Description of a heat transfer model suitable to calculate transient processes of turbocharged...

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Applied Thermal Engineering 26 (2006) 66–76

Description of a heat transfer model suitableto calculate transient processes of turbocharged diesel engines

with one-dimensional gas-dynamic codes

J. Galindo a, J.M. Lujan a, J.R. Serrano a,*, V. Dolz a, S. Guilain b

a CMT-Motores Termicos, Universidad Politecnica de Valencia, Camino de Vera, s/n. 46022 Valencia, Spainb Renault s.a.s., 1 allee Cornuel, 91510 Lardy, France

Received 12 October 2003; accepted 18 April 2005

Available online 23 June 2005

Abstract

This paper describes a heat transfer model to be implemented in a global engine 1-D gas-dynamic code to calculate reciprocating

internal combustion engine performance in steady and transient operations. A trade off between simplicity and accuracy has been

looked for, in order to fit with the stated objective. To validate the model, the temperature of the exhaust manifold wall in a high-

speed direct injection (HSDI) turbocharged diesel engine has been measured during a full load transient. In addition, an indirect

assessment of the exhaust gas temperature during this transient process has been carried out. The results show good agreement

between the measured and modelled data with good accuracy to predict the engine performance.

A dual-walled air gap exhaust manifold has been tested in order to quantify the potential of exhaust gas thermal energy saving on

engine transient performance. The experimental results together with the heat transfer model have been used to analyse the influence

of thermal energy saving on dynamic performance during the load transient of an HSDI turbocharged diesel engine.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Full load transient; Turbocharged diesel engine; Heat transfer modelling; Exhaust systems; Air gap insulation

1. Introduction

One of the main handicaps of high-speed direct injec-

tion (HSDI) turbocharged diesel engines is their poor

dynamic response compared to spark ignition engines.

With the main objective being to improve their dynamic

response during load transients, while maintaining the

levels of pollutant emissions under the limits of Euro 4and 5 [1], the correct prediction of the transient evolu-

tion of turbocharged diesel engines is of major interest

in the automotive industry nowadays. Moreover, new

engine designs are suffering a downsizing evolution

1359-4311/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.applthermaleng.2005.04.010

* Corresponding author. Tel.: +34 96 387 96 57; fax: +34 96 387 76

59.

E-mail address: [email protected] (J.R. Serrano).

resulting in smaller turbochargers which are often less

efficient. Also, there is an increasing interest in homoge-

neous charge compression ignition (HCCI) techniques

that yield to lean combustion ratios and therefore lower

exhaust gas temperatures with high quantities of exhaust

gas recirculation.

The causes of the lag in the transient operation of a

turbocharged engine can be classified into three groups:mechanical, fluid-dynamic and thermal phenomena [2].

Therefore, a key point in the prediction of thermal en-

gine performance is the heat transfer calculation [3–7].

This is especially true in turbocharged engines, where

the correct evaluation of the energy at the turbine inlet

determines the engine behaviour both in steady and

transient operations [2,8]. This work presents a heat

transfer model that implemented in a 1-D gas-dynamic

mailto:[email protected]

Nomenclature

Cp gas specific heat

Cs solid specific heatd duct diameter

dc cylinder diameter

h heat transfer coefficient

hi inside heat transfer coefficient

hi-2 inside plus wall 1–2 heat transfer coefficient

hi-3 inside plus wall 1–2–3 heat transfer coefficient

ho outside heat transfer coefficient

ho-2 outside plus wall 2–3 heat transfer coefficientho-1 outside plus wall 1–2–3 heat transfer coeffi-

cient

hor outside radiation heat transfer coefficient

HSDI high-speed direct injection

K thermal conductivity

L coolant tube length

Ll liner thickness

Lb bowl depthM0 torque at maximum engine power

N engine speed

Nu Nusselt number

Pr Prandtl number

Re Reynolds number

S stroketc engine cycle duration

Ti fluid temperature inside ducts and cylinders

To fluid temperature outside ducts and cylinders

Tw1 wall temperature at the inner calculation

node

Tw2 wall temperature at the central calculation

node

Tw3 wall temperature at the outer calculationnode

u fluid velocity

X distance to the exhaust valve

Z number of cylinders

a diffusivity coefficient defined as a = K/(q Æ CS)

Fo Fourier number defined as Fo = a Æ Dt/(Dx)2

Bi Biot number defined as Bi = h Æ Dx/kl fluid viscositylf fluid viscosity at the fluid temperature

lw fluid viscosity at the wall temperature

q density

J. Galindo et al. / Applied Thermal Engineering 26 (2006) 66–76 67

code [7,8] enables to calculate the air management pro-

cess in turbocharged engines with enough accuracy to

predict diesel engines transient evolutions.

The heat transfer model uses the meshing of the en-

gine pipes performed by the 1-D gas-dynamic code to

define a discrete spatial distribution of temperature in

the duct walls. From the point of view of heat transfer

coefficient calculation the engine is divided into four dif-ferent zones that show different calculation hypothesis:

the intake line, the engine cylinders, the exhaust ports

and the exhaust line. With respect to the temperature

of the engine walls, the heat transfer sub-model has been

programmed to deal with either constant time or vari-

able, considering the thermal inertia of the walls. An

additional possibility has also been regarded for steady

operation calculations in which the temperature evolu-tion is calculated without thermal inertia but variable

with time. The thermal inertia is defined as the inverse

of the diffusivity [8]. The model description and valida-

tion is presented in Section 2.

Finally, the heat transfer model has been used to

analyse the potential of thermal energy saving during

constant speed load transient tests of a HSDI turbo-

charged diesel engine. This study is supported withexperimental tests carried out in a dynamic dynamome-

ter which is able to provide variable resistant torque,

fast enough to hold constant engine speed during the

load transients. The results obtained are shown in Sec-

tion 3 of this work.

2. Heat transfer model

The main inputs for the heat transfer model are the

wall materials and the coolant physical properties that

have any influence on the heat transfer process such

as: density, specific heat, thickness, thermal conductivity

and viscosity. The four different areas for the heat trans-

fer coefficient calculation are the following:Intake line. The Dittus Boelter and McAdams [9,10]

correlation has been used to calculate the internal heat

transfer coefficient within the intake ducts. In spite of

this correlation being developed and validated for non-

pulsating conditions, it has been successfully used by

other authors in engine modelling with 1-D gas-dynamic

codes [11,12]. The Hilpert correlation [13] is used to cal-

culate the heat transfer coefficient at the outside of theintake ducts, which is generally accepted in the case of

horizontal pipes with perpendicular flow [10]. Neverthe-

less, the influence of the intake line thermal model in en-

gine performance is very low compared with the cylinder

and exhaust line heat transfer models, due to the low

temperature of the intake air.

Engine cylinders. Three different walls are considered

for the calculation of heat transfer within the combus-tion chamber: the head cylinder, the liner and the piston

wall. These three walls have different temperature values

but a common internal heat transfer coefficient is con-

sidered and calculated from the Woschni equation

[14]. Some modifications to the Woschni coefficients

68 J. Galindo et al. / Applied Thermal Engineering 26 (2006) 66–76

are proposed, in order to adapt them to every particular

engine. Details about how to fit the coefficients can be

found in [15,16]. Outside the cylinder the equation pro-

posed by Cipolla [17] is used, due to the short length of

the coolant tubes and the water is working in forcer con-

vection conditions. Nevertheless, the nucleate boilingpart of the correlation proposed by Cipolla has not been

used to simplify the model because it does not greatly al-

ter total heat transferred energy [3]. For lack, a specific

coolant flow of 0.8 l/min per kW of maximum engine

power is used to relate Reynolds number of the coolant

fluid with engine parameters. This is an average value

found by the authors after testing some cooling systems

of HSDI diesel engines. By rearranging Cipolla�s corre-lation [17] the external heat transfer coefficient can be

calculated as a function of Z, L, N and M0 as shown

in (1):

ho ¼ 0.063þ 0.733 � Z � LN �M0

� �0.25 !

N �M0

Z

� �0.8L�1.8

ð1Þwhere the characteristic length L is L = 1.1 · dc in the

cylinder head cooling ducts and L = S in the liner cool-

ing ducts. For simplicity, the same equation is employedfor the heat transfer coefficient in the cooling side of the

piston wall. In this case, the equivalent surface of heat

transfer between the gas and the water is supposed to

be equal to the piston surface in the gas side, and the

conductivity thickness is the distance between the cen-

tral point of the piston head and the waterside of the

liner through the oil-scraper piston ring (Fig. 1). Sup-

posing a squared piston with height equal to the diame-ter and the oil-scraper ring is placed at a quarter of the

diameter from the top of the piston (Fig. 1). Then the

model does not take into account the cooling effect of

the lubricant oil in the piston wall temperature.

Exhaust ports. In the exhaust ports the difference of

temperature between the gas and walls is very high,

therefore the Sieder–Tate correlation [18] is used but

with some modifications (Eq. (2)) based on engine testing

Fig. 1. Piston wall thickness scheme.

experience [19]. Eq. (2) has been deeply validated in other

works [20–24] and the modifications take into account

the shape, length and other issues of the port geometry

that influence the flow turbulence for a given engine.

Nu ¼ 0.10 � Re0.8 � Pr0.33 lf

lw

� �0.14ð2Þ

Rearranging Eq. (2), hi can be calculated as shown in

(3):

hi ¼ 6.8� 10�3q0.8u0.8T 0.3

i Cp

d0.2ðT i þ 110.4Þ0.2lf

lw

� �0.14ð3Þ

The correlations proposed by Sutherland [10] have been

used to obtain l. Ti and u are obtained from the 1-D

gas-dynamic model in an iterative procedure and are up-

dated at every time step in every node of the mesh. Onthe outside surface of the exhaust port wall, Cipolla�scorrelation [17,20] is used in the same way as for the cyl-

inder head walls.

Exhaust line. Finally, within the exhaust line the heat

transfer is highly increased by the turbulence generated

at the cylinders discharge (4). This effect decays with

time after the discharge and with the distance to the ex-

haust valve (5). The correlation used here is that pro-posed by Reyes in [25] where a Nusselt versus

Reynolds correlation is affected by the turbulence gener-

ated and the turbulence effect is reduced with time and

with the exhaust valve distance.

Nu ¼ 1.6 � Re0.4n � Cpos ð4Þ

Cpos ¼ 1þ 3 � e� 14Xdð Þ ð5Þ

where Ren is the Reynolds number calculated with a spe-

cial flow velocity ð�unÞ obtained as an weighted averageof the velocity of previous calculation instants [26] and

Cpos is the turbulence coefficient that accounts for the

distance between the duct and the exhaust valve (X).

Rearranging Eq. (4), hi can be calculated as shown in

(6). These correlations have been deeply validated in

previous works [20–24]

hi ¼ 7.2094� 10�4q0.4�u0.4n CpT 0.9

i

d0.6ðT i þ 110.4Þ0.6Cpos ð6Þ

The correlation for the outside heat transfer coefficient isobtained by adding the Hilpert heat transfer coefficient

[13] to the radiation heat transfer coefficient (7) where

r = 5.67 · 10�8 W/(m2 K4) and e = 0.5.

hor ¼e � r � ðT 4

w3 � T 4oÞ

T w3 � T o

ð7Þ

2.1. Wall temperature calculation

An important feature of the heat transfer model is the

calculation of the wall temperatures, which are mainly

Fig. 2. Scheme of wall mesh for temperature calculation with thermal inertia model (left) and scheme of thermal resistance for wall temperature

calculation without thermal inertia model (right).


ducts in the 1-D codes. Only radial heat transfer is con-

sidered since the axial flow is limited because of thesmall wall thickness. The model offers two possibilities

for the temperature calculation either considering or

not the thermal inertia of the walls. In both cases, the

general differential equation of conductive heat transfer

(8) is solved by an explicit finite-differences method of

three nodes (left part of Fig. 2). This method means

an improvement with respect to previous works [20]

where only one node was used to calculate thermal iner-tia. This is because the external wall temperatures are

calculated with more consideration to the inertia effects,

which is especially important if the aim is to carry out

studies on the wall properties such as wall thickness or

composition.

1

aoT w

ot¼ o2T w

ox2ð8Þ

2.1.1. Calculation with thermal inertia

The method is based on the application of Eq. (8) to a

wall element (left part of Fig. 2) with the initial condi-

tions defined in Eq. (9):

T w ¼ T w0; t ¼ 0 ð9ÞTo obtain the finite-difference form of Eq. (8), the cen-tral difference approximations to the spatial derivatives

and the forward difference to the time derivative are

used [27]. Temperatures are evaluated at the previous

(p) time, using the explicit method of the solution. Eval-

uating terms on the right-hand side of the equation at p

and substituting into Eq. (8), the explicit form of the

finite-difference equation for the interior node n is:

T pþ1w2 ¼ FoðT p

w3 þ T pw1Þ þ ð1–2FoÞT p

w2 ð10Þwhere Fo is a finite-difference form of the Fourier num-

ber. The stability criterion for a one-dimensional inte-

rior node is Fo 6 0.5. Assuming convection transfer

from an adjoining fluid, inner and outer tube, and nogeneration, it follows that:

T pþ1w1 ¼ 2FoðT p

w2 þ Bii � T iÞ þ ð1–2Fo� 2Bii � FoÞT pw1

ð11ÞT pþ1w3 ¼ 2FoðT p

w2 þ Bio � T oÞ þ ð1–2Fo� 2Bio � FoÞT pw3

ð12Þ

where Bi is the finite-difference form of the Biot number

and the stability criterion is Fo(1 + Bi) 6 0.5.This heat transfer model enables the calculation of

engine thermal transients implemented in a 1-D gas-

dynamic model, but it can be too slow to calculate

engine steady conditions if the initial value is far from

the final one because of thermal inertia. Therefore, to

accelerate the convergence to the final wall temperature,

other strategies may be established.

2.1.2. Strategy for fast convergence

The solution to speed up the convergence in engine

steady calculations, where the wall temperatures are

unknown is to impose that the cycle-averaged heat flow

is steady. Therefore, the wall temperature at every

node is updated once per cycle from the energy balance

during the last cycle. The cycle average is calculated

considering that there is transient fluid dynamics butsteady heat flow and using the thermal resistance

scheme shown in the right part of Fig. 2. Since the heat

flow is constant during the whole engine cycle it is pos-

sible to write the following equation at the three nodes

[26].

0 ¼ ho-xðT o � T wxÞ þ hi-xðT i � T wxÞ ð13Þ

where ‘‘x’’ is the node number and:

hi-1 ¼ hi; hi-2 ¼1

hiþ e2K

� ��1

; hi-3 ¼1

hiþ eK

� ��1

ho-3 ¼ ho; ho-2 ¼1

hoþ e2K

� ��1

; ho-1 ¼1

hoþ eK

� ��1

ð14Þ

Integrating Eq. (13) in a complete engine cycle (tc) with

ho constant and assuming small variations with Tw1, Tw2

and Tw3, Eq. (15) is obtained:Z tc

0

hi-xðtÞT iðtÞ dt � T wx

Z tc

0

hi-xðtÞ dt

¼ ho-xT wxtc � ho-xT otc ð15Þ

Rearranging and simplifying Eq. (15), Tw1, Tw2 and Tw3

can be calculated as a function of hi-2, hi-3, ho-2, ho-1, hi,

Ti, ho, To and tc as shown in (16):


T w3ðd;jÞ ¼tchoT o þ

Pnk¼1hi-3ðd;j;kÞT iðd;j;kÞDtðkÞ

tcho þPn

k¼1hi-3ðd;j;kÞDtðkÞ;

T w2ðd;jÞ ¼tcho-2T o þ

Pnk¼1hi-2ðd;j;kÞT iðd;j;kÞDtðkÞ

tcho-2 þPn

k¼1hi-2ðd;j;kÞDtðkÞ;

T w1ðd;jÞ ¼tcho-1T o þ

Pnk¼1hiðd;j;kÞT iðd;j;kÞDtðkÞ

tcho-1 þPn

k¼1hiðd;j;kÞDtðkÞð16Þ

where d and j subscripts represent the duct number and

node number and k represents the calculation time step

used to integrate the heat flow during the whole engine

cycle.

2.1.3. Discussion about the model sensibility

A calculation of wall temperature evolution in a sin-

gle cylinder engine (at full load, 2000 rpm steady opera-

tion) will be used to discuss the heat transfer model

sensitivity computing with thermal inertia or coupling

both with and without thermal inertia. The evolution be-

gins from an initial guessed temperature up to the final

value that depends on engine operative conditions. Thecycle-averaged results for the cylinder wall temperatures

are shown in the left part of Fig. 3. The dashed lines cor-

respond to 2000 cycles (120 s) computed with thermal

inertia and without the strategy to speed up the conver-

gence. The x-axis to read these curves is that plotted

above. In the same graph, the calculation of the wall

temperature evolution, with the strategy for fast conver-

gence is plotted in solid lines with squares. These curveshave to be read with the x-axis below, so that the conver-

gence is attained only in nine engine cycles (0.54 s). It is

important to stress that the final temperature value is the

same with and without the strategy for fast convergence.

Right part of Fig. 3 shows details of the temperature

evolution during one engine cycle. From the graph it can

be seen that the gas temperature has important varia-

tions (it has to be read in the left y-axis) whilst the wall

Fig. 3. Average (left) and instantaneous (right) values of wall t

temperature (right y-axis) is almost constant during the

cycle due to thermal inertia. However, at the end of the

cycle, the wall temperature is updated according with

the strategy to speed up the convergence shown in Sec-

tion 2.1.2.

These results show that the strategy defined to accel-erate the convergence of wall temperatures for engine

steady calculations yields the correct final value with a

reduced time compared to the real evolution from the

guessed to the final value. Also it can be concluded that

once the wall temperature is updated at the beginning of

every cycle, wall temperature remains almost constant

and therefore it is not necessary to calculate the wall

temperature at every time step with thermal inertia(Eqs. (11) and (12)). Instead the updated wall tempera-

ture value may be maintained till the next cycle.

In-cylinder gas temperature is quite difficult to mea-

sure accurately, even wall temperatures are, because of

the geometrical complexity of the engine block. There-

fore, to check the robustness of the model hypothesis,

an additional sensitivity study with the piston wall

(Fig. 1) thickness parameter has been done. This is themost uncertain parameter to input the cylinder heat

transfer model. In this study, the piston wall thickness

has been increased and decreased 40% to observe the re-

sults on engine performance. In Fig. 4, it is possible to

observe negligible effects (0.1%) in calculated turbo-

charger speed and small differences (1%) in piston wall

temperatures. Turbocharger speed reflects the inappre-

ciable effect in turbocharger energy, the piston wall tem-perature being the most affected variable.

2.2. Model validation

The engine ducts thermophysical properties (density,

specific heat, thermal conductivity . . .) have been

emperatures calculated with and without thermal inertia.

Fig. 4. Sensitivity study of the load transient at 1500 rpm.


obtained from the literature [28,29] and from the engine

manufacturer. The experiment used to validate the heat

transfer model consists of a full load transient test

[2,23,30] at 1500 rpm of constant engine speed, with a

turbocharged HSDI diesel engine of four in-line cylin-ders and 1900 cm3 of total swept volume [8]. Some val-

idation with results from the engine steady state

operation can be found in [20]. The calculated load tran-

sient test results have been compared with the measured

data. Nevertheless, it is impossible to compare the gas

temperature results provided by the model with accurate

measurements. This is because the thermocouples that

can resist engine exhaust gas temperature do not provideenough dynamic response during the few seconds that

the load transient takes (Fig. 5). This is especially true

in pulsating flow environments such as the exhaust

manifold of four stroke cycle engines.

To compare variables that are related with the energy

balance in the turbocharger is a useful but indirect way

of validating the heat transfer model. The energy bal-

ance in the turbocharger shaft is evidenced by its accel-eration caused by the excess of mechanical power in the

system [21]. This acceleration torque is provided by the

positive difference between the turbine and compressor

effective power [2] and the turbine effective power is a

direct function of the exhaust gas temperature.

Other important variables that influence the turbine

power are: air mass flow, turbine inlet pressure and tur-

bocharger speed. They are shown in Fig. 5 where a goodagreement between the measured and modelled vari-

ables can be observed. Since the exhaust gas tempera-

ture is quite linear with the air to fuel ratio, the

injected fuel (Fig. 5) is also a key variable in the indirect

model validation procedure. In summary, if all the vari-

ables related to the turbocharger energy balance but the

exhaust gas temperature have been well modeled, it is

possible to state that the exhaust gas temperature has

been also well calculated to fit the turbocharger ener-getic balance [21]. It should be pointed out that the final

objective of the heat transfer model is to calculate prop-

erly turbocharged engine transients.

In spite of this, with a K-type thermocouple welded to

the external surface of the duct walls [20] it has been pos-

sible to measure the outer wall temperature evolution of

the turbine inlet duct, which is the hottest point in the

exhaust manifold. The comparison with calculated datais plotted in the bottom right part of Fig. 5. The wall

temperature measurement not only provides a base of

comparison for the heat transfer model, but reinforces

the indirect assessment procedure of the exhaust gas

temperature calculation.

3. Potential of thermal energy saving in transientperformance

It has been concluded in previous works [8] that be-

sides the thermal insulation it is necessary to reduce

thermal inertia to avoid the loss of thermal energy from

the exhaust gas at the exhaust manifold during an engine

load transient. An exhaust manifold with low thermal

inertia material in its internal walls (1 mm of iron) andexternal insulation by air gap was manufactured, tested

and modelled. After that, the results were compared

with another manifold with the same layout but without

any insulation and with 13 times higher thermal inertia

Fig. 5. Measured versus modelled load transient at 1500 rpm.


in its walls (2 mm of stainless steel). Details about the

design procedure can be found in [8], schemes and pic-

tures of the low thermal inertia manifold layout ob-

served at the top part of Fig. 6. Load transient tests

with these two manifolds were performed at a constant

engine speed of 1500 rpm. The results obtained havebeen plotted versus time in the bottom part of Fig. 6.

The stainless steel manifold results are labelled as

‘‘Higher thermal inertia’’ and those with the low thermal

inertia plus air gap insulation manifold are labelled as

‘‘Lower thermal inertia’’. Bottom part of Fig. 6 shows

that the boost pressure, air mass flow and turbine inlet

pressure have faster evolution with the insulated dual-

walled manifold. Nevertheless, the improvement on en-

gine dynamic performance is not so important as it

could be expected from the high increment of air mass

flow. The delivered energy during the first two seconds

has been only increased 1.7% with respect to ‘‘Higher

thermal inertia’’ configuration [8].Following this, the explanations for the described

experiment are obtained with the model help. The air

velocity within the gap has been set at 0.1 m/s to simu-

late its insulation effect. This velocity value has been ob-

tained from the Raithby and Hollands expressions [31]

with the hypothesis of natural convection in the annular

space between concentric horizontal cylinders. It means

Fig. 6. (Top) Exhaust manifold scheme with dual-walled air gap and two steps of the manufacturing procedure. (Bottom) Comparison of load

transient tests at 1500 rpm, with and without dual-walled air gap manifold.


an important reduction of the constant factor from the

Hilpert correlation [13], which was obtained assuming

an external airflow velocity of 1 m/s, quite usual for

engine test cells [32].

In addition to the two exhaust manifolds; a third

calculation has been performed expecting for further

saving of thermal energy also in the exhaust ports.The interest in calculating this case is justified by

previous analyses of thermal power losses along the

exhaust line [29,19,8] where it was stated that there

is an important amount of energy lost in the exhaust

ports due to the high convective heat transfer coeffi-

cient and the high cooling power that protects the cylin-

der head. The study is more interesting when it is

considered that nowadays high power HSDI diesel en-

gines have quite long ports, between 100 mm and

200 mm length.

In the case of the studied engine, with exhaust ports

of 100 mm that have a 90� bend in the middle of their

length, the study considers the possibility of insulatingonly the most external straight part of the ports that

connects with the exhaust manifold. The modelled insu-

lation technique is also based on a dual-walled duct. The

idea is to insert a duct of iron (1 mm thickness) inside

the straight part of the exhaust ports in such a way that

a gap remains between the duct and the port wall. This

Fig. 7. Scheme of the port with insertion for thermal insulation.

Fig. 8. Modelled results with different exhaus


inserted duct is fixed to the zone between the port outlet

and the exhaust manifold inlet (Fig. 7).

The calculated results are compared amongst them-

selves in Fig. 8, where the stainless steel manifold is re-

ferred as ‘‘Higher thermal inertia’’, the manifold with

low thermal inertia and air gap insulation as ‘‘Modified

manifold ’’ and the results that also include insulated

ports are labelled as ‘‘Modified manifold & ports’’.

Fig. 8 shows several cycles calculated at constant low

load conditions to stabilise engine variables like turbo-

charger speed and especially engine wall temperatures

before the load transient evolution begins. This load is

determined by the minimum fuel injected to keep the en-

gine running at the desired speed (1500 rpm) but with

t manifold configurations at 1500 rpm.


0 bmep. During the stabilization phase the model with-

out thermal inertia is activated, Eq. (16), and a wall tem-

perature consistent with the engine operative conditions

is calculated in a reduced number of cycles. When the

convergence is completed Eq. (16) is deactivated, mak-

ing it possible to calculate the actual evolution of enginewall temperatures.

The main conclusions obtained from the results plot-

ted in Fig. 8 are the following:

• The higher turbine inlet gas temperature always cor-

responds to the configuration with insulated ports,

followed by the configuration with only the exhaust

manifold insulated. The ranking of the turbine inletgas temperature is partially justified by the turbine

inlet wall temperature ranking, also represented in

Fig. 8. It is also necessary to consider the important

effect of the insulation and inertia reduction on the

exhaust ports. This causes an increase in the turbine

inlet gas temperature with respect to the insulated

exhaust manifold, which in turn is also important

with respect to the high thermal inertia and non-insu-lated exhaust manifold.

• Consequently, the turbine work (Fig. 8) is increased

in the case of the insulated configurations according

to the ranking exposed in the previous point. As a

result of the turbine work increasing, the boost pres-

sure and the air mass flow are also increased. It is

interesting to note that the increase in air mass flow

causes additional increments of turbine work. There-fore there is a re-fed process between these two vari-

ables that benefit the configuration with initially

higher turbine work. This can be observed in the pro-

gressive increment of the difference between the

curves. The progressive separation trend is observed

not only in all the calculated variables from Fig. 8,

but also in the measured variables represented in

Fig. 6.• Despite of the relevant increments of boost pressure

and the corresponding air mass flow rate, the injected

fuel is not significantly increased as it is shown in Fig.

8. The reason is that a sufficiently relevant increment

in wall temperatures takes place too late in the tran-

sient process. This is because the reduction in thermal

efficiency and the insulation needs some time to

become really effective. This effect can be observedin the plot of the wall temperature at the turbine inlet,

where only differences of about 50 �C are obtained

during the first 2 s of the transient evolution. Taking

into account that the temperature difference between

the gas and the wall is about 300 �C, they are not

strong enough to increase boost pressure in an effec-

tive way. In the case of the experimental study in Fig.

6, between 0.5 and 2 s the fuel injected is a function ofthe air mass flow, but in this period the air mass flow

increment is not so important as it is from second 2

onwards. Therefore, the delay in the separation of

air mass curves is due to the low thermal inertia

wall that continues absorbing energy during the

first instants of the transient evolution as a conse-

quence of the non-instantaneous increment of its

temperature.

4. Conclusions

A heat transfer model suitable to predict transient

operation of HSDI turbocharged engines when imple-

mented in a 1-D gas-dynamic model has been presented.This model includes some selected convective correla-

tions for the heat transfer coefficient for the different

ducts and cylinder of the engine. An important contri-

bution of this work is the calculation of the wall temper-

atures by a three-node finite-differences scheme

accounting for thermal inertia. A strategy has been

established to accelerate the convergence in the calcula-

tion of wall temperatures for engine steady operationsimulations from a cycle-averaged thermal balance. This

results in a drastic reduction of the convergence time. It

has been proved that for this kind of calculations it is

not necessary to consider thermal inertia.

The heat transfer model has been validated with tests

carried out on a dynamic engine test bench. Since the

instantaneous gas temperature cannot be accurately

measured, the calculated temperature has been assessedindirectly with regard to other variables that are highly

dependent on it. The mechanical energy balance in the

turbocharger showed that the calculated thermal energy

balance was in agreement with the experiments.

Experimental tests with a low thermal inertia exhaust

manifold showed the potential of this technique to im-

prove the transient response of the turbocharged HSDI

engine. Further calculations have proved that similarimprovements could be expected if the exhaust ports

thermal inertia is also reduced.

Finally, it is worth to note that the studied engine has

a fairly fast load transient (it only takes two seconds to

achieve the maximum injected fuel rate), and therefore

the increment of air mass flow rate takes place too late

to strongly influence its dynamic performance. The ther-

mal inertia effect on the transient response is increasedas transient duration is increased. Otherwise, the only

way to improve dynamic response is to increase air mass

flow at the first stage of the process.

Acknowledgements

The authors wish to thank Antonio Peris and JoseGalvez for their support in the engine testing and work-

shop activities.


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