AE 412

THERMODYNAMIC CYCLE SIMULATION II

Prof.Dr. Demir Bayka

The development of an engine for a particular application can be approached either directly by exploratory testing or indirectly by using a mathematical model to predict the engine behaviour. For experimental investigations, extensive testing of the prototype is necessary, besides, selecting the best design from such testings is a task of considerable magnitude.

On the other hand reduction in time and costs for the development and design of new engines can be achieved through simulation models that give a good representation of the engine system.

The principle on which a simulation of the engine working cycle is based is essentially a step-by-step integration of the First Law of Thermodynamics applied to the working gas

This is an instantaneous account of the energy balance.

STATE OF THE MIXTURE AT THE BEGINNING OF THE CYCLE

The spark ignition engine cycle consists of the following sequence of events:

1. A compression stroke to raise the temperature and the pressure of the air-fuel mixture.

2. An expansion stroke during which the heat released by the combustion of air-fuel mixture is converted into useful mechanical work.

3. An exhaust stroke to expel the burned gases from the cylinder.

4. An intake stroke to induct air,fuel and if exists recycled exhaust gas.

The compression period will be analyzed starting from the inlet valve closing up to the point which the spark is ignited.

The complete cycle will be analyzed starting from the compression stroke when the intake valve closes, while the piston is moving upward. So the intake valve closing will be selected as the beginning of the cycle.

State of Mixture at the Beginning of the Cycle

The clearance volume of the reciprocating engine contains the products of combustion at the end of gas exhaust period.

When the intake valve opens the air-fuel begins to mix with the clearance gases which have a high temperature, the final temperature being the temperature of the mixture at the beginning of the compression process.

So the unburned gas mixture for a spark ignition engine during intake and compression consists of air,fuel and previously burned gases.

State of Mixture at the Beginning of the Cycle

The composition of the unburned mixture does not change significantly during intake and compression. It is sufficiently accurate to assume the composition is frozen.

The mass of charge trapped in the cylinder (mc ) is the inducted mass per cycle (m i ) ,plus the residual mass (m r ) left over from the previous cycle. The residual fraction (x r ) is :

)1(..........mm

m

m

mx

ri

r

c

rr

State of Mixture at the Beginning of the Cycle

If the inducted mixture is fuel and air, then the burned gas fraction (xb ) in the unburned mixture during compression equals the residual fraction.

However, in some engines ,a fraction of the engine exhaust gases is recycled to the intake to dilute the fresh mixture for control of NO X emissions. If the percent of recycled exhaust gas %EGR) is defined as the percent of the total intake mixture which is recycled exhaust,

)2...(..........100xm

m(%)EGR

i

EGR

State of Mixture at the Beginning of the Cycle

)3......(xx1100

EGR

m

mmx rr

c

rEGRb

where m EGR is the mass of exhaust gas recycled, then the burned gas fraction in the fresh mixture is:

Then. the chemical formula for the reactants. per mole fuel in the mixture can be written:

)4.......(..........nnnnnnx

A044.0N73.3O2

L

4

MNOHCx1

22222 NOHCOOHCOb

22LMNb

where n i moles of species and a is the excess air coefficient.

Thermodynamic Analysis of Compression Stroke

The process of compression in an actual cycle takes a very complicated course.

Initially, when the inlet valve closes the temperature of the mixture is below that of the surfaces enclosing the space inside the cylinder, hence heat flows from the walls to the charge.

At a certain moment, the mean temperatures of the charge and the wails are equalized . and heat is rejected from the charge to the walls when the piston continues to move until the process of compression is completed.

Thermodynamic Analysis of Compression Stroke

Writing the first law of thermodynamics for the cylinder charge in differential form,

)5(..........WdEQw

where

Qw = heat transfer through cylinder walls, (kJ)E = internal energy of the cylinder gas. (kJ) W = work done by the cylinder gas. (kJ)

Thermodynamic Analysis of Compression Stroke

The differential work term dW is

)6.(..........dV.PW

where

P = pressure of cylinder gas, (kN/m2)

V = volume of cylinder gas. (m3)

Thermodynamic Analysis of Compression Stroke

The energy term E can be written as:

)7.(..........E.PE.KUE

where

K.E and P.E represent kinetic and potential energy of the system,

thus U is the internal energy in the absence of motion gravity . etc.

Thermodynamic Analysis of Compression Stroke

Inserting equations (7) and (6) into equation (5)neglecting the changes in kinetic and potential energies and dividing both sides by dt,

the first law equation becomes:

)8.....(..........dt

dV.P

dt

dU

dt

Q

Internal energy U can be expressed as:

Thermodynamic Analysis of Compression Stroke

)9..(..........dT.C.mdU v

where

m = mass of cylinder gas. (kg)C v = specific heat at constant volume, (kJ/kg.K) T = temperature of cylinder gas, (K)

Thermodynamic Analysis of Compression Stroke

)10......(....................dt

dVP

dt

dTC.m

dt

Qv

Inserting into equation (8)

and replacing

)11.........(....................N6

ddt

wheret = time, (sec)a =crank angle. (deg)N = engine speed. (rpm)

Thermodynamic Analysis of Compression Stroke

)12...(....................d

dVP

d

dTC.m

d

Qv

)13.......(....................T.R.mV.P

The energy equation becomes ;

Expressing the relative change of the gas properties through the equation of state;

)14.........(..........d

dTR.m

d

dVP

d

dPV

Thermodynamic Analysis of Compression Stroke

)12...(....................d

dVP

d

dTC.m

d

Qv

)13.......(....................T.R.mV.P

)14.....(..........d

dVP

d

dPV

R.m

1

d

dT

)14.........(..........d

dTR.m

d

dVP

d

dPV

Substituting (14) into (12) ;

V

1

d

Q

C

R

d

dVP

C

R1

d

dP

vv

PROCEDURE

Assume

• Cylinder Gas Pressure,

• Cylinder Gas Temperature and

• The Residual Gas Fraction

in the chamber at the beginning of the cycle.

The Residual Gas Fraction

Residual gases initially are assumed to be the combustion products from the previous cycle, its composition being fixed at the beginning of the exhaust stroke where the dissociation is considered to be complete. So, composition of residual gasses, xp is determined from the calculation of equilibrium composition of combustion products.

The composition of the charge at the beginning of the cycle is determined from the relation

xi = xpixres + xairxai ............(1)

xi = mole fraction of ith specie in the cylinder.

xpi = mole fraction of ith specie in the residual gas alone.

xres = residual gas mole fraction in the cylinder.

xai = mole fraction of ith specie in air alone (if any).

xair = mole fraction of air in the cylinder.