CONSEIL INTERNATIONAL
DES MACHINES A COMBUSTION20th INTERNATIONAL CONGRESS ON COMBUSTION ENGINES
ESTIMATION FOR POWER AND
SPECIFIC FUEL CONSUMPTION FOR A
VESSEL DURING VOYAGE
byZheng Yuan kang Shanghai Shipyard
INTERNATIONAL COUNCIL
ON COMBUSTION ENGINES
LONDON 1993
© CIMAC 1993D16
aESTIMATION FOR POWER AND SPECIFIC
FUEL CONSUMPTION FOR A VESSEL DURING VOYAGE
ZHENG YUANKANG VICE DIRECTOR
SHANGHAI SHIPYARD DIESEL DIVISION
ABSTRACT
This paper is mainly dealt with the power curve and two parameters- engine speed and fuel pump rack position. While explaining the meaning and perpose
of power curve, the author tries to give a method to be used for power estimation of voyaging vessels,
simultaneously to present some formulas and charts for estimation of specific fuel consumption.
In order to keep the accuracy of what has been
estimated,
some countermeasures based
on a diesel
engine's technology in conbination with mathematical treament have been introduced. According to them a ecconomic neviagation condition can easily be picked
up.
INTRODUCTION
In a diesel engine, the speed indicates the frequency of a work being done and the fuel pump rack position (FRP) shows the magnitude of a
work, these two parameters, therefore, are the paramount ones among the others, especially for a propulsional engine of a ship, in which the output feature of the torque is bound to the characteristics of a propeller.
Based on the above two parameters this paper is intended to state the meaning of so-called power curve, the method being used for estimation
and finally develop the equations for calculation. The estimation in a
geometrical mode valid for two main types of fuel pumps, all the given charts and equations which are supported and corrected by measurement results in engine tests are of practical value for obtaining the estimated
power and SFC for a vessel in voyage..
2. CHAR ArTFRISTICS OF A MARINE PROM TT ,SIONAT, ENGINE
2.1 ENGINE OUTPUT FEATURE AT SPA CONOMON
Under normal and steady condition, the operational output for a given
"propusional engine is shown in Fig. 1, where the curve HG is considered as
Ne (%) lOG 90 BO 70 Hex Nexo 30 Fig. 1
Propulsional engine output feature at sea condition,
BIM
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rene
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,B0 nx 85 %90 95 na 100 n 60 2 Iii
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propulsional limit, while conditions H and are to be tested in a prototype
engine required by IACSM50 [Ref'. 1].
In Fig. 1, the torque limitcorresponds to
Ne = c ni (where 2< i < 3, n ç0.9 n0),
and is subject to the characteristics of an engine. Between torque limit and curve 2 are service range with operational limit where the running hours are
restricted. Curve 3 is the propeller charateristics (in this paper refered as
100% propeller law). In a calm sea, the operating output of a main engine with smooth hull shall be at point X between curves 3 and 4. Curve 5 refers to 75% propeller law, only in very rare conditions does this curve apply to
the main engine of a vessel.
2.2 ENGINE CHARACTERISTICS
2.2.1 BEI ATIONSHIP BETWEEN FRP AND FUFL FEED QUANTITY
Generally, an equation showing the relationship between fuel pump rack position (FRP, marked L) and fuel feed quantity (FFQ, marked Q) can be
found for any type of diesel engine. In order to get such an expression, a
mathematical mode should be established in line with the driving scheme.
With resolution of the mode, the simplified relation Q =
(L) is thus
obtained, where L is the simple variable of Q.
In terms of above method, one can find out the equation for a Sulzer
engine with plunger type fuel pump ( P-pump, regulated by slide sleeve)
Q1 k1 - k2 - tg (8 - 8/4 I.) [dm3 / cycle] (1)
where B --- fuel rack full angle, constant
ki, k2 -- geometrical constant coefficients
In some diesel engines, valve type fuel pumps (V-pump, regulated by suction and spill valves) are applied, as commonly found in Sulzer Diesel
(RTA52-84). For V-pump, Q related to L is shown in eqution (2) [Ref. 2]
Q2 = cat + c2sin(c< L - cf.+ cs - [dm3 / cycle] (2)
where initial angle when FRY is in position 0
--- rotation angle perFRP
-- constant for mutual relationship between various
in-jection time (V1T) and turning angle of the eccentric shaft for suction valve
VIT angle
cf, c2, c5, c6 --- geometrical constant
Since the function of WI is to optimize the combustion condition and reduce the fuel consumption thereby, it can vary only in a small range,thus have slight influence on the effective stroke (S) of V-pump, and further on the fuel feed rate. Fig. 2 has presented such a value in an extreme condition,
where So indicates the effective stroke when Vii = 0. If the influence of
VII is negligible, equation (2) is simplified as
=
Q2- = c 4- C2 sin( -%) [dm3 / cycle] Pr .(3k
As known from geometrical mode, the angle in trigonometric funtion is
small both for Eq. (1) and (3) (As a matter of fact, the target of every engine
designer is to keep the linear relation between FRP and fuel rack turning angle, thus the latter should be small), therefore, Eq.(1) can be written
approximately as
Q3' = ki - k2 (8 - 6 /
L) 180/n = k3 - k4
[dm3 / cycle] . (4)where 1(3, kg constants
From the above equation, it is learned that Q' and L are in linear relation. Consequently, Eq (3) may similarly be written as
Qfl2 = ca + c4 L [dm3 / cycle] (5)
where c3 , c4 -- constant factors
10 .99
Fig. 2
The influence for fuel effective stroke related to VII angle
2.2.2 SPEED CHARACTERISTICS
The conventional method for taking the speed characteristics is to keep
FRP unchanged, then to measure the correspondent output torque in
various speed. However, in a marine engine trial, the common way at
present is to keep the constant torque instead of constant FRP to measure
the correspondent parameters in various speed. This method has been
specified in IACSM50 accordingly.
Fig. 3 has given the speed characteristics in various output torque for a RTA48 engine, from which one can learn that there is a AL with reference
to constant Me, thus enabling L to be bigger in higher speed than that in
lower speed. Fig. 3 has also shown the speed characteristics of FFQ, which
is obtained by the measurement with some mathematic treatment.
if
4
[ 0]
L
--Fig. 3
Speed characteristics
for a given SITS 6RTA48
engine(Eng.No.SE2 - 46) where W is the actual fuel feed quantity per cycle
600 50 50 0.88 0.06 U.84 0.82 0.80 100 90 80 Me=9070 Q. L(%) me-..t00% _e90 I... o ea I 1 Me= 100% -41 n 100 n(%) 800 900 1000 1100 1200 nxL 9p
it
load C%1 net., 70 90 100nxL [%/
Fig. 4Power curve for Shanghai Shipyard-Sulzer 7RTA48 Engine (Eng. No. SE2-65)
Alri
r 1iAIP.
. 7,6k.Liii
Pr
Vill,
. When So = LCV=42390Oil
density
15°c i=0.84-8/cm2
FRP(L)=P0E029.50
kJ/kg
mmat
I 85 rib 90 95 100 90 80 Ne 1%3kin
9 10 8 90 Neo. Nea-6 50 5 Q I--3. Fs-twit-nom FOR POWF.R AND SFC
3.1 POWER CURVE AND POWER ESTIMATION
The curve composed by the product of n and L as variable and Ne as
function is called power curve, in which all data are taken from a shop trial according to 100% propeller law. Fig. 4 has shown the power curve for a
given RTA48 engine.
As known From Eq.(4) and Eq.(5), L and Q appear to linear relation,
that is, the magnitude of L indicates that of Q. On the other hand, from the diesel technology of a speed characteristics, under certain speed range, Q and Me are also approximately in linear relation, so it is easy to conclude
that L (in some engines named as load indicator) also indicates the
magnitude of Me, the ratio of the product of L and n to that of Me and it,
therefore, should be a constant. Nevertheless, ina diesel engine,
Ne = v (Men) [kw]
(6)where v --- constant factor
Me--- torque
thus the product of L and n has logical relationship with Ne. And it makes meaningful in a power curve for the product of L and n being variable and Ne being the function, which can be used to estimatepower for a vessel in voyage.
3.2 ESTIMATION FOR POWER
The power obtained in a test bed is taken from the readout of the water
dynomometer and it has a accuracy of +0.5%, therefore, if the actual
service condition at sea conforms to 100% propeller law tested in the shop, the power estimated according to the given power curve has high accuracy.
Should the service condition be away from what has been tested in the
shop, the accuracy of the power estimated has to be analysed.
Supposed the servi,e condition is at point "a" (Fig.1), where engine
speed is at na, FRP at La and output torque at Med, the Med constant curve
and 100% propeller law shall intersect at point "b", at which the engine
speed is nb. As described before (as per Fig.3) there is a L, followed by AL = La - Lb, thus (in Fig.4)
ZINea Wed
N ea [kw] (7)where Ned = w La
w --- slope of j(na La) at point "a"
Y
ea --- estimated power from power curveaccording to the product of nd and La
-From the above observation, it can be inferred that, when point "a" is positioned at the right side of 100% propeller law, N'ed shall be bigger than Ned, vice vesa. Thus it is necessary to correct the power estimated when the
service condition is
off 100% propeller law. Therefore, the power
coefficient p is introduced in order to keep the accuracy of the power
estimated.
Fig.5 has shown curve with reference to variable ci / co, which is
named as factor of propeller's characteristics, the curve is obtained by
statistical method among the measurment data from more than ten sets of
engines.
Fig.5
Corrected coeffient tocurve for power estimation
For instance, if the engine runs at point x at sea the estimated power after correction can be gained
Nex
px N'ex [kw]
(8)where px is obtained by Fig.5
The following example can give clear explanations:
Supposing an engine runs at point x (Fig.1), the power estimated N'ex can be acquired by the product of nx and Lx indicated in Fig.4, as known from the propeller characteristics
N'ex. ex n3x [kw]
since c'x cx
then N'ex
cx n3x [kw]
(9)similarly Nexo co n3x [kw] (10)
where co the factor at 100% propeller law If Eq.(10) is divided by Eq.(9), then
cx / co N'ex / Nexo
According to the value of cx / co, one can gain x in Fig.5, and further obtain Nex according to Eq.(8) for point x.
/3
1.011.00
0.99
= =(10
/33.3 ESTIMATION FOR SW
0:82
tin
047
074
The specific fuel consumption (SFC) ina diesel engine can be given by
go = G / Ne [kg / kwh] (12)
where G [kg / h] --- fuel consumption
6=60 Q9n jYlv [kg/h]
(13)where Q tdm3 / cycle] achieved by Eq. (1), (3)
[kg / dm3 fuel density
j --- number of cylinders
.fl
efficiency of fuel feedif Eq.(13) is subsititutd with Eq.(1) and (3) , the following equation can
be obtained (for P-pump)
gel [Ki - K2 tg (8 - / 4- L) ] / (Ne
nv )
[kg / kW h] (14),where Ki, K2 constant
Ki = 60 +57. kl
K2 = 60. k2
And similarly for V-pump
ge2 = [D1 D2 sin ( cX L -where DI, D2 --- constant
Di = 60
D2 = 60 c2
While Ne
in above two equations can be evaluated in the
way mentioned in 3.1. As for it is subject to different types of pumps andfeed, or to various engines in the
same type with different matching clearance that causes different leakage.To improve the accuracy of whathave been estimated, it is necessary to introduce that is ,every engine is
introduced by its own fly.
f on
(Ne fly) [kg / kw hi
(15) rI 8. III o I I I ! I I 1 H D . 11 r ftj
I -1 .-,
,
I I I t L - 1 I FPI I 80 rsz 90 100 60 70 n (%) Fig. 6Fuel feed efficiency in v cuevefor a given 6RTA52 engine
80 tin 9 100 Me GO,
-
--j SvFig.6 has shown v for a given RTA52 engine. The dots in the
picture are the real measurement data with mathematics treatment.
To achieve the value of(, at point x, at first, Mex( = Nex/(v nx) ) has to be figured out according to Eq.(6). With nx and Mex,
vx can be
obtained (see dotted line in Fig. 7). Corresponing to the same engine shown
in Fig. 7, Fig. 8 presents constant curves of SFC either for measured or
estimated ones for a given 6RTA52 engine, while the latter is evaluated by Eq.(15) with the help of Fig .7. All figures are introduced by percentage.
Fig. 7
Specific fuel consumption feature for a given 6RTA52 engine
If a given diesel have no nv curve for estimation, it can be acquired by resoluting the unknown fly according to Eq. (14) and Eq. (15), where ge, L, n and Ne are known from shop trial according to 100% propeller
law in each condition (conditions B, C, D, E, F), then putting obtained (five in total) into Fig.7. As known from 2.2.2, the speed characteristics of a fuel pump are of decline feature (Fig.4), the declined rate in Fig.7 can be confirmed by speed characteristic test of a prototype engine with conditions
80 95 100 105
G, E and H (Fig.1). To be simplified, all declined lines are supposed in
parallel. With reference to the left picture 'of Fig.7, all at different speed
shall be commuted into that at nominal (100%) speed, which can form Me- Iv curve (as per right chart of fig.7).
3.5 THE CONVERSION OF POWER AND SFC
As mentioned before, all power and SFC estimated are based on the measurement results from the shop trial, however, it is impossible for a
vessel
during voyage to select the same kinds of fuel oil in the same
viscosity, density and low caloricity value (LCV), therefore, a different
FRP will be presented in the same running conidition with different fuel or
with same fuel in different enviroment, thus a deviation will occur when evaluing the power and SFC for a voyaging vessel according to what has
been described.
In order to avoid such a deviation and achieve conversion, at first it is
supposed that the engine is running at point x with nx, Lx, and that the
engine has an equal thermal efficiency and equal fuel feed efficiency when burning differenrt kinds of fuel. The influence of viscosity on the leakage quality of the plunger and nozzles is hence negligible(as a matter of fact, if
an engine runs with heavy fuel oil,it has to be heated to a certain
temperature, therefore no bigger difference at viscocity, for example,therequirement of fuel pump inlet viscosity shall be between 13 and 17 cst for
low speed engine). Therefore, the relationship between shop trial and
voyage for fuel density (1) ), LCV and Q can be expressed as
Qt PoDuo'Qo
[LI / cycle] (16)where Pop Huo, Q0 --- values in shop
Qx --- values in voyage, la is the
density before fuel pump
Substituting above equation with Eq/(4) the following can be' obtained (for V-pump)
Lol = El E2 (17)
where Ez = fa Hu&I (fo Hu()) = constant
El k3 / k4 ( E2 - 1) = constant
Loi converted fuel pump rack position (FRP) for P-pump
Consequently, for V-pump, the conversion can be achieved by
isubtituting k3 with c3 and Li with LI in above equation.
After converting Lx into Lo, one can put Lo instead of Lx into various equations in 3.2 and 3.3 for estimation of power and SFC.
10
et.
C,
a, IIua,
41 000
40000
39000
0.84
0.88
0.92
0.96
1.00
fuel density at 15.600
Ckg/dm33 Fig. 8Fuel LCV related to density and sulphur content
...11.411.1. MIN111%M:
1.11116%..11
%rniii
Ill
IML
aim
rareMEEM
%
4
I
1
a,11%-;111111%16111,_111MIIIIIIII
. 1.71.111"RR%
Furthermore, since the plunger and sleeve in a fuel pump are the worn-off parts,liv will be reduced after long terms of running Before proceeding estimation for power and SFC, a correction is to be carried out.The reason
for 1, reduction is the high leakage in fuel pumps and nozzles, thus
enabling FRP to be bigger than before as reference to the same condition. Since the leakage quantity is measurable both for shop trial and voyage, the
increment is obtainable
QL= QLv -41,5 [ kg / cycle] (18)
where QLv --- leakage quality in sea with fuel plunger
wron-off seriously.
QLs leakage quality in shop trial
Subseqently, the increment 6 Li. can be figured out by Eq.(19)
A LL1= (A QL1 - k3) / kg (19)
where LI QL1 is obtained by Eq.(18)
The calibration method caused by high leakage then is given by
L'0=Lx- ALL (20)
where L'o calibrated FR?
Noted Lx has to be substituted by L'o when calculating Lo of Eq.(17).
Apart from FRP conversion, one thing has to be pointed out that the
LCV is usually not indicated in the oil analysis supplied by oil company,
the density and sulphur content of a oil will be given instead, by which
LCV can be judged. And Fig.8 [Ref.3] has shown such a relation.
LCV
ricJ/kg1
42000
12
4. ESTIMATION FOR BRAKE POWER AND BRAKE SPECIFIC FUEL CONSUMPTION (BSFC)
4.1 ESTIMATION FOR BRAKE. POWER
Since the condition with reference to shop and sea is not the same, one
might pick out the difference in order to achieve the real shaft power
estimated.
As for the difference, a vessel has a propulsional force (or thrust force)
and equipped with an exhaust gas boiler, and in some cases a vibration detuner (Geislinger) are installed, which might not be fitted during shop
trial. The diefference can influence the load condition.
Though the power curve is originated from a shop trial, and the power in the curve is taken from a water brake, it is brake ( or shaft) power only in the shop. The power estimated according to what has been explained for a vessel in the sea is so-called overall power. If interested in the brake power,
one has to deduct the power consumed at thrust bearing or vibration
detuner if applicable and what ever consumes power which is not equipped
in the shop.
The frictional power (NO consumed at thrust bearing is given by
Nf=
n R Ft/ 9547 [kw!
(21)where 4,1-[ - ] --- frictional factor
R [m] --- equivalent radius for force acting at thrust bearing Ft [Newton] --- the propulsional force
The propulsional force Ft is obtained from measurement or from the
chart of a speed-propulsional force curve supplied by the designing
document of a propeller.
The power dissipated approximately at vibration detuner (NG) can be
found in the General Technical Data (GTE)) submitted by the engine maker, for instance, the values for RTA engines can be ranged from 20kw (small bore) to 80kw (big bore). [Ref.4]
It should be noted that only when there is difference between shop and
sea condition, is
it necessary to consider deduction. For an example,
should a shop trial be similated a back pressure of exhaust boiler the
deduction is not applicable. Another example is the
1st or 2nd order
balancer, though it consumes power, it is an engine built-in device and it is not necessary to consider it.
Therefore, the brake power Nbex in condition x is named
where Nex --- given by Eq.(8) as estimated power
NG power consumed at vibration detuner
Np-ro power for power taken-off plant
NE --- power that consumed for increment of back pressure for exhaust
remark s to be considered only if applicable
4.2 ESTIMATION FOR BRAKE SPECIFIC FUEL CONSUMPTION(BSFC)
From above analysis, it is understood that ge 1 and ge2 in Eq. (14), (15)
are not the brake specific fuel consumption. If interested in BSFC at point x,
one can achieve it by following equation
gbex = Nex / Nbex gex [kg / kw h] (23)
5. COMPUTERIZED ESTIMATION FOR BRAKE POWER AND BSFC
The estimation method expressed in Article 3 is based on the actual
measurement of speed and FR?. To make the estimation meaningful, one
has to keep the same effective stroke of fuel pump with the original one
when regulated, that is, at the same FR?, the volume of fuel feed in sea
service should be the same with that in shop trial. On the other hand, n and L measured may be away from the real one. In case only one measurment being taken, for instance, the deviation of power estimated in full load will be +1.25% if L deviated 0.1 scale, and +1% deviation occurs at SEC for a
RTA engine. In order to decrease such a deviation caused
by visual observation, the average value is taken for estimation, therefore, severalmeasurements with intervals shall be carried out.
Applying a microcomputer can give lots of benefit for estimation, and avoid unexpected deviation.
Before calculation, one has to input the curves for plotting and constants
for estimation. The pick up signal of dynamic speed and FRP is to
beconnected with computer as input data.
The block program is shown on Fig. 9, from which one can see that the input of dynamic parameters is designed as a cycling system (as per block B) only the average values are taken for estimation. And if the estimated
data are not in the range as expected, the computer will automatically
feedback to bridge control.
The block program is a estimation process that gives better
under-standing for what has be expressed by this paper as well as a good
I pick up ni,Li nsi5_ S(1+ )nst
(1-Wst
ii-(144)1,st nt -nt+ni, Lt=Lti-L nent /it Lst=Lt / i finish pickup. output: i, nx, LoL_
ñ=n5tL0Lt I
11.Nbex = Eq.(22)Brake power 2.gbe = Eq.(23)
and BSEC 3.N ex =Nbex, gex =gbex
rom block A or bridg,e
i=0,nt=0,LtIi
comparision
2.
Fig. 9
Block programme for estimation power and SEC,
-<411)111111110P7 N 1.plotting: geo=i(nx,Nex) 2.geol=(14)geo 3.ge02=(1+b)ge0
Lo=a1.0
I. ordering: n=n, L=Lo, Ne=Nex, G=Gx,ge=gex2. print n, L , Net ge, G, geo
change ni _go to B
1. chart: powercurve, 13,14c-urve3FC feature (gee curve
2. geometric constant, figure out E2, EL 3. fuel and pump leakage feature
4. setting expected speed (mit), FRP (Lst), deviation ( $ )
....
A
Definituni
-and input
i
IF -
engine data input(ni,L) and treatment,detail as per below cornerBA 1.
QL 4LL, Uo
conversion 1
2. L0=k+E2 L'o
1. plotting: N'ex = j(nx Le), Px =i(cx
k0), rivxlnx. Mex)
estiamtion 2. Nex =(3x Nex gex = Eq.(14) or (15)
N
tbridge control 1 lend I
1 F output 14 end I i=i+1, 7) conversion
CONCLUSION
Every engine can obtain its own power curve which is composed by the
measured revolution, FR!' and power in a shop trial according to 100%
propeller law. For a vessel with unfixed pitch propeller can be done
according to load characteristic. Based on measured n and L during
voyage, one can obtain the estimated power and SFC. To keep the
estimated values as exactly as possible, one has to convert the measured L with some equtions.
The estimation of power and SFC (or brake power and BSFC) given by this paper is of rather high accuracy, therefore are reliable for a vessel to pick out the ecconomic neviagation condition. Since the brake power and
BSFC can be predicted by equations and charts, once considering the
relation, between shaft power and ship speed, the optimized running
condition under navigation speed shall easily be achieved. REFERENCE
Internal Association of Classification Society, M50.3,
IACS Req.. 1986
Zheng Yuankang, "The Calculation for Fuel Volume Feed Quantity for
RTA Engine with VII Device" Science & Technology for SHS, Aug.,
1990. pg.21-24
Sulzer. "Average Heat Values of Fuel Oils Related to Specific Gravity and Sulphur Content" March 1971, 0722 / 710310, Sulzer Diesel
New Sulzer Diesel, "General Technical Data for RTA52-84 Marine
Diesel Engines" issued 1988/1989, A3-5 6..
7, [11
