is considered. Work lost due to friction is given by [5],

Ap – The piston section, V – Swept volume

Specific Heat: Thermodynamic properties of all species are built as ideal gases and obtained from the constant pressure specific eat capacity, Cp,i, that is expressed as the following temperature depending polynomial [5] where T is operating temperature.

Optimized Thermodynamic Path: It is necessary to identify the internal state variables and optimize potential of these internal variables so that to extract maximum work. Objective is to reduce entropy generation within the finite time availability.

III. Simulation of Intake model with Classical Reversible Thermodynamic Model

A Pressure Model for the Air-Path is simulated from literature. This is model capture the dynamics of pressure changes at intake exhaust manifold and they are regulated by EGR and VGT for a diesel system [7]. The diesel engine air-path schematics are shown in Fig 4.

Fig 4: Diesel engine air-path scheme

Based on the mass and energy conservation as well as ideal gas law: The engine intake and exhaust dynamic model

Intake dynamics is given by

------(1)

Wie, is the Engine intake gas flow rate:

------(2)

Vdis the displacement volume

volume efficiency

Pressure and temperature of the exhaust system as:

------(3)

Dynamics of the power transferred by the turbocharger Pc

------(4) making zero dynamics

Wf  Fuel flow rate, Wci Compressor mass flow rate, Wxi  is the EGR mass flow rate

Compressor mass flow rate:

------(5)

Compressor efficiency, Cp  is the specific heat at constant pressure

Pc is compressor power:

------(6)

Ta and pa are the ambient temperature and pressure, respectively.

The EGR mass flow rate: standard orifice flow equation [8]

------(7)

Aegr(Xegr)represents the effective area of the EGR, Tx is the exhaust manifold temperature, R is the specific gas onstant, (Gamma) – Ration of specific heats Cp and Cv.

The turbine flow Wxt:

------(8)

represents the effective area of the VGT valve that depends of the position Xvgt

Where Pt is turbine power, it can be calculated as

, ------(9)

Dynamic model can be summarized in the equations that follow:

Note: Since it is difficult to measure the temperatures with sufficiently fast responses, in this paper we ignored their dynamics

Constant Values:

Thus, the system can be rewritten in a general State Space form as

-- (13)

Fig 5: Matlab/Simulink Pressure Model

The equation 13 represents the dynamic state space third order model. The steady state model is derived for the above equation by the following

IV. Simulation Results from Literature Model

The dynamic behavior of the model is verified by simulation by changing the engine speed from 1000-1500 rpm. Initial value of Pi is set to 120.6 kPa, Px at 170.2 kPa and Compressor power Pc at 1800 watts. The dynamic variation of intake pressure, exhaust pressure and compressor power is shown in Fig 6. The rate of mass flow through EGR and VGT are given in Fig 7. A comparison of simulation results v/s results of engine models from literature is shown in Fig 8.

Fig 6: Pressure at intake, exhaust and compressor power simulated for with engine speed change from 1000 – 1500 RPM.

Fig 7: EGR, VGT variation with engine speed change from 1000 – 1500 RPM.

Fig 8: % deviation of intake and exhaust pressure from literature.

V. Updated Model

An update to literature model is made by addition of variable fueling conditions depending on engine speed. For a practical four stroke diesel engine the fuel injected is 50mg/stroke, which is then converted to Kg/hour and passed as disturbance parameter to the model.

A small signal analysis is done for the model adding a low pass filtered square pulse of 500 rpm to a fixed engine speed of 1500 rpm in order to check the robustness of the model and it is observed that the system comes back from a disturbed position with minimal delay.

Fig 9: Small Signal analysis

VI. Simulation Results & Analysis

Fig 10: Simulation results showing small signal analysis

Fig 11: Simulation results showing small signal analysis

Observation: The glitch in the intake pressure is due to the fact that sudden increase in the RPM will cause the sucking of air from intake manifold, and the EGR flow and exhaust pressure takes a finite time to build up, as result the slope of intake pressure become more negative until there is sufficient build up of EGR flow and exhaust pressure.

Fig 12: Simulation results showing small signal analysis

1. Large variation in co-efficient of ‘pi’ due ‘N’.
2. Negligible changes in EGR flow and Compressor Flow during transients.

VII. Conclusions

A non-linear dynamic pressure model for intake and exhaust system of diesel engine equipped with EGR and VGT from literature is simulated. As observed from the results shown in Fig 6 and 7, the modeled behavior is in close approximation with ideal engine. The desired intake and exhaust pressures can be achieved. Also a comparison of the simulated model with ideal models from literature is done as shown in Fig 8 and model simulated shows minimal deviation with respect to intake and exhaust pressure which also triggers further investigation by inclusion of dynamics of fuel flow with different engine speeds.

A small signal analysis is made on the literature model in-order to check for robustness and it is shown that the model is robust enough to cope up with small disturbances.

Scope for future work:

1. Statistical anaylsis of the developed model with respect to the reference.
2. Identification of Model Influencing Parametrs (MIP).
3. Monte carlo analysis to arrive at control parameters
4. Small signal analysis of steady state model with gaussian noise.

APPENDIX

N / Engine Speed / 1500 rpm
Pc / Compressor power / 1800 watts
Pt / Turbine power / watts
R / Specific gas constant / (cp - cv)
Ta / Ambient temperature / 300 K
Ti / Intake manifold temperature / 313 K
Tx / Exhaust manifold temperature / 600 K
Vd / Displacement volume / 0:002m3
Vi / Volume of the intake manifold / 0:006m3
Vx / Volume of the exhaust manifold / 0:001m3
Wci / Compressor mass flow rate / kg/s
Wie / Total mass flow rate / kg/s
Wf / Engine fueling mass rate / 0.0016 kg/s
Wxi / EGR mass flow rate / kg/s
Wxt / turbine mass flow rate / kg/s
cp / Specific heat at constant pressure / 1014.4 J/kg oK
cv / Specific heat at volume pressure / 727.4 J/kg oK
pa / Ambient pressure / 101.3 kPa
pi / Intake manifold pressure / Pa
px / Exhaust manifold pressure / Pa
/ Compressor isentropic efficiency / 0.65
/ Turbocharger mechanical efficiency / 0.95
/ Turbine isentropic efficiency / 0.75
/ Volume isentropic efficiency / 0.82
/ Specific heat ratio / cp/cv
/ Time constant / 0.11
/ effective area of the EGR valve / 0 - 0.00018 m2
/ effective area of the VGT valve / 0 - 0.00018 m2

References:

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