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Comparative evaluation of various methodologies to account

for the effect of load variation during cylinder pressure

measurement of large scale two-stroke diesel engines

D.T. Hountalas a,⇑, R.G. Papagiannakis b, G. Zovanos a, A. Antonopoulos a

a Internal Combustion Engines Laboratory, School of Mechanical Engineering, National Technical University of Athens, 9 Heroon Polytechniou St., Zografou Campus,

157 80 Athens, Greeceb Thermodynamic & Propulsion Systems Section, Department of Aeronautical Sciences, Hellenic Air Force Academy, Dekelia Air Force Base, 1010 Dekelia, Attiki, Greece

h i g h l i g h t s

Use of cylinder pressure data for engine tuning leads to false results if load varies.

 Using two pressure sensors detects and accounts for the effect of load variation.

 Use of two pressure sensors is equivalent to simultaneous cylinder pressure measurement.

 Inlet pressure can be used to estimate load variation and correct engine performance data.

 A new computational method has been developed to account for load variation effect.

a r t i c l e i n f o

 Article history:

Received 22 May 2013

Received in revised form 14 August 2013

Accepted 17 August 2013Available online 12 September 2013

Keywords:

Diagnosis

Engine condition monitoring

Load variation

Electric power station

Diesel engine

a b s t r a c t

A significant number of fault-detection and fault diagnosis methods are based on the use of the measured

cylinder pressure to estimate critical engine parameters i.e. cylinder brake power, fuel consumption,

compression condition, injection timing etc. But, the results derived from the application of these tech-

niques depend strongly on the quality of data used. A common problem which has been identified bymany researchers is load variation during cylinder pressure measurement. This for some applications

(marine) can become significant and in some cases makes unusable utilization of cylinder pressure mea-

surement. According to the conventional measurement technique for field applications, cylinder pressure

is measured sequentially instead of simultaneously due to issues related mainly to cost, applicability and

complexity. Because of this, the operating parameters that are estimated for each cylinder depend on

instantaneous engine load. Therefore when an operating problem or a mistuning is identified, the distinc-

tion for the actual cause (i.e. if it is attributed to a malfunction, mistuning or to engine load variation dur-

ing measurement), is difficult because cylinders are not measured simultaneously. For this reason, in the

present work, threemethodologies that have been developed to account for the effect of load variation on

diagnosis results are presented and evaluated in an attempt to be offered an alternative against simulta-

neous cylinder pressure measurement. For this purpose, a well validated diagnostic technique, developed

by the present research group, is employed and modified accordingly. The aforementioned methodolo-

gies have been applied on a large-scale two-stroke diesel engine used for power generation in a Greek

island at two different operating conditions. From the application of each method, diagnosis and tuning

results are derived which are then compared against the respective ones obtained from the conventional

diagnosis technique which neglects the effect of load variation during measurement. The evaluation is

basedon thecomparisonof vital engine performance data i.e. brake power output, cylinder fuel flowrate,

peak firing pressure, ignition angle and compression quality. From the comparison of the diagnosis

results it is revealed that the three methodologies provide adequate results while the one which is based

on the use of two cylinder pressure sensors provides a very competitive alternative against simultaneous

cylinder pressure measurement, offering the advantage of simplicity and low cost. Most important it is

demonstrated the potential for all three methods to propose the required engine tuning to guarantee uni-

form cylinder operation despite variation of load during measurement.

 2013 Elsevier Ltd. All rights reserved.

0306-2619/$ - see front matter  2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.apenergy.2013.08.036

⇑ Corresponding author. Tel.: +30 210 772 1259; fax: +30 210 772 3475.

E-mail addresses:   dx1961@central.ntua.gr (D.T. Hountalas),  r.papagiannakis@gmail.com (R.G. Papagiannakis).

Applied Energy 113 (2014) 1027–1042

Contents lists available at   ScienceDirect

Applied Energy

j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / a p e n e r g y

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1. Introduction

The diesel engine remains the most efficient liquid fuel burning

unit yet devised and therefore it holds a dominant position in

many applications, i.e. marine propulsion, land transport – both

road and rail, power generation etc. [1–3]. Thus the proper and effi-

cient operation of a diesel engine is a major objective, especially for

marine and stationary applications (i.e. power generation etc.)

[4–6]. For this reason, condition monitoring and fault diagnosis

techniques hold an important position in the field especially for

the large-scale two-stroke diesel units due to their high power

output and fuel consumption  [4–6]. The diagnosis procedure (i.e.

detection of the actual cause of a fault, engine mistuning etc.) is

usually very complicated, since engine performance is affected

from a large number of parameters, which are usually very difficult

to measure or estimate. Therefore the actual cause of a malfunction

cannot easily be determined using conventional methodologies. Up

to now, various diagnostic methods and techniques have been

proposed from researchers and manufacturers   [7–10]. Most are

based on the processing of measurement data which are obtained

during engine operation   [11–13]. A number of these techniques

make use of the measured cylinder pressure trace to estimate

critical engine parameters such as brake power, fuel consumption,

ignition angle etc. [14–16]. But for the acquired data to be reliable,

the measurement conditions must meet certain requirements

[7,17–19]. One of these which, is the subject of the present work,

is engine load which should remain constant during cylinder

pressure measurement   [20–22]. According to the conventional

cylinder pressure measurement methodology, one pressure sensor

is used and cylinders are measured consequently one after the

other. The reason is that the simultaneous measurement requires

a great number of sensors, connections, sampling lines etc. that it

is not practical for field applications and moreover that this results

to high cost. Thus, if load variation occurs during cylinder pressure

measurement and is not accounted for, inaccurate results may be

derived for cylinder condition [20–22] and specifically for cylinder

tuning if these are directly utilized to adjust per example the fuel

flow (rack position) of individual cylinders. This will most possibly

result to engine mistuning with negative impact on engine perfor-

mance. Therefore it is important to precisely record load variation

during measurement.

As already mentioned one methodology to avoid the effect of 

load variation during measurement is the simultaneous pressure

measurement of all cylinders, but for practical field applications,

it has various drawbacks. For this reason in the present work are

examined and evaluated three methodologies to detect record

and account for load variation during cylinder pressure measure-

ment. The first is based on the conventional cylinder pressure mea-

surement technique (i.e. cylinders are measured consequently one

after the other) and the simultaneous estimation of the charge

pressure corresponding to compression initiation, which is obvi-

ously affected by fluctuation of load. The second methodology is

based on the direct recording of the scavenging air pressure using

a fast response sensor with adequate accuracy, because the

Nomenclature

 A   area (m2)CF    correction factor (–)CQ    cylinder compression quality (%)CR   compression ratio (–)c r    radiation constant (W/m2 K4)

D   cylinder bore (m) f    number of cycles per secondhc    heat transfer coefficient (W/m2 K)i   cylinder number (–)l   length (m)L   percentage of full engine load (%)m   mass (kg)_m   mass flow rate (kg/s)

P    pressure (N/m2)P e   cylinder brake power output (W)P ind   cylinder indicated power output (W)Q    heat (J)t    time (s)T    temperature (K)V    volume (m3)

 X    cylinders’ parameter (–)Y    cylinder performance parameter (–) z    number of cylinders

Greek lettersb   matrixbo   matrixD   deviation (%)dr    equivalent cylinder ring clearance (m)g   efficiencyh   crank angle (deg)k   thermal conductivity (W/m/K)

Subscriptsbl blow-bycalc calculatedcompr compressioncumul cumulative

curr currenteff effectiveexp experimentalG electric generatorgros grossg gashl heat lossm meanmax maximummeas measurednet netref referencescav scavengew wall

Dimensionless groupPr Prandtl number (–)Re Reynolds number (–)

 AbbreviationsCA crank angledeg degreesLHV lower heating value (kJ/kg)rpm rotations per minuteSOI start of injection (deg CA)TDC top dead center (abbreviations)

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scavenging air pressure is obviously affected by load variation. The

last methodology, which is the most sophisticated one, is based on

the use of two cylinder pressure sensors, one of which is mounted

periodically on each cylinder as usual and the second is perma-

nently mounted on one cylinder (usually no. 1), called from here

on as the ‘‘reference cylinder’’. According this methodology, the

comparison of all measured cylinder pressure traces to the refer-

ence provides the potential to detect load variation directly from

the ‘‘reference’’ cylinder power output.

Beyond load variation detection the purpose of these methodol-

ogies is to generate, if possible, results equivalent to the ones that

would have been derived if all cylinders were measured simulta-

neously. Measured cylinder pressure data are processed using an

existing diagnostic technique which has been applied up to now

on a great number of diesel engines the ability of which to estimate

engine operating condition and tuning has been verified by ex-

tended lab and field tests [23–26]. To evaluate the aforementioned

methodologies on the field a detailed experimental investigation

has been conducted on a large-scale two-stroke diesel engine used

for power generation on a Greek island. The use of a stationary en-

gine for the present work is more favorable compared to marine

due to the controlled environment and the constant rotational

speed which guarantees variation of engine load alone. Another

advantage is the direct recording of engine power from the mea-

sured electric power, utilizing of the known generator efficiency.

Cylinder pressure measurements have been obtained from the en-

gine together with various periphery engine parameters at two dif-

ferent engine operating points, corresponding to 50% and 100% of 

full engine load at 143 rpm engine speed respectively (constant

due to the nature of the engine i.e. electric power generation).

The diagnostic procedure  [27–30]   is applied at both load points

to derive cylinder power, cylinder fuel consumption, cylinder com-

pression quality etc., using the following methods:

(a) Sequential cylinder pressure measurement (conventional

methodology).

(b) Sequential cylinder pressure measurement and estimationof charge pressure at compression initiation which for a 2-

stroke engine corresponds to the exhaust valve closure event

(first methodology).

(c) Sequential cylinder pressure measurement and in parallel

precise measurement of scavenging air pressure using an

appropriate pressure sensor (i.e. second methodology).

(d) Use of two cylinder pressure sensors, one sensor mounted

periodically on each cylinder and a second permanently

installed on cylinder No.1, which is the ‘‘reference cylinder’’

(i.e. third methodology).

The evaluation of all methodologies is based on the comparative

evaluation of the diagnosis results estimated at each operating

point examined. From the comparison it is revealed that the meth-odology based on the use of two cylinder pressure sensors (i.e.

methodology [d]) is advantageous because it detects accurately

load variation during the measurement since it is always measured

in parallel the cylinder pressure of the same cylinder (reference).

From the analysis it is first shown that with the use of the con-

ventional methodology (i.e. methodology [a]) improper conclu-

sions can be derived for cylinder loading or compression

condition. This is a common problem, especially for marine appli-

cations, where relatively high power fluctuations can occur during

cylinder pressure measurement. Furthermore it is demonstrated

that utilization of the conventional diagnosis methodology to tune

the engines can finally result to cylinder power misbalancing and

deterioration of performance.

As shown the problemis overcame using the proposed method-ologies. Results obtained from the application of methodology [d]

are the most promising and practically independent of engine load.

Satisfactory results are also obtained from methodology [c]. Final-

ly, acceptable results are obtained using the purely computational

methodology based on the estimation of the in-cylinder charge

pressure at compression initiation (i.e. methodology [b]). Despite

the promising results additional validation is necessary, especially

for marine engines. However, indications exist that the methodol-

ogy based on the use of two cylinder pressure sensors (i.e. method-

ology [d]) is a very promising alternative against simultaneous

cylinder pressure measurement. The remaining two methodologies

based on the instantaneous charge air pressure could offer an ade-

quate, low cost solution to detect and account for the effect of load

variation during measurement. Finally, methodology [c] is a good

alternative solution but it requires use of an additional high fre-

quency response scavenging air pressure sensor. On the other

hand, methodology [b] could offer an acceptable low cost and eas-

ily applicable solution even though its accuracy is relatively lower.

2. Brief description of the engine simulation model

The diagnosis technique used in the present work is based on

the processing of measured cylinder pressure data using an enginesimulation model. The simulation model is a phenomenological

one based mainly on thermodynamics and it is capable of describ-

ing a variety of engine configurations. For the compression stroke a

single zone model is used while a multi-zone one is used during

combustion and expansion. The use of a multi-zone combustion

model instead of a two-zone one, as in the past, expands model

prediction capability on different engine configurations and re-

duces the need for constant tuning with engine operating condi-

tions because a more realistic representation of the air–fuel

mixing mechanism is used. The last is important for diagnosis

which is based on the comparison of current constants values

against the reference (derived from shop test data). Furthermore

it provides emission prediction capabilities for future use. An ana-

lytical description of the multi-zone simulation model has beenpublished by detail in the past [23,25,31–36]. Since the basic scope

of the present work is not to describe the simulation code but its

use for estimation of cylinder brake power output, fuel consump-

tion and engine tuning, in the following paragraphs is given only

a general description of the diagnosis methodology with special

emphasis on the mechanisms (i.e. sub-models) related to the

determination of the TDC position and the heat release rate from

which the power output and fuel consumption are derived.

 2.1. Brief description of the sub-models affecting estimation of brake

 power, fuel consumption and compression quality

In the present diagnosis methodology TDC position is estimated

form a thermodynamic methodology developed in the past whichhas been extensively tested and evaluated during both lab and field

tests [37]. The method has been introduced to overcome practical

difficulties since for field applications, it is usually not possible to

install a TDC sensor and measure with the required accuracy. The

proposed TDC estimation methodology and thus all values derived

from its use are affected from the mechanisms which affect the

compression stroke [33,34]. For this reason in the following para-

graphs are summarized these mechanisms with special reference

to the constants values that are used for their calibration using

the measured cylinder pressure trace from compression initiation

up to ignition.

 2.1.1. Heat transfer 

An important parameter which affects TDC estimation and thuscylinder power and heat release is heat transfer between the

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cylinder charge and the surrounding walls. In the thermodynamic

simulation model a turbulent kinetic energy viscous dissipation

rate k-e approach is adopted to determine the characteristic veloc-

ity for the heat transfer calculations as proposed by Assanis and

Heywood   [38–40]   and described by detail in references

[31,32,41]. The heat transfer coefficient is estimated from the fol-

lowing relation,

hc  ¼  c   Re0:8 Pr0:33   klcar

ð1Þ

while the instantaneous heat transfer rate is obtained from:

dQ hl

dh  ¼ A    hc   ðT  g    T wÞ þ c r     T 

4 g    T 4w

h i  ð2Þ

The mean gas temperature (T  g ) is derived taking into account the

specific heat capacity, the local temperature and the mass of each

zone. Moreover, after combustion initiation the overall estimated

heat exchange rate obtained from Eq. (2) is distributed among the

surrounding air and the jet zones according to their mass, temper-

ature and specific heat capacity  [31,32,41]. For the compression

stroke the procedure is simpler due to the existence of only one

zone.

 2.1.2. Cylinder blow-by

Blow-by affects all the processes of the closed cycle and thus

[34,39–41]  TDC estimation. The last affects also the heat release

rate, from which fuel consumption is determined, as described lat-

ter on. In the proposed methodology a simplified model, developed

by the authors in the past  [34], is used instead of a detailed one

which requires the knowledge of engine data which are usually

not available during field applications. According to this simplified

model approach, blow-by rate is estimated using an equivalent

blow-by area ( Aeq) between the cylinder rings and the cylinder

bore [23] as follows:

 Aeq ¼  p  D  dr    ð3Þ

where (dr ) is the equivalent cylinder-ring clearance that defines thelevel of cylinder liner–ring wear. The corresponding mass flow

(blow by) rate is then calculated using standard isentropic com-

pressible flow relations [34,39–41]. As long as the fresh air zone ex-

ists blow-by is abstracted from it assuming that this is mostly in the

vicinity of the combustion chamber walls. When the burning zone

(i.e. fuel jet) occupies the entire combustion chamber, blow-by

mass is distributed to each zone taking into account its mass and

the total instantaneous cylinder charge mass.

 2.1.3. Inlet and exhaust system

In the present work the filling–emptying method

[29,30,39,40,42]  is used to estimate the pressure–temperature ver-

sus time history in the two manifolds (intake–exhaust). The mass

flow rate through the turbine nozzle is calculated using isentropicflow relations and the effective turbine nozzle flow area. This is

adequate for the specific engine which is equipped with a constant

pressure turbo-charging system.

 2.1.4. The scavenging model

Scavenging is an important process for a two-stroke turbo-

charged engine  [29,30,39,40]. For this reason a two-zone scaveng-

ing model is used  [29,30,39,40,42], which divides the combustion

chamber contents into two parts: one consisting only of fresh en-

trained air, and a second consisting of combustion products from

the previous cycle and freshly entrained air. With this approach,

part of the intake air escapes directly into the exhaust manifold

(short-circuiting) affecting the exhaust gas temperature. At the

end of scavenging (start of compression stroke), perfect mixing be-tween the two zones is assumed resulting into a single zone which

is a mixture of fresh air and combustion products from the previ-

ous cycle.

 2.2. Brief description of the constants determination methodology and

the diagnosis procedure

For diagnosis, use is made of both cylinder pressure and con-

ventional data (i.e. pressure, temperature of the engine subsys-

tems). But their values are influenced from a number of 

subsystems making the distinction of the actual cause for a fault

extremely difficult. For example, a low peak combustion pressure

may be the result of low fuel flow rate, a faulty injector, low SOI

advance, low boost pressure or increased blow-by, etc. Therefore,

it is necessary to develop a methodology to provide the actual

cause. This is achieved using a stepwise approach which manages

to distinguish the parameters affecting the compression stroke, the

combustion expansion stroke and the gas exchange. The method is

based on the determination of model constants that express the

quality/condition of subsystems or mechanisms. The simulation

model is initially auto-calibrated using shop test data (i.e. brake

power output, fuel flow rate, peak compression pressure, peak fir-

ing pressure, etc.). From the aforementioned brief description of 

sub-models it has been show that a number of constants are used

in the corresponding mathematical relations/correlations which

are generally unknown even though statistical values are available.

These constants are related to geometrical characteristics of the

engine (i.e. compression ratio, equivalent piston ring clearance

etc.) and other physical processes inside the combustion chamber

(i.e. heat transfer). The TDC position is also considered to be an un-

known constant which represents the angular phasing of the mea-

sured cylinder pressure   [37]. The cylinder pressure trace is

obviously affected by various mechanisms and for this reason a

methodology is required to define the effect of each one upon it.

For this reason it has been conducted a detailed sensitivity analysis

fromwhich the following important conclusions have been derived

[28,30]:

 Compression ratio has the strongest effect on the initial part of 

the compression stroke.

 Constant (dr ), which provides the degree of cylinder/ring wear,

affects mostly the part around TDC, shifting the peak compres-

sion pressure angle to the left relative to TDC.

 Cylinder wall temperature has a similar effect, as (dr ), but less

pronounced.

 Constant (c ) in Eq. (1) affects mainly the late part of compres-

sion and is obtained using the shop test data, because it is a

characteristic for a specific engine.

Utilizing these results it is derived the methodology for their

determination and also their relation to the condition of engine

components. Thus, constants’ value is considered to be an indexfor the current condition of the various engine components or sub-

systems. The constants values for the compression part are esti-

mated so that the calculated cylinder compression pressure trace

(up to ignition) matches accurately the measured one using a spe-

cial constant determination procedure developed in the past

[24,27–30]. The procedure is applied initially using the shop test

data providing a set of constants values that are the ‘‘reference’’

and the corresponding engine simulator is referred to as the ‘‘refer-

ence’’ engine. A detailed description of the mathematical proce-

dure for the determination of model constants is provided in

[24,27–30]. The procedure is then applied at the present operating

conditions and a new set of model constants is estimated. The cor-

responding engine simulator is now referred to as the ‘‘current’’

engine. Matrix (boj) lists model’s constants corresponding to the‘‘reference’’ engine while matrix (b j) lists the respective constants

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corresponding to the ‘‘current’’ engine. The direct comparison, on a

percentage basis, of the aforementioned matrices provides an indi-

cation for the condition of the various engine subsystems. Taking

these into account, a fault or malfunction exists if the following cri-

terion is satisfied:

b j  boj

boj 100%P 3%   ð4Þ

The three percent error limit is used to account for measurement

error or inaccuracies. The condition of an engine component or

subsystem results from the estimation of the following parameter:

(b j/boj) 100%.

3. Estimation of critical engine performance parameters

As already mentioned, the present work focuses on the effect of 

load variation on cylinder pressure, cylinder loading and compres-

sion condition, which are parameters extremely important for en-

gine performance. For this reason it is of critical importance the

accurate estimation of these parameters. Results for cylinder load-

ing are more critical because an error can result to improper engine

tuning and thus deterioration of engine performance. Toward this

direction it is necessary to have an appropriate assessment of TDC

position and estimation of heat release rate including heat losses.

In the following paragraphs is given a brief description of the

methodology developed and adopted for the estimation of both

parameters.

 3.1. Methodology for determination of TDC position

A significant advantage of the proposed technique is that it re-

quires no measurement of TDC position. This is significantly

important for field applications especially on large scale two-stroke diesel engines where it is extremely difficult, if not impossi-

ble, to use an angle encoder or other equivalent hardware. Further-

more even if this was the case there would still exist an uncertainty

between cylinder phasing due to torsional vibrations etc. For this

reason a new methodology has been employed to overcome this

difficulty which has been developed by the authors in the past

[37]. This methodology allows the estimation of the TDC position

of each cylinder individually avoiding thus the effect of deflections,

vibrations, oscillations etc. The method is based purely on thermo-

dynamics and is generally applicable on any type of reciprocating

engine. TDC estimation is based on the precise matching of the

compression part of the calculated cylinder pressure diagram –

for which the TDC position is obviously known – to the compres-

sion curve of the measured cylinder pressure diagram for whichno crank angle reference exists. This is achieved, as described by

detail in [37], considering TDC as an unknown constant together

with compression ratio, initial pressure, blow-by, heat transfer

etc. These are calculated using a multi-parameter optimization

technique the criteria of which is the least possible deviation be-

tween the calculated and the measured cylinder pressure traces.

The methodology has been extensively validated by both lab and

field measurements. The error is in the range of 0.1–0.2 deg CA.

A basic criterion for the reliability of the proposed technique is

the accurate prediction of engine power output, because an error

of 1 deg CA for TDC position results to an error of about 8–10% in

indicated power output   [37,43,44]. The last evaluation was

adopted in the present work because generated power was avail-

able and at the same time both engine mechanical efficiency andgenerator efficiency were also known from the official shop tests.

 3.2. Estimation of cylinder brake power 

Estimation of cylinder brake power output is based on the pos-

sessing of the measured cylinder pressure trace. Having deter-

mined TDC position the measured cylinder pressure – crank

angle diagram is converted into a P – V diagram from the integra-

tion of which is derived the indicated power as follows:

P ind ¼I   PdV 

  f    ð5Þ

Using the mechanical efficiency (gm) which is reported in the en-

gine shop test data and the efficiency of the electric generator

(gG), the corresponding calculated electric power is derived, as

follows:

P G ¼  gG  gm  z   P ind   ð6Þ

 3.3. Estimation of cylinder fuel flow rate

For a multi-cylinder engine operating on the field, it is extre-

mely difficult if not impossible to measure the fuel flow rate of 

each cylinder especially in cases where injection pressure mea-

surements are not available. For this reason, a computational

method has been developed in the past  [30] to estimate cylinder

fuel flow rate which is based on the processing of the measured

cylinder pressure diagram. An estimate for the actual amount of 

fuel mass burnt inside the combustion chamber is obtained from

the heat release rate analysis procedure as follows [39,40],

_m f   ¼ Q  g ;cumul

LHV   ð7Þ

where (LHV ) is the lower heating value of the fuel and (Q  g ,cumul) rep-

resents the cumulative gross heat release obtained from the inte-

gration of the instantaneous gross heat release rate given from

the following relation:

dQ grosdh  ¼ dQ net

dh  þ dQ hl

dh  ð8Þ

In the net heat release rate   dQ net

dh  are considered the losses due to

blow-by (derived from the procedure described in Section  2.1.2.)

and the enthalpy of the injected fuel, using an iterative procedure

until the net heat release rate converges. The instantaneous heat

losses (dQ hl

dh ) to the cylinder walls are estimated using Eq.  (2), where

the instantaneous mean gas temperature (T  g ) is obtained from the

ideal gas state equation and the measured cylinder pressure as

follows,

T  g  ¼ P   V 

R  m  ð9Þ

The mass of the cylinder charge (m) is obtained from the simulation

model using the measured values of inlet pressure, temperature etc.while constant (hc ) in Eq.  (1)  and the corresponding cylinder wall

temperature are obtained from the constants determination proce-

dure. The specific methodology has been validated by laboratory

experiments and filed tests   [30]  and its accuracy is in the region

of ±1.5%.

4. Experimental setup and test cases examined

Each of the three methodologies used to account for load varia-

tion has been applied on a large-scale, two-stroke, seven-cylinder

diesel engine installed on a Greek island. The diesel engine was

coupled to an electric generator for electric power generation. In

Table 1 are given the main technical data of the engine while in

Fig. 1 is given a schematic layout of the setup. For cylinder pressuremeasurement, an air cooled Kistler piezotron pressure sensor is

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used which is mounted on the indicator valve of each cylinder.

Sensor signal is transferred to a high-speed sampling system (i.e.

USB/AD Card) and after transformation it is stored in the memoryof a portable personal computer (PC) where the diagnostic soft-

ware has been installed. Cylinder pressure data is recorded using

a sampling rate equivalent to 0.5 deg CA. For the present applica-

tion a number of  50 cycles have been recorded from each cylin-

der. From these, a mean cylinder pressure trace is estimated after

processing, which is the input for the diagnostic technique.

Measurements have been conducted at actual operating condi-

tions at two different load points as shown in Table 2. With refer-

ence to  Table 2 it is made clear that measured power is electric

power and is obtained from the conventional instrumentation of 

the station which has an accuracy of ±1%. In the 5th column of 

Table 2   is also given the net engine power, estimated from the

electric power and the generator efficiency. As observed from

Table 2  engine speed is constant during all measurements sincethe engine is used for electric power generation.

5. Description of the methodologies used to account for load

 variation

With the conventional measurement methodology, the value of 

each engine cylinder performance parameter (i.e. brake power, fuel

flow rate, peak firing pressure and compression condition) is deter-

mined from the diagnostic technique by processing both the corre-

sponding measured cylinder pressure trace and the mean value of 

scavenge air pressure, temperature etc. But, this data may vary

during measurement due to load fluctuation which will obviously

affect derived results resulting to improper conclusions concerningcompression condition, loading, start of injection etc. Thus, it is

necessary to develop a methodology to detect and account for

the effect of load variation during measurement. Towards this

direction, in the present paragraph, it is described the main philos-

ophy of the three methods that have been developed to detect and

account for load variation.

5.1. Conventional methodology: Sequential cylinder pressure

measurement 

Using the conventional cylinder pressure measurement meth-

odology, engine cylinders are measured sequentially – not simulta-

neously – one after the other. For the diagnosis of each cylinder, it

is used the instantaneous measured cylinder pressure trace and

also the mean values of scavenge air pressure and other conven-

tional operating parameters which are taken during measurement.

For the current two-stroke seven-cylinder diesel engine, cylinders

are measured consequently one after the other which results to a

total of seven cylinder pressure measurements for each engine

operating point (Fig. 2).

Thus, the values of cylinder’s parameters derived from this pro-

cedure may deviate from reality if load fluctuates during cylinder

pressure measurement. Their use may also result to engine

mistuning.

5.2. Methodologies based on the instantaneous value of the charge air 

 pressure

According to the literature [29,30], a basic operating parameter

related to engine load for turbocharged engines is the scavenging

air pressure which affects the pressure at compression initiation.

The variation of the last will obviously affect derived results for

both cylinder performance and condition. For this reason in the fol-

lowing sub-paragraphs is described the main philosophy of two

methodologies developed and adopted herein to account for scav-

enging air pressure variation due to load fluctuation. The first

(experimental) is based on the utilization of the measured instan-

taneous charge air pressure and the second (computational) on theprocessing of the measured cylinder pressure trace.

 Table 1

Technical data of the engine.

Engine type 2Stroke, T/C, 7K60MC_S

Cylinder bore 600 (mm)

Piston stroke 1650 (mm)

Connecting rod length 2280 (mm)

Number of cylinders 7

Number of exhaust valves 1 (per cylinder)

Reference engine speed 143 (rpm)

Turbochargers 2

Intercooler 1

Nominal brake power 11.2 (MW)

Fig. 1.  Schematic layout of the test installation.

 Table 2

Engine operating conditions at which measurements were conducted.

Test

case

Engine speed

(rpm)

Load

(%)

Electric power

(kW)

Engine power

(kW)

1 143 50 5770 6272

2 143 100 11,352 11467

Fig. 2.  Schematic layout of the conventional measurement procedure.

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5.2.1. Sequential cylinder pressure measurement and calculation of 

instantaneous scavenging air pressure. (1st methodology)

A new technique has been developed to calculate the scaveng-

ing air pressure from the measured cylinder pressure trace. To

achieve this, the cylinder pressure at exhaust valve closure (com-

pression initiation for 2-stroke engines) is assumed to be an addi-

tional unknown constant in the constants determination

procedure, as described previously. The corresponding instanta-

neous calculated scavenging pressure (i.e. (P scav)calc) is then

calculated using an iterative procedure to provide the calculated

initial pressure at compression initiation. This value (i.e. (P scav)calc)

is then used to correct derived cylinder performance parameters,

following the methodology described in Section 5.2.3.

5.2.2. Sequential cylinder pressure measurement and parallel precise

measurement of instantaneous scavenging air pressure. (2nd

methodology)

The present methodology is similar to the previous but it is

based on the processing of both the cylinder pressure and the cor-

responding instantaneous scavenging air pressure obtained from

an accurate fast response boost pressure sensor. Both signals are

recorded simultaneously when measuring each cylinder. The mea-

sured scavenging air pressure (i.e. (P scav)meas) is then used to cor-

rect cylinder performance parameters as described in Section 5.2.3.

5.2.3. Load correction using the value of the scavenging air pressure

Having derived the diagnosis results, it is then possible to cor-

rect cylinder performance parameters (Y: brake power, fuel con-

sumption, peak pressure, compression pressure etc.), as follows:

Y cor;i ¼  Y meas;i þ ðCF Þi   DY 

DL

i

ð10Þ

where ‘‘i’’ denotes the measured cylinder, ‘‘CF ’’ is the correction fac-

tor for load variation and (DY /DL)i  is the sensitivity coefficient of 

the specific cylinder performance parameter (Y ) with load. The cor-

rection factor for load variation ‘‘CF ’’ is the variation of engine load

and is estimated from the variation of scavenging air pressure as

shown below while the sensitivity coefficient represents the corre-

sponding effect of load variation on the specific cylinder perfor-

mance parameter (Y ). According to the engine shop test data, the

variation of scavenging air pressure with load, which is depicted

in Fig. 3, for the present application is approximately linear and de-

scribed by the following relation:

P scav  ¼  a1  Lð%Þ þ b1   ð11Þ

where ‘‘L(%)’’ denotes the percentage of full engine load and  a1,  b1

are constants which for the specific engine have been found to be

a1 = 0.026 and b1 = 0.33. Using the first derivative of Eq. (11) with

respect to load (L), the correction factor for load variation is pro-

vided from the following formula:

DðP scavÞ

DL  ¼ a1  ) ðCF Þi  ¼  a1  DðPscavÞ ¼  a1 

 ðPscavÞi  ðPscavÞmðPscavÞm

ð12Þ

where for the specific application  a1 = 0.026, ‘‘i’’ denotes the mea-

sured cylinder and ‘‘m’’ the mean value during the measurement.

Furthermore, according to the shop test data depicted in  Fig. 4,it is revealed that two other critical performance parameters i.e.

fuel consumption and compression pressure also correlate  line-

arly with engine load which is described mathematically as

follows:

_mfuel ¼  a2  Lð%Þ þ b2   ð13aÞ

P compr ¼  a3  Lð%Þ þ b3   ð13bÞ

where   a2   to   b3   are constants which for the specific engine are

a2 = 24.9,  b2 = 302.8,   a3 = 1.07 and   b3 = 27.25. On the other hand,

from Fig. 4 it is revealed that the variation of the peak cylinder pres-

sure with load is approximately a second order polynomial function

as follows:

P max ¼  a4 þ b4  Lð%Þ þ c 4  ½Lð%Þ2

ð13cÞ

where, for the specific engine the aforementioned constants take

the following values: a4 = 29.71, b4 = 1.66 and c 4 = 0.0054.

0 20 40 60 80 100 120  

Engine Load (%)

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

3.0 

   S  c  a  v  e  n  g  e  a   i  r   P  r  e  s  s  u  r  e   (   b  a  r   ) Engine Shop Tests

Engine speed : 143 rpm

Fig. 3.  Engine shop test data: Variation of scavenge air pressure as a function of engine load.

0 20 40 60 80 100 120  

Engine Load (%)

800 

1200 

1600 

2000 

2400 

2800 

3200 

   F  u  e   l   C  o  n  s  u  m   t   i  o  n   (   k  g   /   h   )

Engine Shop Tests

Engine Speed : 143 rpm

60 

80 

100 

120 

140 

160 

   P  e  a   k   P  r  e  s  s  u  r  e   (   b  a  r   )

40 

60 

80 

100 

120 

140 

160 

   C  o  m

  p  r .   P  r  e  s  s  u  r  e   (   b  a  r   )

Fig. 4.   Engine shop test data: variation of (i) compression pressure, (ii) fuelconsumption and (iii) peak pressure with engine load.

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The sensitivity coefficient of each parameter with load, i.e. (DY/

DL)i is estimated by derivation of Eqs.  (13a)–(13c). Eq. (10) is used

for all engine performance parameters examined i.e. brake power

output, fuel consumption, peak firing pressure and compression

pressure. Obviously for brake power correction the sensitivity coef-

ficient with load is unity.

5.3. Methodology based on the use of two cylinder pressure sensors.(3rd methodology)

5.3.1. Brief description of the measurement procedure

In an effort to overcome the problem of load variation during

measurement and generate results equivalent to the ones obtained

using simultaneous cylinder pressure measurement, a new mea-

surement technique is proposed herein. It is based on the use of 

two pressure sensors to acquire simultaneously measurements

from two engine cylinders each time, one of which is always the

same and is called the ‘‘reference’’ cylinder. In Fig. 5 are presented

the measurement steps that constitute the new measurement

methodology. According to  Fig. 5, during cylinder pressure mea-

surement, one pressure sensor (i.e. reference one) is permanently

mounted on the indicator valve of the reference cylinder whichfor the present application is cylinder No. 1, while the second pres-

sure sensor is periodically mounted, as usual, on each of the

remaining cylinders until all are measured i.e. the measurement

sequence is (Nos. 1–2), (Nos. 1–3). . .(Nos. 1–7), i.e. in total 6 mea-

surements. In Fig. 6 are given the results for cylinder brake power.

In this figure are shown the brake power output of the reference

cylinder (No. 1) and the remaining cylinders at 100% load and

143 rpm engine speed. The first two power values for Cyl. 1 are

the same since they refer to the same measurement i.e. Cyls. ‘‘1–2’’.

Observing Fig. 6, it results that there exist significant differences

between cylinder power output, while at the same time it is also

observed a fluctuation of reference cylinder power output. This is

a clear indication of brake power fluctuation during measurement,

which affects the acquired individual pressure cylinder data.

Therefore the estimated brake power output of each cylinder, using

the conventional technique, is affected from the power fluctuation

of the engine and does not represent the actual case. To obtain the

actual brake power output of each cylinder i.e. the one to be ex-

pected if no power fluctuation exists during cylinder pressure mea-

surement, the effect of engine load variation has to be nullified. A

significant advantage of the specific methodology is that the

instantaneous load variation during the measurement procedure

is directly noticeable and accurately detected from the variation

of the reference cylinder power output. This gives the potentiality

of accurate identification of load variation effect on engine perfor-

mance, enabling thus the proper tuning of all engine cylinders to

guarantee, after adjustment, uniform cylinder loading and

operation.

5.3.2. Load correction method using two cylinder pressure sensors

As already described, cylinder performance parameters are esti-

mated from the diagnostic technique by processing the measured

cylinder pressure traces. Having processed the measured data of 

both cylinders i.e. the current and the reference, it is then possible

to correct the derived cylinder performance parameter (Y ) directly

as follows:

Y cor;i  ¼  Y meas;i þ ðCF Þi  Y meas;i   ð14Þ

where ‘‘i’’ denotes the measured cylinder and (CF) represents the

load correction factor of the examined parameter which is derived

from the following formula:

ðCF Þi  ¼ Y ref ;i¼1  Y ref ;i

Y ref ;ið15Þ

where ‘‘Y ref ’’ represents the value of the reference cylinder perfor-mance parameter. Obviously for the first measurement, i.e. mea-

surement No. 1 (i  = 1), no load variation exists and thus the load

correction factor is zero.

6. Results and discussion

6.1. Effect of load fluctuation on the measured cylinder pressure trace

In Fig. 7a and b are given the raw measured cylinder pressure

traces at the two operating points examined i.e. at 50% load and

143 rpm and at 100% load and 143 rpm engine speed, respectively.

The diagrams depict the ‘‘mean’’ cycle for each cylinder, without

crank angle reference. These diagrams provide only a first indica-

tion for cylinder performance and possibly condition. From thesefigures are obvious the differences exist between engine cylinders.

Fig. 5.   Schematic layout of measurement procedure based on the use of twocylinder pressure sensors.

1 2 3 4 5 6 7  

Cylinder Number 

1550 

1600 

1650 

1700 

1750 

1800 

1850 

1900 

   B  r  a   k  e   P  o  w  e

  r   (   k   W   )

0 1 2 3 4 5 6  

Measurement number for Ref. Cylinder 

100% Load

Reference cylinder 

measured cylinder 

Fig. 6.  Estimated brake power output (i) for the reference cylinder and (ii) for each

one of the remaining cylinders, at 143 rpm and 100% load.

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However, these can be attributed to cylinder condition (i.e. com-

pression quality, injector condition etc.), tuning (i.e. cylinder flow

rate, injection advance etc.) or/and load variation during the mea-

surement. To identify the possibility for load variation and define

its effect the measurements of the reference cylinder are utilized,

as already mentioned.

During the measurement procedure, six (6) measurements

were taken for the reference cylinder at each load point. In

Fig. 8a and b are displayed the corresponding pressure diagrams

of the reference cylinder (i.e. Cylinder No. 1) vs crank angle, for

each measurement conducted and for both operating points exam-

ined (i.e. 50% load and 143 rpm and 100% load and 143 rpm engine

speed). The aforementioned pressure-crank angle diagrams have

been obtained after processing the measured raw cylinder pressure

data using the diagnostic technique. From these graphs it is

obvious that the pressure of the reference cylinder fluctuates.

The differences become more evident during the last stages of 

compression and the initial stages of combustion. This is an

indication that the deviation of reference cylinder pressure history

is most possibly attributed to load fluctuation during themeasurement.

6.2. Effect of load variation on cylinder performance parameters

As already mentioned, the present work focuses on the effect of 

load variation during measurement on cylinder brake power, fuel

consumption compression quality and ignition angle which are

critical engine operating parameters. For this purpose, in the fol-

lowing paragraphs are provided results for the aforementioned

parameters having accounted and corrected for the effect of load.

The evaluation is conducted by compassion to the results of the

conventional methodology (i.e. sequential cylinder pressure

measurement).

6.2.1. Estimated cylinder power output 

In  Fig. 9a–b is given the brake power output of the reference

cylinder, the actually measured cylinder power and the corrected

(i.e. estimated with 1st, 2nd or 3rd methodology) brake power out-

put of each cylinder, for 50% and 100% of full engine load at

143 rpm engine speed. Measured cylinder power is the one derived

from the application of the conventional diagnosis technique

which does not account for load variation (i.e. conventional brake

power). On the other hand, cylinder corrected power is the one de-

rived from the application of the three methodologies that are used

to account for the effect of load variation. Observing reference cyl-

inder brake power during measurement, it is revealed that for both

loads examined, a considerable fluctuation exists. This is an indica-

tion for engine load variation during the measurement. For this

reason, the measured cylinder power (i.e. the one derived through

the conventional methodology) has to be corrected properly, as al-ready described, in order the corrected power of each cylinder to

represent the actual power value, i.e. the one which would be re-

corded if engine load was kept constant during measurement.

Observing the corrected cylinder brake power output, esti-

mated from the first methodology, based on the variation of the

calculated cylinder charge pressure, it is shown that both the cor-

rected and the conventional brake power values follow a similar

variation trend among the cylinders. This becomes more evident

at full load condition. On the other hand, observing the corrected

cylinder brake power output estimated from the other two

0 

20 

40 

60 

80 

100 

120 

140 

   C  y   l   i  n   d  e

  r   P  r  e  s  s  u  r  e   (   b  a  r   )

50% Load

Mean Cycle

No1No2    No3  No4   No5  No6   No7 

(a)0 

20 

40 

60 

80 

100 

120 

140 

160 

180 

   C  y   l   i  n   d  e  r   P  r  e  s  s  u  r  e   (   b  a  r   )

100% Load

Mean Cycle

No1   No2   No3   No4  No5   No6 

No7 

(b)

Fig. 7.   Mean cylinder pressure diagrams at (a) 50% load and 143 rpm engine speed and (b) 100% load and 143 rpm engine speed.

Crank Angle (deg)

80 

82 

84

86 

88 

90 

92 

9496 

98 

   C  y   l   i  n   d  e  r   P  r  e  s  s  u  r  e   (   b  a  r   )

1st measurement 

2nd measurement 

3rd measurement 

4th measurement 

5th measurement 

6th measurement 

50% Load

Ref. cylinder 

(a)

176 180 184 188 192 196  

Crank Angle (deg)

120 

122 

124

126 

128 

130 

132 

134136 

138 

   C  y   l   i  n   d  e  r   P  r  e  s  s  u  r  e   (   b  a  r   )

1st measurement 

2nd measurement 

3rd measurement 

4th measurement 

5th measurement 

6th measurement 

100% Load

Ref. cylinder 

(b)

176 180 184 188 192 196  

Fig. 8.   Cylinder pressure versus crank angle diagrams of the reference cylinder at (a) 50% load and 143 rpm engine speed and (b) 100% load and 143 rpm engine speed.

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methodologies, based on the variation of the measured scavenging

pressure and the use of two cylinder pressure sensors, it is revealed

that both corrected brake power values follow an almost similar

variation trend among the cylinders but it is different compared

to the one of the first methodology. The difference is more obvious

at full engine load.

Using the cylinder brake power values reported in the previous

graphs are generated Fig. 10a–c, which provide the patterns of cyl-

inder power deviation around the mean value, for each methodol-

ogy at the two loading points examined. Power deviation of eachcylinder, on percentage basis, is estimated as follows:

DP e;ið%Þ; ¼  P e;i

P e;m

  1

  100   ð16Þ

where (P e,i) represents the corrected brake power of the (ith) cylin-

der and (P e,m) represents the mean value. Observing Fig. 10a, it re-

sults that, for the two load points examined, the power deviation

of each cylinder, derived from the first methodology is qualitatively

similar only for cylinders Nos. 1–3 and 5. On the other hand, this is

not the case for the remaining cylinders. Since the power deviationpattern for all cylinders should remain qualitatively the same with

Cylinder Number 

850 

900 

950 

1000 

   B  r  a   k  e   P  o  w  e  r   (   k   W   )

Measurement Number for Ref. Cylinder 

50% LoadRef. cylinder 

conv. method 

1st method 

2nd method 

3rd method 

(a)

1 2 3 4 5 6 7 1 2 3 4 5 6 7  

Cylinder Number 

1550 

1600 

1650 

1700 

1750 

1800 

1850 

   B  r  a   k  e   P  o  w  e  r   (   k   W   )

0 1 2 3 4 5 6 0 1 2 3 4 5 6  

Measurement Number for Ref. Cylinder 

100% LoadRef. cylinder 

Conv. method 

1st method 

2nd method 

3rd method 

(b)

Fig. 9.   The actual and the estimated brake power output for each cylinder at (a) 50% load and 143 rpm engine speed and (b) 100% load and 143 rpm engine speed.

Cylinder Number 

-6 

-4

-2 

0 

2 

4

6 

    (   b  r  a   k  e  p  o  w  e  r   ) ,   (   %   )

1st method

50 % Load 

100 % Load 

(a)Cylinder Number 

-6 

-4

-2 

0 

2 

4

6 2nd method

50 % Load 

100 % Load 

(b)

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8  

0 1 2 3 4 5 6 7 8  

Cylinder Number 

-6 

-4

-2 

0 

2 

4

6  3rd method

50 % Load 

100 % Load 

(c)

   (   b  r  a   k  e  p  o  w  e  r   ) ,   (   %   )

    (   b  r  a   k  e  p  o  w  e  r   ) ,   (   %   )

Fig. 10. Comparisonof thedimensionless brake power output variationamong thecylinders for 50% and100%of full engine load, by using (a) the 1stdiagnosis methodology,

(b) the 2nd diagnosis methodology and (c) the 3rd diagnosis methodology.

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engine load, this is an indication that the first methodology does not

totally detect and account for the effect of engine load variation.

Observing the results of the second methodology it is revealed

that cylinder power deviation pattern for cylinders Nos. 1–5 and

7 is similar for the two load points examined, while for No. 6 a dif-

ferent pattern is observed which could be attributed to a random

error during measurement. Moreover, comparing the absolute val-

ues of the power deviation of each cylinder for the two loading

points it is revealed that these are similar since only small differ-

ences exist.

Finally using the third methodology where load variation is di-

rectly detected form the power variation of the reference cylinder,

the patterns of power deviation all of cylinders appear to be similar

for both engine loading points examined, despite the small differ-

ences of absolute values attributed most possibly to measurement

error (normal).

Considering the previous, it is made obvious that the last two

methodologies adequately detect and account for the effect of en-

gine load variation on the cylinder pressure measurement and the

derived diagnosis results. Therefore, their advantage to properly

correct individual cylinder power considering for the effect of load

variation, is clearly demonstrated. However, it is to be noted that

the results of the first methodology can also be considered up to

a certain point as satisfying since the corrected results are close

to the reality. This is important because the specific methodology

is completely computational requiring not additional equipment

or measurement effort creating a strong motivation for further

investigation and improvement.

6.2.2. Cylinder tuning 

Based on experience, cylinder power deviations in the range of 

(±3%) are considered acceptable for the specific engine type. Differ-

ences above this range generate the necessity to adjust cylinder

power through fuel rack position adjustment. Considering the pre-

vious results two possibilities exist for cylinder tuning i.e. fuel rack

adjustment: Use of the primary measured cylinder brake power

(i.e. conventional brake power) and use of the corrected one which

estimated from the three methodologies examined in the present

work. As known in practice, the standard methodology is to use

the measured cylinder brake power output to analyze cylinder per-

formance. But, in the case of an engine load variation, as in the

present, there exists the risk for mistuning. For this reason in

Fig. 11a–b are given the estimates for cylinder brake power output

after having adjusted cylinder fuel racks using the corrected and

un-corrected vales of cylinder power output. It is evident that

the use of the uncorrected cylinder brake power output results to

significant distortion of engine operation in the case of a load

variation during the measurement. As shown, the first methodol-

ogy, based on the calculated of the cylinder charge pressure at

compression initiation would lead to a slight improvement, espe-

cially at low load but cannot guarantee uniform cylinder operation.

On the other hand the second methodology based on the measure-

ment of the instantaneous scavenging air pressure, results to

considerable improvement for both load points examined. How-

ever, the third methodology (i.e. the engine load variation is de-

tected through the brake power variation of the reference

cylinder) leads to uniform distribution of the brake power output

among the cylinders, clearly indicating that its advantageous and

capable to detect properly and eliminate accurately the effect of 

engine load fluctuation during cylinder pressure measurement.

Consequently, considering the results provided in Fig. 11a and

b, it is obvious that the diagnosis technique should consider for

load variation during measurement, otherwise there is a risk for

engine mistuning. Finally, comparing the results it is revealed the

superiority of the third methodology for a correct cylinder power

tuning in the case of varying load during measurement.

6.2.3. Cylinder fuel flow rate

In Fig. 12a and b are given the corresponding values, corrected

and uncorrected, for each cylinder at 50% and 100% of full engine

load at 143 rpm engine speed. Cylinder fuel flow rate has been esti-

mated by applying the methodology described in Section 3.3 of the

present work. Since engine power is almost directly related to fuel

consumption, it is possible to correct cylinder fuel flow to account

for the effect of load variation using the three methodologies de-

scribed in the present work. Thus, in Fig. 12a and b is given the va-

lue for the corrected fuel flow rate of each cylinder which

corresponds to the value that would be observed if load had been

kept constant during measurement. The use of the conventional

cylinder fuel flow rate, without considering the load variation ef-

fect, for fuel rack adjustment will result to improper cylinder tun-

ing and most possibly to deterioration of engine performance.

Observing Fig. 12a–b it is revealed that for both loading points

examined, the comparison of the absolute values for the conven-

tional and corrected cylinder fuel consumption reveals that the

first methodology does not manage to account adequately for the

effect of load variation, since the results appear to be quite similar.

Moreover, the corrected fuel consumption, derived from the first

methodology, appears to follow a trend which is quite similar to

the respective one of the conventional methodology revealing its

difficulty to properly account for the effect of load variation.

On the other hand comparing the corrected fuel consumptions

of the remaining two methodologies, the results appear to be

rather similar. Both methodologies properly account for the effect

Cylinder Number 

840 

860 

880 

900 

920 

940 

   B  r  a   k  e  p  o  w  e  r  a   f   t  e  r   t  u  n  n   i  n  g   (   k   W   )

1st method 

2nd method 

3rd method 

50% Load

(a)

1 2 3 4 5 6 7 1 2 3 4 5 6 7  

Cylinder Number 

1620 

1640 

1660 

1680 

1700 

1720 

1740 

   B  r  a   k  e  p  o  w  e  r  a   f   t  e  r   t  u  n  n   i  n  g   (   k   W   )

1st method 

2nd method 

3rd method 

100% Load

(b)

Fig. 11.  Actual cylinder brake power versus estimated one after tuning using each one of the three methodologies, at (a) 50% load and 143 rpm engine speed and (b) 100%load and 143 rpm engine speed.

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of load variation which is revealed from the fact that the corrected

fuel flow rates follow an almost similar variation trend among the

cylinders, which however is slightly different compared to the one

of the first methodology. The difference is more obvious at full en-

gine load.

Applying Eq.  (16) for the corrected cylinder fuel consumption

are derived the graphs shown in Fig. 13a–c, which provide the cyl-

inder fuel consumption deviation around the mean value for both

load points examined.

Observing Fig. 13a, it results that, for both load points, the fuel

consumption deviation of each cylinder, derived from the first

methodology is qualitatively similar only for cylinders Nos. 1, 3,5 and 7. Furthermore, for both loads examined, the results ob-

tained from the second methodology provide the same pattern

for all cylinders except for the cylinder No. 6 where a slight differ-

ent pattern is observed. On the other hand, for both engine load

points, the pattern of the results obtained from the third method-

ology follow the same trend among all cylinders. Furthermore, very

small differences are observed between absolute values. The differ-

ence is almost the same for all cylinders revealing thus that it could

be attributed to experimental procedure.

Consequently, the second and third methodologies, based on

the use of the measured scavenging air pressure and the use of 

two cylinder pressure sensors respectively, enable more accurate

estimation of the fuel flow rate to each cylinder compensatingfor the effect of load variation during the measurement. This is

Cylinder Number 

160 

165 

170 

175 

180 

   F  u  e   l   C

  o  n  s  u  m  p   t   i  o  n   (   k  g   /   h   )

Conv. method 

1st method 

2nd method 

3rd method 

50% Load

(a)

1 2 3 4 5 6 7     1 2 3 4 5 6 7  

Cylinder Number 

275 

285 

295 

305 

315 

   F  u  e   l   C

  o  n  s  u  m  p   t   i  o  n   (   k  g   /   h   )

Conv. method 

1st method 

2nd method 

3rd method 

100% Load

(b)

Fig. 12.   The actual and the estimated fuel consumption for each cylinder at (a) 50% load and 143 rpm engine speed and (b) 100% load and 143 rpm engine speed.

Cylinder Number 

-6 

-4 

-2 

0 

2 

4 

6 1st method

50 % Load 

100 % Load 

(a)

0 1 2 3 4 5 6 7 8     0 1 2 3 4 5 6 7 8  

Cylinder Number 

-6 

-4 

-2 

0 

2 

4 

6 

   (   f  u  e   l  c  o  n  s  u  m  p   t   i  o

  n   ) ,   (   %   )

2nd method

50 % Load 

100 % Load 

(b)

0 1 2 3 4 5 6 7 8  

Cylinder Number 

-6 

-4 

-2 

0 

2 

4 

6 3rd method

50 % Load 

100 % Load 

(c)

   (   f  u  e   l  c  o  n  s  u  m  p   t   i  o  n   ) ,

   (   %   )

   (   f  u  e   l  c  o  n  s  u  m  p   t   i  o  n   ) ,   (   %   )

Fig. 13.   Comparison of the dimensionless fuel consumption variation among the cylinders for 50% and 100% of full engine load, by using (a) the 1st diagnosis methodology,

(b) the 2nd diagnosis methodology and (c) the 3rd diagnosis methodology.

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most important for tuning and cylinder power balancing because

fuel rack adjustment is made possible despite load variation during

the measurement.

6.2.4. Peak cylinder pressure

In Fig. 14a and b is given the peak cylinder pressure of the con-

ventional methodology and the corresponding corrected (i.e. esti-

mated with 1st, 2nd or 3rd methodology) values, which have

been derived from the application of all methodologies, for 50%

and 100% of full engine load at 143 rpm engine speed. From

Fig. 14a and b it results that, for both loads examined, the values

of corrected and un-corrected peak firing pressure follow the same

trend for all cylinders. Furthermore, comparing the absolute values

it results that the corrected ones derived from the first methodol-

ogy are almost the same to the ones of the conventional one. The

same conclusion is observed for the third methodology, exceptfor 50% of full load, where the corrected values for cylinders Nos.

3–5 and 7 appear to be slightly higher compared to the conven-

tional one. However, this could also be attributed to improper tun-

ing or to the function of the fuel injection system. On the other

hand it is revealed that, for both load conditions examined and

for all cylinders, the corrected values derived from the second

methodology are slightly lower compared to those of the other

two and the conventional methodology. However, it should be

Cylinder Number 

90 

94 

98 

102 

106 

   P  e  a

   k   P  r  e  s  s  u  r  e   (   b  a  r   )

Conv. method 

1st method 

2nd method 

3rd method 

50% Load

(a)

1 2 3 4 5 6 7 1 2 3 4 5 6 7  

Cylinder Number 

130 

134 

138 

142 

146 

150 

   P  e  a   k   P  r  e  s  s  u  r  e   (   b  a  r   )

Conv. method 

1st method 

2nd method 

3rd method 

100% Load

(b)

Fig. 14.   The actual and the estimated peak firing pressure for each cylinder at (a) 50% load and 143 rpm engine speed and (b) 100% load and 143 rpm engine speed.

Cylinder Number 

-6 

-4

-2 

0 

2 

4

6 

   (  p  e  a   k  p  r  e  s  s  u  r  e   ) ,

   (   %   )

1st method50 % Load 

100 % Load 

(a)

Cylinder Number 

-6 

-4

-2 

0 

2 

4

6 2nd method

50 % Load 

100 % Load 

(b)

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8  

0 1 2 3 4 5 6 7 8  

Cylinder Number 

-6 

-4

-2 

0 

2 

4

6 3rd method

50 % Load 

100 % Load 

(c)

   (  p  e  a   k  p  r  e  s  s  u  r  e   ) ,   (   %   )

   (  p  e  a   k  p  r  e  s  s  u  r  e   ) ,   (   %   )

Fig. 15.   Comparison of the dimensionless peak firing pressure among the cylinders for 50% and 100% of full engine load, by using (a) the 1st diagnosis methodology, (b) the2nd diagnosis methodology and (c) the 3rd diagnosis methodology.

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noted that, for both engine operating points examined, all three

methodologies provide qualitatively similar trends since absolute

differences are quite small.

Applying Eq. (16) for the corrected peak firing pressure are de-rived the graphs shown in Fig. 15a–c, which provide the peak firing

pressure deviation around the mean value for both load points

examined.

Observing Fig. 15a–c it results that for all methodologies cylin-

der peak firing pressure deviation is practically the same for both

load points examined. Moreover, it is noted that the resulting error

when neglecting the effect of load variation is considerably lower

compared to the one of cylinder power. Therefore, as demon-

strated, the observed differences of peak firing pressure between

cylinders are not mostly attributed to load variation but mainly

to differences in tuning or component condition. The previous is

most important for engine tuning because the use of the corrected

cylinder firing pressure eliminates the possibility to exceed maxi-

mum permissible firing pressure.

6.2.5. Cylinder compression condition

The estimation of cylinder compression condition is based on

the evaluation of the measured cylinder compression curve i.e.

from exhaust valve closure up to ignition. To estimate it properly,

account should be taken for the effect of cylinder pressure at ex-

haust valve closure, geometrical compression ratio, heat exchange

and mass leakage due to blow-by. This is achieved by the diagnos-

tic software [28,30]. Having determined all constant values, com-

pression quality is estimated from the comparison of the

effective compression ratio to the reference one (estimated from

the calibration procedure), as follows:

CQ ð%Þ ¼  CReff ;

curCReff ;ref 

100   ð17Þ

where the effective compression ratio (CReff ) is the one definedfrom

the relation:

CReff  ¼  P com

P o

1g

ð18Þ

where ‘‘P com’’ is the peak compression pressure estimated from the

diagnostic technique corresponding to the value if fuel flow was

instantaneously interrupted, ‘‘P o’’ is the cylinder charge pressure

at initiation of compression process, estimated from the diagnosis

procedure and ‘‘g’’ is the polytropic exponent. The reference effec-

tive compression ratio is obtained from the shop test data. In

Fig. 16a and b is given the compression quality derived from theapplication of the conventional cylinder pressure measurement

and the corrected values for each cylinder, for 50% and 100% of full

engine load at 143 rpm engine speed using the three methodolo-

gies. For constant load compression quality should remain almost

constant allowing only for the effect of load on blow-by since en-

gine speed is kept constant.

Observing the corrected values depicted in  Fig. 16a and b it is

concluded that the first two methodologies, based on the estima-

tion or measurement of the instantaneous charge air pressure pro-

vide similar results for both load points examined. On the other

hand the third methodology provides results similar to the ones

Cylinder Number 

80 

84

88 

92 

96 

100 

   C  o  m  p  r

  e  s  s   i  o  n   Q  u  a   l   i   t  y   (   %   )

Conv. method 

1st method 

2nd method 

3rd method 

50% Load

(a)

1 2 3 4 5 6 7 1 2 3 4 5 6 7  

Cylinder Number 

80 

84

88 

92 

96 

100 

   C  o  m  p  r  e  s  s   i  o  n   Q  u  a   l   i   t  y   (   %   )

Conv. method 

1st method 

2nd method 

3rd method 

100% Load

(b)

Fig. 16.   The actual and the estimated compression quality for each cylinder at (a) 50% load and 143 rpm engine speed and (b) 100% load and 143 rpm engine speed.

Cylinder Number 

-0.8 

-0.4 

0.0 

0.4 

0.8 

1.2 

1.6 

2.0 

2.4 

   I  g  n   i   t   i  o  n   A  n  g   l  e   (   d  e  g   C   A   A   T   D   C   )

Conv. method 

1st method 

2nd method 

3rd method 

50% Load

(a)

1 2 3 4 5 6 7 1 2 3 4 5 6 7  

Cylinder Number 

-0.8 

-0.4 

0.0 

0.4 

0.8 

1.2 

1.6 

2.0 

2.4 

   I  g  n   i   t   i  o  n   A  n  g   l  e   (   d  e  g   C   A   A   T   D   C   )

Conv. method 

1st method 

2nd method 

3rd method 

100% Load

(b)

Fig. 17.   The actual and the estimated ignition angle for each cylinder at (a) 50% load and 143 rpm engine speed and (b) 100% load and 143 rpm engine speed.

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of the conventional methodology since it is based on the process-

ing of the actually measured cylinder pressure and no additional

direct correction.

6.2.6. Ignition angle

The ignition angle is defined as the crank angle relative to TDC

position, where combustion initiates. Thus, the proper estimation

of ignition angle depends on the accurate determination of TDC po-sition   [37,39,43]. According to its estimation methodology, TDC

position depends significantly on cylinder charge pressure at com-

pression initiation   [37], which is obviously affected from engine

load. Therefore, the main purpose of the present paragraph is to

make a comparative evaluation of the ignition angle derived from

the three methodologies. In Fig. 17a and b is given the ignition an-

gle for each cylinder estimated from the conventional measure-

ment and the values derived from the three methodologies, for

50% and 100% of full engine load at 143 rpm engine speed. Observ-

ing the results depicted in Fig. 17a and b it is shown that, for both

load points, the results derived from the conventional and the

three methodologies are almost the same. Thus, it is revealed that

load variation, in the magnitude experienced, does not affect the

derived results as far as ignition angle is concerned which is impor-tant for engine tuning.

7. Conclusions

As widely recognized, the cylinder pressure trace is of signifi-

cant importance for diagnosis and performance analysis of heavy

duty DI diesel engines used in marine and power generation appli-

cations. But, cylinder pressure is affected by engine load and so is

the results derived from its processing. For this reason engine load

should be kept constant during cylinder pressure measurement

which is not always possible for field applications, especially mar-

ine. The only method to overcome the problem is simultaneous

cylinder pressure measurement which for a multi-cylinder engine

operating on the field results to high complexity concerning bothmeasurement hardware and cost. For this reason the conventional

measurement methodology is adopted which is based on the use of 

only cylinder pressure sensor and sequential cylinder measure-

ment. But as demonstrated in the present work this method is sub-

 ject to errors if load variation during measurement occurs. In an

effort to provide a solution three alternative methodologies have

been proposed and evaluated herein. The criteria for their develop-

ment have been cost reduction, simplicity and accuracy. The first

two are based on the effect of load on the cylinder charge air pres-

sure corresponding at compression initiation. In the first method

this is calculated from the constants determination procedure

accounting thus for the effect of load variation while in the second

it is monitored using a precise fast response pressure sensor. The

third methodology makes use of two cylinder pressure sensors,one of which is mounted periodically on each cylinder and a sec-

ond one which is permanently mounted on a specific cylinder

called the ‘‘reference’’ cylinder.

The validation of the methodologies is based on their capability

to detect and account for the effect of load variation during mea-

surement. For this purpose, a detailed investigation has been con-

ducted on a large-scale, two-stroke, seven cylinder diesel engine

used for electric power generation at two different load points.

For the evaluation it has been used a well validated diagnostic

technique, properly modified to make use of the two simultaneous

cylinder pressure signals and the instantaneous value of charge air

pressure (2nd methodology).

From the results derived it has been clearly demonstrated that,

in the case of load variation during measurement, the results de-rived from the conventional cylinder pressure measurement, i.e.

brake power output, fuel consumption, peak pressure, compression

quality and ignition angle are misleading and may finally result to

engine mistuning. It is also demonstrated that derived diagnosis

results may lead to improper conclusions as far as cylinder com-

pression condition and tuning (ignition angle, power density) is

concerned. The first methodology which is purely computational

and requires no additional effort and hardware manages to account

for the effect of load variation on individual cylinder loading and

compression condition even though the results obtained are less

accurate compared to the other two methods. The second method-

ology provides quite satisfactory results for performance and com-

pression condition managing to detect and account for load

variation during measurement. But the requirement for an addi-

tional precise fast response pressure to monitor scavenging air

pressure is a serious disadvantage.

Finally the third methodology, based on the use of two cylinder

pressure sensors, is the most advantageous and practically equiva-

lent to simultaneous cylinder pressure measurement. This results

from the fact that it can directly identify engine load variation dur-

ing measurement from the fluctuation of reference cylinder power

output and account for its effect on derived diagnosis results. On

the other hand, as far as ignition angle is concerned, all three meth-

odologies provide equivalent results, in the range of load variation

examined, which are similar to the ones derived from the conven-

tional methodology.

It is most encouraging that the methodologies examined are

capable to adequately correct cylinder power output and fuel con-

sumption contributing to proper engine tuning in the case of load

variation, while the third being more advantageous. However, de-

spite the positive results, further evaluation is required before

deriving general conclusions. This necessity becomes more pro-

nounced in the case of marine engine applications where power

fluctuation is usually higher and the engine rotational speed varies

more frequently.

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