A new method for optimum selection of two-stage turbocharger for heavy duty diesel engine
Sepehr Sanaye*, Shahram Sedghi Ghadikolaee and Seyed Ahmad Akbari Moghadam School of Mechanical Engineering, Energy Systems Improvement Laboratory, Iran University of Science and Technology, Narmak, Tehran, 16844 Iran Email: [email protected] Email: [email protected] Email: [email protected] *Corresponding author
Abstract: For selecting an optimum two-stage turbocharger, a new approach is proposed here which uses thermodynamic and turbomachinery modelling, genetic algorithm (GA) optimisation technique and GT-Power software. In the primary step, the optimum high pressure (HP) and low pressure (LP) turbochargers were selected by minimising an objective function (the sum of losses in compressors and turbines). Design parameters in the optimisation procedure were geometrical and aerodynamic parameters of compressors and turbines. The final step consisted of adding control valves to achieve the optimal engine performance at various engine speeds. In this step, brake specific fuel consumption (bsfc) was the objective function which was minimised. Based on the results of optimum value of design parameters in the final step, HP and LP turbochargers were reselected with 9.2% increase in brake power and 2.4% decrease in bsfc as the mean values in comparison with a single-stage turbocharger for a specific studied engine.
Keywords: two-stage turbocharging; control valve position; genetic algorithm optimisation technique; heavy duty vehicle turbocharging.
Reference to this paper should be made as follows: Sanaye, S., Ghadikolaee, S.S. and Moghadam, S.A.A. (2015) ‘A new method for optimum selection of two-stage turbocharger for heavy duty diesel engine’, Int. J. Heavy Vehicle Systems, Vol. 22, No. 1, pp.42–72.
Biographical notes: Sepehr Sanaye is a Full Professor at Mechanical Engineering of Iran University of Science and Technology (IUST). His scientific activities are mainly in the field of the system modelling and optimisation. He teaches ‘Internal combustion engine’, ‘Heat exchanger design’, ‘Turbulence’ and ‘Advanced thermodynamics’, in the mechanical engineering department. He has published more than 60 ISI and about 150 conference papers. He is also the chair of Energy Systems Improvement Laboratory (ESIL) at IUST.
Shahram Sedghi Ghadikolaee has PhD in Mechanical Engineering from Iran University of Science and Technology. His research interests are internal combustion engines including heavy duty diesel engines, turbocharging and applying evolutionary algorithms in solving engineering problems.
A new method for optimum selection of two-stage turbocharger 43
Seyed Ahmad Akbari Moghadam is a MS student in Mechanical Engineering Department of Iran University of Science and Technology. His research involves internal combustion engines and heavy duty vehicles.
1 Introduction
For achieving the higher specific power output (increasing brake mean effective pressure or bmep) and lower brake specific fuel consumption (bsfc), a single-stage turbocharger might be used for light and medium duty engines.
In a heavy duty engine and at high engine speeds, a small turbocharger experiences higher back pressure due to small equivalent area of turbine. Furthermore, due to the need for high air mass flow rates at high engine speeds, choking may occur. On the other hand, at low engine speeds, a big turbocharger with a larger time lag decreases the boost pressure and engine power output which increases bsfc (Zhang et al., 2013). Thus, to improve the engine power output and bsfc at various low and high engine speeds, two small and big turbochargers could play their roles more appropriately. The smaller turbocharger works at lower engine speeds at which the air mass flow rate is low. The bigger turbocharger works at higher engine speeds at which the air mass flow rate is high. At medium engine speeds, both turbochargers work.
Most of research works in turbocharger selection for an engine are either based on trial-and-error method followed by empirical tests (Korakianitis and Sadoi, 2005; Zhang et al., 2008; 2012; Tancrez et al., 2011; Ying-hong and Guo-zhang, 2004) or are based on using data maps of compressors and turbines combined with different engine modelling software such as GT-Power and AVL Boost (Jingping et al., 2011; Vitek et al., 2006).
Vitek et al. (2006) modelled a diesel engine and a turbocharger with GT-Power software. They obtained the operating points of several turbochargers for which the compressor and turbine maps were obtained by regression techniques. They used these compressor maps for optimum selection of a single-stage turbocharger.
Cui et al. (2014) performed two-stage turbocharger matching for their engine at 1365 rpm and 75% load, using an iterative method. Two bypass valves were used to prevent entering surge–choke regions, preventing the maximum cylinder pressure and maximum turbocharger speed. They reported 30% reduction in NOx and 6.7% reduction in bsfc.
In two-stage turbocharger selection and matching, the effects of altitude on engine intake pressure and engine power output were studied by Li et al. (2014). The matching of turbocharger and engine was performed for 3000 m altitude at maximum torque speed and full load. To adjust and improve the boost pressure at various altitudes, two low pressure turbine bypass valve and a low pressure compressor bypass valve as well as three operating modes of closed, partially open and full open situations were investigated.
A new method of two-stage turbocharger matching with light duty diesel engine was proposed by researchers at Ricardo-Josef Bozek Research Centre (Fsik, 2004). In the primary step, a two-stage turbocharger was selected based on previous experience (Ricardo database twin turbo 1.9 dm3 engine turbochargers by satisfying the constraints). Then with changing the mass flow multipliers of HP and LP compressors and turbines, modifications of turbochargers and updated constraints were performed.
44 S. Sanaye et al.
Watel et al. (2010) studied two-stage turbocharger matching to reach Euro 6 fuel consumption standard. Three control valves were used to trade off between engine fuel consumption and emissions.
The widely used trial-and-error method which is based on information maps of compressors and turbines is very time-consuming and expensive due to the need for performing many experimental tests (Jingping et al., 2011). This method of analysis is difficult for selecting two-stage turbocharger owing to increased degrees of freedom or optimised variables (simultaneous selection of two compressors and turbines).
In this paper, two-stage HP and LP turbochargers are selected for a heavy duty diesel engine using thermodynamic and turbomachinery analyses, genetic algorithm optimisation technique and modifying mass flow multipliers to achieve the optimal engine performance. The goal was minimising the sum of losses in compressors and turbines as an objective function (for turbocharger design and selection) in the primary step, as well as minimising bsfc as an objective function (for matching the turbocharger with engine) in the final step.
This paper includes the following contributions:
• providing a new method in optimum two-stage turbocharger selection using system modelling and optimisation methods
• proposing two new objective functions (sum of losses in compressors and turbines in the primary step and bsfc in the final step which both should be minimised), to reach the target power output
• choosing new design parameters (geometrical and aerodynamic parameters of compressors and turbines, flow control valve positions, the mass flow multipliers of HP and LP compressors and turbines and fuel injection mass flow rate) in optimising approaches
• choosing a new group of constraints in optimisation process such as locating the turbocharged engine operating points at suitable position on the map of compressors (by defining a new index parameter), satisfying the maximum cylinder pressure, maximum exhaust temperature and compressor to turbine diameter ratio.
2 Primary selection of optimum HP and LP turbochargers
2.1 Two-stage turbocharger and its control valves
Two turbochargers might be used in parallel, sequentially or in series (two-stage or dual-stage) configurations. When two parallel turbochargers (each for half of total number of cylinders) are used, they operate independently and similarly with the same compression ratio, at all engine speeds to provide similar boosting pressure for their corresponding cylinders (Wan, 2002).
In sequential turbochargers, at low engine speeds, all engine exhaust gas is directed to drive one of turbochargers leaving the other one idle. At high engine speeds (when the engine exhaust flow is sufficient to drive both turbochargers), the second turbocharger intervenes and helps reaching the maximum boost pressure. Complicated connection pipes and its occupying space are disadvantages of this configuration (Galindo et al., 2010; Wan, 2002).
A new method for optimum selection of two-stage turbocharger 45
Serial (two-stage or dual-stage) turbochargers consist of HP and LP turbochargers (Figure 1). An intercooler may be placed between HP and LP compressors to decrease the LP air exit temperature (to achieve higher air density and mass flow rate) and increasing overall system efficiency.
Figure 1 A typical two-stage turbocharger in series with three control valves
There could be three control valves for adjusting air and exhaust gases passing through compressors and turbines, respectively:
• high pressure turbine bypass (HPT bypass), which is used to adjust the boost pressure in HP turbocharger
• high pressure compressor bypass (HPC bypass), which besides HPT bypass, enables complete bypassing of HP turbocharger in high speeds
• low pressure turbine waste-gate (LPT waste-gate), which with decreasing the exhaust gases passing through LP turbine, prevents over speeding of LP turbocharger.
At high engine speeds (for which high amount of engine exhaust mass flow rate exists), the HP turbine experiences choking as well as increasing the engine back pressure which decreases engine power output due to reducing the maximum gas mass flow rates passing through HP turbine. To keep the appropriate engine power output, the boost pressure is required which dictates increasing the cylinder pressure up to a permitted maximum value. To avoid undesired engine back pressure (as well as controlling the cylinder maximum pressure), one might use HPT bypass control valve to adjust HP turbine mass flow rate. Thus, at high engine speeds, with opening HPT bypass valve, a portion of engine exhaust gas bypasses HP turbine and therefore the engine back pressure (as well as the cylinder pressure) would be controlled to get specific engine power output.
At high engine speeds using HPC bypass valve is necessary besides HPT bypass valve due to the fact that with increasing the engine speed and with opening both control valves, HP turbocharger would be bypassed and LP turbocharger would be the main
46 S. Sanaye et al.
provider of the boost pressure. This prevents the engine back pressure as well as HP compressor and turbine choking.
Another technical point in turbocharger selection is LP turbocharger overspeeding. A method for preventing LP turbocharger overspeeding is selecting suitable sizes of turbine and compressor for that turbocharger. Alternatively, one might use LPT waste-gate for controlling engine exhaust gas mass flow rate passing through LP turbine. However, using three control valves not only increases the turbocharger weight (which increases the response time in low engine speeds) but also simultaneous adjusting of three control values would be difficult (Cui et al., 2014; Fsik, 2004). In this paper, HPT and HPC bypass valves have been used as control valves.
2.2 Two-stage turbocharger modelling
Primary selection of optimum HP and LP turbochargers was performed by modelling compressors and turbines (relations listed in Tables 1–3), intercoolers (relations listed in Table 4), and engine (relations listed in Table 5) as well as using GA optimisation technique. It is worth mentioning that the relations listed in Table 5 are in terms of crank angle (θ), for more accurate computation of pressure distribution during a thermodynamic cycle (720 degree in 4 stroke diesel engine). This makes the estimate of engine power output (by integrating pressure variations ( .d )W P V= ∫ for the whole 720 degrees for a complete cycle) more accurate. Modelling input parameters were categorised as thermodynamic parameters, geometrical parameters and empirical parameters (Table 6).
Table 1 Centrifugal compressor governing equations (radial turbine is the same)
From the velocity triangle at the compressor impeller inlet
From the velocity triangle at the compressor impeller outlet
The impeller mean diameter ( )2 2
1 121 2
t hD DD
+=
The impeller blade linear velocity
2 22
22 60
D NrU πω= =
The impeller blade linear velocity at mean radius
1 11
22 60D NrU πω= =
The flow area at the impeller outlet
2 22A r bπ=
The fluid absolute velocity at impeller mean radius
11 1
1tanxUC C
β= =
The radial component of the air absolute velocity at the impeller exit
com2
2 2r
mCAρ
=
The flow area ( )2 21 1 1t hA r rπ= − The air tangential
component 2 2 2 2.tanrC U Cθ β= −
The mass flow rate and The air static density
com 1 1 1xm ACρ=
11
1
PRT
ρ =
The air absolute velocity 2 22 2 2rC C Cθ= +
The air relative velocity 2
22cos
rCWβ
=
Euler and thermodynamics equations
Estimating of compressor power consumption from Euler equation
( ) ( ) ( )0,com 02 01 2 2 1 102 01 2 2
1 0h h h C U C U
h h C UC
θ θθ
θ
∆ = − = − ⇒ − ==
where 20 2h h C= + is stagnation enthalpy
A new method for optimum selection of two-stage turbocharger 47
Table 1 Centrifugal compressor governing equations (radial turbine is the same) (continued)
Euler and thermodynamics equations By perfect gas assumption with constant cP
( )02 01 2 2 02 01 2 2P Pc T T C U T T C U cθ θ− = ⇒ = +
The isentropic stagnation temperature and the compressor total pressure ratio
0, loss
0,
isis
is
h hh
η∆ − ∆
=∆∑
( )02, ,com 02 01 01is isT T T Tη= − +
( )102,02
01 01
isTPP T
γ γ −
=
Turbine and compressor power and speed relations which are on the same shaft
.. com
tur tur commech
,WW N Nη
= =
Source: Watson and Janota (1982)
Table 2 Various types of compressor losses
Loss type Equation References Incidence loss ( )
2.21 1 1 1 1
inc inc 101 1
inc
.tan .tan2 2
0.5 0.7
x b inc bU C C f mh f UA
f to
θ β βρ
− − ∆ = = −
=
Botha and Moolman (2005), Gravdahl et al. (2004) and Jiang et al. (2006)
Blade loading loss
( ) ( )( )
2 2 2bld 2
1
22
1 2 1 2 1 2
Euler 2 2 1 1
0.05 , 1
0.751 2
f ft
Eu
t b t t
Wh D U DW
h UW W N D D D D
h U C U Cθ θ
π
∆ = = −
∆+ − +
∆ = −
Botha and Moolman (2005), Gravdahl et al. (2004) and Schiffmann and Favrat (2010)
Skin friction loss
( )
2 1 2 1 1 2
hyd
2 2 2hyd0.25
2
2 32 ,8
0.6328 4, Re ,Re
b t t hsf f
f
L C C W W Wh C W WD
U b AC Da
ρµ
+ + + +∆ = =
= = =
Botha and Moolman (2005), Erickson (2008), Gravdahl et al. (2004) and Jiang et al. (2006)
Clearance loss
( )( )
0.52 2
2 1 1 12
2 2 2 1 2 1
2
40.6 ,1
0.002
c t hcl
b t
c
C C r rh Cb b N r r
D
θθ
ε πρ ρ
ε
−∆ = − + =
Botha and Moolman (2005) and Schiffmann and Favrat (2010)
Mixing loss 2 22
mix 22
1 1 , 0.2 0.31 cot 1 2
b Ch ε εα ε
∗ − −∆ = ≤ ≤ + −
Botha and Moolman (2005) and Gravdahl et al. (2004)
48 S. Sanaye et al.
Table 2 Various types of compressor losses (continued)
Loss type Equation References Disk friction loss ( )
( )
0.1 0.5 52 3back 22 2 2
. 0.1 0.2 5back 2
2 2 2back 2
2
3.7 Re Re 3 10,
0.102 Re Re 3 104
Re , 0.05
df df df
C rr Uh f fC rm
U r C r
ρ
ρµ
−
−
< ×∆ = = > ×
= = ×
Botha and Moolman (2005), and Schiffmann and Favrat (2010)
Recirculation loss
2 22 20.002 tanrc fh D U α∆ =
Schiffmann and Favrat (2010)
Leakage loss ( )
( )
22.
2 2 1 1
1 2 1 22
, 0.816 2 ,2
, ,2 2
cl cllk cl cl
mcl
b
cl b c cl
m U Uh U Pm
m r C rCP
N rbLr r b br b m N L U
θ θ
θ
θ
ρ
ρ ε
∆ = = ∆
− ∆ =
+ += = =
Botha and Moolman (2005)
Table 3 Various types of turbine losses
Loss type Equation References Stator kinetic energy loss 2
2
1 2
2
1 ,2 1
0.0076 cos1 ,cos 0.025 0.7 2
ss s s
s
sts st
eh Ce
e
ζ ζ
α α ααα
∆ = =−
+ = + = −
Rohlik (1968)
Rotor kinetic energy loss
( ) ( )
23
3
3 2 2
2 3 2 2 3 2
1 ,2 1
1.90.017 1 1cos 0.003 0.017
0.5 / 0.8 1 /,
rr r r
r
prr
b r
p rb p
eh We
S beN b b
D D D D D DS
N S
ζ ζ
σβ σ
πσ
∆ = =−
= + + − −
+ −= =
Benson (1977) and Rohlik (1968)
Clearance loss ( )2 3 32 3 2 2 2
3 3
2 2, sin
1cl t
clh t
h H rh h U C
r rα−
−
∆∆ = ∆ =
−
Romagnoli and Martinez-Botas, 2011)
Disk friction loss 2 32 2 2 2 2 2
.0.2 2
0.02125 , ReRe
dfr U U rh
m
ρ ρµ
∆ = = Romagnoli and Martinez-Botas (2011)
Exit loss 23 , 0.4 0.5
2ex ex exCh f f∆ = ≤ ≤
Rohlik (1968)
A new method for optimum selection of two-stage turbocharger 49
Table 4 Heat exchanger governing equations
Equation
( )( )
( )( )
1 2 2 1
min 1 1 min 1 1
h h h c c c
h c h c
C T T C T TC T T C T T
ε− −
= =− −
Kakac et al. (2012)
Table 5 Engine governing equations
Equation References The mass conservation equation
cyc
inj loss
The mass flowrate passingthrough valves
The fuel The mass lossesspray rate in the cylinder
dVariations of mass inside the d d:cylinder with crank angle d d d
d dd d
in exm m m
m m
θ θ θ
θ θ
= −
+ −
The energy conservation equation
loss
comb loss
The heat Rate of worklosses rate performed by
moving piston
Rate of the heatreleased bycombustion
The energy variationsd d dinside the cylinder :d d d
with crank angle
d d d dd d d d
u
in exin ex
E Q VP
Q m m mh h
θ θ θ
θ θ θ
= − −
+ + − − loss
Rate of energy variationsdue to massentrance, exite and losses
hθ
The total heat rate released by combustion
end
start
d dd
chch
QQθ
θ
θθ
= ∫ Chmela and Orthaber (1999) and Heywood (1998)
The burning rate ( )
( )( )
( )
( )
( )
1 2
Rate3 cyl
mod 1 2
, ,
1
2 cyl
d fuel availability mixingd
,LHV
where
,
f t cyl
t
el
f m Q f k V
f f
kC
Vt
Q C f f
Qf m Q m
f k V e
θ=
= −
=
Chmela and Orthaber (1999) and Lakshminarayanan et al. (1986)
Thermodynamic parameters Geometrical parameters Empirical parameters Ambient pressure (Pamb) and temperature (Tamb)
Turbine A/R ratio Exit loss coefficient (fex)
Gas constant (R)
Impeller width (b) Wake fraction of blade-to-blade space (ε)
Air specific heat at constant pressure and volume (cp, cv)
Impeller inlet and exit diameters (Din,ex)
Model constant (Cmod)
Fuel lower heating value (LHV)
Impeller inlet and exit angles (α, β) Constant for the mixing rate (Crate)
2.3 Primary selection of optimum HP and LP turbochargers
2.3.1 The procedure for primary selection of optimum HP and LP turbochargers
The optimum turbocharger selection procedure is as follows:
1 The maximum power boost by the engine at a given speed was estimated based on the engine design limitations (thermal and pressure stresses) for the required air pressure and temperature at the inlet manifold (equations (1)–(6)):
. . .120a v dNm Vη ρ= (1)
where in equation (1), air density for perfect gas was computed from equation (2).
.PRT
ρ = (2)
By substituting equation (2) in equation (1), the air mass flow rate would be obtained by equation (3):
. . . .120a v d
P Nm VRT
η= (3)
Brake specific fuel consumption (bsfc) would be defined as:
bsfc .f
br
mW
= (4)
where in equation (4), the fuel mass flow rate would be obtained by equation (5):
( ).a
fm
mA F
= (5)
By substituting equation (5) in equation (4), the engine brake power would be obtained by equation (6):
A new method for optimum selection of two-stage turbocharger 51
( ).
bsfca
brm
WA F
= (6)
Therefore, with known values of N, Vd, T, P, bsfc and A/F, the brake power for an engine could be estimated in this step.
2 Starting with an initial guess for design parameters of the compressor and turbine and compressor speed (in acceptable range) and by trial-and-error method, compressor mass flow rate, as well as exit pressure and temperature were obtained from equations in Table 1 (Watson and Janota, 1982).
3 The compressor exhaust air after passing through an intercooler (a compact heat exchanger) enters the inlet manifold. The pressure drop from the compressor outlet to the engine inlet manifold was assumed to be 6.8–28 kPa (BorgWarner Catalogue, 2012; Garret catalogue, 2009).
4 After that, engine air induction, compression, combustion and expansion strokes were modelled. If the estimated engine power output did not meet the desired value mentioned in step 1, the computations returned to step 2.
5 The combustion products enter the engine outlet manifold and then enter the turbine. If the turbine power is not approximately equal to the compressor power, the computations returned to step 2.
6 In the last step, the primary selection of optimum HP and LP turbochargers was performed and optimum values of design parameters were obtained by minimising the objective function (the sum of losses in compressors and turbines which are defined and expressed by relations in Tables 2 and 3).
Figure 2 shows the flowchart of the above procedure in detail.
2.3.2 Objective function
The above-mentioned objective function (total losses in compressors and turbines) should be modified due to the following reason:
HP turbocharger is supposed to work mainly at low engine speeds (at which both HPT and HPC bypass control valves are closed) while LP turbocharger (which has higher pressure ratio than HP one) is going to be used mainly in high engine speeds (at which both HPT and HPC bypass control valves are open). Thus, the optimum HP and LP turbochargers should be selected such that they give appropriate service to the engine at various speeds. Thus, in this paper, the optimum HP and LP turbochargers (with the minimum value of the objective function) was selected with giving weighting factors for various engine speeds in objective function as described in equation (7).
2
tot1
.ii s
i
OF w OF=
= ×∑ (7)
Weighting factors (w1 and w2) are used in equation (7) to find the objective function based on the estimated average values of engine operating time (as well as HP and LP turbochargers) at various engine speeds (s1 and s2) based on selected engine driving cycle. More information regarding the studied engine is explained in case study (Section 4).
52 S. Sanaye et al.
Figure 2 Optimum turbocharger selection procedure
A new method for optimum selection of two-stage turbocharger 53
2.3.3 Design parameters (decision variables) and constraints
The geometrical and aerodynamic design parameters of compressors and turbines and their range of variations are also given in Table 7.
Table 7 Design parameters and their range of variations
Design parameters Range of variations References Blade tip radius at impeller inlet of compressor
( ) ( )1,com15 mm 35 mmtr≤ ≤ BorgWarner Catalogue (2012) and Garret catalogue (2009)
Number of impeller blades of compressor and turbine
b,com b,tur5 , 12N N≤ ≤ Benson (1977), Perdichizzi and Savini (1985) Schiffmann and Favrat (2010)
Ratio of blade tip radius at impeller outlet to blade tip radius at impeller inlet for compressor and turbine
2,com 1,com 3,tur 2,tur1.25 1.5, 0.75 0.95t tr r r r≤ ≤ ≤ ≤ BorgWarner Catalogue (2012), Garret catalogue (2009) and Watson and Janota (1982)
Blade angle at compressor impeller inlet
o o1b,com20 70β≤ ≤ Elkin et al. (2012),
Perdichizzi and Savini (1985) and Schiffmann and Favrat, 2010)
Blade angle at compressor impeller exit (backward swept)
o o2b,com0 60β≤ ≤ (Elkin et al., 2012;
Perdichizzi and Savini (1985); Schiffmann and Favrat (2010)
Turbine A/R ratio ( ) ( )8.89 mm 40.64 mmA R≤ ≤
BorgWarner Catalogue (2012) and Garret catalogue (2009)
Locating the turbocharged engine operating points in appropriate regions (at suitable position on the map of compressors) was also an important constraint in turbocharger selection procedure. By defining and using a new index (equation (8)), the distance of compressor operating point from surge and choke lines is estimated. Therefore, by using this index, locations of the turbocharged engine operating points in the map of compressors and their closeness to surge and choke margins are evaluated.
sur,
cho, sur,
SCI B B B A
B B C A
m m m mm m m m
− −= =
− − (8)
where indices A, B and C are shown in Figure 3. Based on data available for turbochargers, range of 0.15–0.85 was selected for this parameter (Watson and Janota, 1982).
Furthermore, the maximum cylinder pressure (170 bar (Mercedes-Benz catalogue, 2009a, 2009b)) and the maximum exhaust temperature (580oC (Mercedes-Benz catalogue, 2009a, 2009b)) were used as constraints.
54 S. Sanaye et al.
Finally, turbine blade speed ratio and turbine efficiency are important parameters for designing and matching of turbine and compressor. Turbine blade speed ratio is considerably affected by compressor impeller diameter as well as turbine effective area ( )2 2
eff,tur . / .n r n rA A A A A= + Thus, the diameter of compressor impeller as well as turbine effective area should be properly selected. There is a unique relation between the ratio of compressor to turbine diameter (r2,com/r2,tur), turbine blade velocity ratio (U2,tur/Cis) and compressor slip factor (σcom) to obtain the maximum turbine efficiency (ηis,tur) as presented in equation (9) (Watson and Janota, 1982):
,tur com2,com
2,tur 2,tur
2.is
is
rr U C
η σ= (9)
The compressor to turbine diameter ratio is between 0.7 and 1 as a constraint (BorgWarner Catalogue, 2012; Garret catalogue, 2009).
Figure 3 A typical compressor map
2.3.4 Genetic algorithm optimisation technique
Owing to existing local optimal points in the solution domain, the final optimal result (objective function) found by gradient-based optimisation methods may land on a local optimum rather than the global solution. The genetic algorithm (GA) optimisation technique is a powerful tool to recognise the global optimum point due to random choosing of decision (design) parameters in the solution domain. The GA optimisation technique (as one of the evolutionary algorithms) mimics the natural evolution and is an iterative process. The evolution usually starts from a population of possible solutions. Then they generate repeatedly new populations from the last one based on the survival of fitter solutions (with the hope of finding solutions with better objective functions).
The objective function in the primary step (the sum of compressors and turbines losses) was minimised using GA optimisation technique to get the optimum design parameters.
A new method for optimum selection of two-stage turbocharger 55
The steps of applying genetic algorithm optimisation technique as shown in Figure 4 are briefly described below (El-Mahdy et al., 2010; Gen and Cheng, 2000; Hartmut, 2004; MATLAB Toolbox, 2005).
Figure 4 Genetic algorithm flowchart
2.4 Formation of the initial population
The first step in the GA procedure is the formation of the initial population (generation). A population consists of a number of chromosomes (each a string of coded bits or genes). Each chromosome represents a single solution to the problem under study. The first population is created by randomly choosing the binary value of 0 or 1 for each bit.
2.5 Selection process and the mating pool
The next step is to select some individual solutions to produce the offspring (children) for a new generation. Individual solutions are selected through a fitness-based process where fitness function represents the objective function while the individuals with greater fitness functions have a better chance of being selected. A collection of the selected individuals makes up the mating pool.
2.6 Creating the next generation
To produce the next generation, genetic algorithm employs three methods of crossover, mutation and elitism as described in the following:
2.6.1 Crossover
In crossover method, children would be generated from combination of parents. In this process, the children and offspring (new solutions) typically inherit many of the characteristics of their parents.
56 S. Sanaye et al.
2.6.2 Mutation
In the second method of creating the next generation, mutation of children may occur by randomly changing the genes. Creating the next generation may be also occurred by mutation of individual parents. Mutation causes more variety among population and prevents the optimum process and final result to be trapped in a local solution instead of global one.
2.6.3 Elitism
In the third method of creating the next generation, elitism would work and children who provide the best values of objective function (with the best fitness values) would present among the next generation.
2.7 Stopping conditions for the algorithm (termination)
The algorithm stops when the change in the objective function values in a group of consecutive generations is less than a specified tolerance or when the number of generations reaches the maximum value of generations.
The GA operators selected and used in this paper were the Roulette-Wheel selection, single point crossover, uniform mutation rate and the Elitism.
3 Final selection of optimum HP and LP turbochargers
The selection of compressors and turbines in the primary step (Section 2) was improved in this section by using GT-Power software. The input values to GT-Power software were the geometrical and turbomachinery parameters of selected turbochargers, specifications of HPT and HPC bypass control valves, specifications of intercoolers and the engine (included geometrical properties of intake and exhaust manifolds as well as combustion chamber).
To reach the minimum bsfc, the optimum values of mass flow multipliers of HP and LP compressors and turbines, fuel injection mass flow rate and control valve positions at various engine speeds were estimated by GT-Power software and discrete-grid optimisation method.
3.1 Correction of multipliers for HP and LP compressors and turbines
The basic turbomachinery relation can be presented in terms of following non-dimensional parameters which has derived from combination of mass, momentum and energy conservation equations:
01 0 022
01 0101 01
, , , , , .m RT T PND mf
T P DP D RTη γ
µ ∆
=
(10)
Since turbochargers operate with perfect gases (air in compressor and engine exhaust gases in turbine), values of R (gas constant) and γ (ratio of specific heats or Cp/Cv) as well as µ (dynamic viscosity) are known. Reynolds number of gas flow
A new method for optimum selection of two-stage turbocharger 57
2
Re VD VD mD D
ρ ρµ µ µ
= = =
has a small effect on the turbocharger operation and is usually negligible. Furthermore, dimensionless groups of η, ∆T0/T01, and P02/P01 are related as equation (11) and therefore the relation between four mentioned dimensionless groups
01 022
0101 01
, , ,m RT PND
PP D RTη
are finally stated as equation (12).
( )( )
( )
102 01
0 01
1P PT T
γ γ
η− −
=∆
(11)
01 022
0101 01
, , .m RT PNDf
PP D RTη
=
(12)
For a particular machine which the diameter (D) is constant and the equipment performance could be plotted in terms of two parameters
01 02
01 01
andm T P
P P
for various values of η and 01N T (Figures 3 and 5). Therefore, by plotting P02/P01 vs. mass flow parameter ( )01 01 ,m T P for a series of values of 01N T and η, the complete performance of the machine is predictable.
Figure 5 A typical turbine map
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The corresponding values of multipliers relevant to the four above effective parameters 01 01 ,m T P 02 01 ,P P η and 01N T are also named mass flow, pressure ratio,
efficiency and speed multipliers, respectively. By assuming specific values of pressure ratio (to reach specific engine power output at various engine speeds), efficiency (which was optimised in the primary step) and speed (small effect of confronted turbocharger rotational speed on bsfc), the mass flow multiplier would be the most effective parameter among the four above ones. By estimating the optimum values of mass flow multiplier in the final step, the final optimum HP and LP turbochargers were reselected as explained in the next section.
3.2 The procedure for final selection of optimum HP and LP turbochargers
Owing to the existence of seven design parameters (including four mass flow multipliers of HP and LP compressors and turbines, two HPC and HPT control valve positions and one fuel injection mass flow rate value), the below procedure was followed:
a Estimating fuel injection mass flow rate and mass flow multipliers of HP compressor and turbine as design parameters at low engine speeds (at which both HPT and HPC bypass valves are closed).
b Estimating fuel injection mass flow rate and mass flow multipliers of LP compressor and turbine as design parameters at high engine speeds (at which both HPT and HPC bypass valves are open).
c Estimating fuel injection mass flow rate and HPC and HPT control valve positions as design parameters at medium engine speeds by using mass flow multipliers obtained in steps a and b.
Therefore, in the final step, the mass flow multipliers of HP and LP compressors and turbines, as well as HPC and HPT control valve positions and fuel injection mass flow rate could be estimated by running GT-Power to reach the minimum value of bsfc.
4 Case study
The results of optimum selection and matching of a two-stage (serial) turbocharger for OM 457 LA heavy duty diesel engine are presented here. OM 457 LA (which is used in axors and buses) has a single-stage factory specified turbocharger and an intercooler with engine specifications mentioned in Table 8 at atmospheric conditions (1 bar pressure and 25ºC temperature) (Mercedes-Benz catalogue, 2009a, 2009b).
Table 8 Technical characteristics of OM 457 LA engine
Number of cylinders 6 Compression ratio 18.5:1 Displacement (litre) 11.97 Rated power (kW) @ 2000 rpm 260 Bore (mm) × Stroke (mm) 128 × 155 Torque, max. (N.m) @ 1100 rpm 1700
Source: Mercedes-Benz catalogue (2009a, 2009b)
A new method for optimum selection of two-stage turbocharger 59
For our case study, w1 and w2 in equation (7) were set at 1 and 0 for HP turbocharger and 0 and 1 for LP turbocharger at s1 = 1000 rpm and s2 = 2000 rpm.
The geometrical parameters of 44 turbochargers are also listed in Table 9. A geometrical parameter L, which is defined in equation (13) and expressed as the mean value of blade tip radius at the inlet and exit of compressor and turbine impeller, is also included in data presented in Table 9.
2 2 2 21,com 2,com 3,tur 2,tur .
4t tr r r r
L+ + +
= (13)
5 Discussion and results
5.1 Modelling verification
In Figures 6 and 7, variations of pressure ratio and compressor isentropic efficiency in terms of corrected air mass flow rate at various compressor speeds are shown. The average values of difference between pressure ratio obtained from modelling and experimental results for compressors number 1, 32 and 44 were 9%, 5.4% and 5%, respectively. The corresponding values for compressors isentropic efficiency were 5.5%, 8.3% and 4.4%, respectively. Variations of expansion ratio in terms of corrected air mass flow rate for turbines number 1, 32 and 44 are shown in Figure 8 with maximum values of difference between modelling and experimental results equal to 4.2%, 3% and 7%, respectively.
Figure 9 compares variations of pressure in cylinder at different crank angles (θ) obtained from present model and experimental results for OM 457 LA diesel engine equipped with single-stage turbocharger (number 33 with an intercooler) (Mercedes-Benz catalogue, 2009a, 2009b). The mean difference value of results between two graphs was about 6.7%. The engine modelling results for brake power and torque at various engine speeds are verified in Figure 10 (Mercedes-Benz catalogue, 2009a, 2009b). The maximum values of difference between modelling and experimental results equal to 2.1%.
Figure 6 Variations of compressor pressure ratio with air corrected mass flow rate at various rotational speeds of compressor for turbocharger No. 32 from the present model and empirical results (catalogues)
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Figure 7 Variations of compressor efficiency with air corrected mass flow rate at various rotational speeds of compressor for turbocharger No. 32 from the present model and empirical results (catalogues)
Figure 8 Variations of expansion ratio with corrected mass flow rate of turbines for turbochargers No. 1, 32 and 44 from the present model and empirical results (catalogues)
Figure 9 The comparison of results obtained from the present model and experimental results for OM 457 LA engine (Mercedes-Benz catalogue, 2009a, 2009b)
A new method for optimum selection of two-stage turbocharger 61
Table 9 Classification of turbochargers based on the maximum and minimum air mass flow rate and L parameter
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Table 9 Classification of turbochargers based on the maximum and minimum air mass flow rate and L parameter (continued)
A new method for optimum selection of two-stage turbocharger 63
Figure 10 The comparison of engine brake power and torque for various engine speeds obtained from the present model and experimental results from OM 457 LA engine (Mercedes-Benz catalogue, 2009a, 2009b)
The above results show that the modelling results for thermodynamics, turbomachinery and engine modelling as well as single-stage turbocharger selection and matching are reliable enough for engineering applications.
5.2 Optimisation results
Optimum values of design parameters
In the primary step, the GA optimisation technique was applied for 300 generations, using a search population size of 150 individuals, crossover probability 0.8 and gene mutation probability 0.05. The numerical values of optimum design parameters are listed in Table 10.
Table 10 Optimum values of design parameters obtained by the proposed procedure
Design parameters Optimum values for HP stage Optimum values for LP stage
( )1,com mmtr 28.5 37.3
,combN
10 12
2,com 1,comtr r 1.49 1.4
( )o1 ,combβ
61.0 59.0
( )o2 ,combβ
31.5 30.0
,turbN
9 11
3,tur 2,turtr r 0.89 0.95
( )mmA R 28.0 31.9
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The optimum turbocharger geometry selected by the GA can be used to manufacture a new turbocharger or can be used for selecting an appropriate existing turbocharger from a vendor list. In the latter case, a geometrical parameter, L, was defined as described by equation (13). Then a turbocharger with the closest geometry values to L was selected as optimum turbocharger. In the primary step, the values of L for the primary selection of optimum HP and LP turbochargers were about 17.4 and 21.9, respectively.
In the final step and passing the modification procedure, HP turbocharger number 26 (Table 9) with mass flow multiplier 1.17 for compressor (turbocharger number 28 of Table 9) and 0.98 for turbine (turbocharger number 26 of Table 9) was selected. Furthermore, LP turbocharger number 36 (Table 9), with compressor mass flow multiplier 0.92 (turbocharger number 35 or 36 of Table 9) and turbine mass flow multiplier 1.09 (turbocharger number 37 of Table 9) was selected.
The optimum values of flow control valve positions and fuel injection mass flow rate at various engine speeds are shown in Figure 11 for the above selected turbochargers. In this figure, flow control valve position (bypass valve mass flow rate ratio) is defined as the ratio of valve mass flow rate to total mass flow rate by valve tot .m mα = Figure 11 shows that with increasing the engine speed from 1000 rpm to 2000 rpm, HPC bypass valve position changed from 0% (closed situation) to 71.4%. Furthermore, HPT bypass valve position also changed from 0% (closed situation) to 89.8%. Figure 11 also shows an abrupt change in HPT bypass valve position from 23.9% (at 1400 rpm) to 74.1% (at 1600 rpm). This jump is due to small HP turbine effective area (defined in section 2.3.3) for higher engine speeds than 1400 rpm.
Figure 11 The optimum values of flow control valve positions (bypass valve mass flow rate ratio) as well as fuel injection mass flow rate at various engine speeds obtained from modelling results
The pressure ratio of two-stage turbocharger
Figure 12 shows the computed values of the pressure ratio of HP and LP turbochargers of a two-stage turbocharger at various engine speeds. With opening HPT bypass valve, HP turbine gradually became idle (bypassed) and LP turbine engaged in turbocharging completely. In this situation, HPC bypass valve position changed from 9.7%
A new method for optimum selection of two-stage turbocharger 65
(at 1400 rpm) to 45.1% (at 1600 rpm), which caused decreasing the exhaust gas pressure (pressure in the cylinder exit) from 2.55 bar (at 1400 rpm) to 2.02 bar (at 1600 rpm). As a result, the boost pressure of two-stage turbocharger also decreased from 2.8 bar (at 1400 rpm) to 2.5 bar (at 1600 rpm) without decreasing the target power output and increasing the cylinder pressure higher than 170 bar. Figures 11 and 12 also show that with increasing the opening of HPC and HPT bypass valves, HP compressor pressure ratio decreased from 1.8 (at 1000 rpm) to 1 (at 2000 rpm) and inversely LP compressor pressure ratio increased from 1.4 (at 1000 rpm) to 2.7 (at 2000 rpm).
Figure 12 The pressure ratio of HP and LP turbochargers and two-stage one (total of the system) at various engine speeds obtained from modelling results
The efficiency and surge–choke index
The full load operating points of the OM 457 LA diesel engine equipped with a two-stage (serial) turbocharger with two intercoolers are also illustrated in Figure 13. This figure shows that at full load and 1000 rpm engine speed, the HP compressor had about 0.76 efficiency (i.e., surge–choke index or SCI was about 0.5 based on definition at section 2.3.3). At 1400 rpm, SCI for HP compressor was approximately 0.78 which was very close to the maximum value of this index. This maximum occurs close to the choke line in HP compressor map, and thus by opening HPC bypass valve the operating point moved far from very close to choke line. This phenomenon was caused by a jump shown in Figures 11 and 12 by changing engine speed from 1400 rpm to 1600 rpm. At engine speeds 1800 and 2000 rpm, with opening HPT and HPC bypass valves, HP turbocharger became idle (bypassed) completely (operating points related to 1800 and 2000 rpm in Figure 13). Also the LP compressor efficiency of two-stage turbocharged engine operating points with two intercoolers at full load was in the range of 0.74–0.77 (SCI was 0.48–0.53) which shows the reliability of presented turbocharger selection procedure.
Brake power, brake torque and bsfc
Figures 14 and 15 show the comparison of brake power and torque and Figure 16 compares bsfc of engine equipped with a single (number 33) and two-stage turbochargers with one and two intercoolers (HP, number 26 and LP, number 36 with mentioned mass
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flow multipliers in section 5.2). The brake power and torque increased 9.2% and bsfc also decreased 2.4% as the average value, when two-stage turbocharger with two intercoolers was applied in comparison with case in which single-stage was applied. By using one intercooler (omitted intercooler between HP and LP compressors), brake power output and torque decreased 1.8% and bsfc increased 1.1% in comparison with case in which two intercoolers were applied.
Figure 13 Operating points of the engine equipped with two-stage turbocharger on the maps of HP and LP compressors (see online version for colours)
Figure 14 The comparison between the brake power of the studied diesel engine equipped with single-stage and two-stage turbochargers
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Figure 15 The comparison between the brake torque of the studied diesel engine equipped with single-stage and two-stage turbochargers
Figure 16 The comparison between bsfc of the studied diesel engine equipped with single-stage and two-stage turbochargers
6 Conclusions
A new approach for optimum selection of two-stage turbocharger (serial) was presented based on modelling and operating conditions of compressors, turbines, engine, intercoolers (thermodynamic and turbomachinery aspects) as well as using GA optimisation technique. The optimum turbochargers had minimum sum of losses in compressors and turbines as well as the minimum value of bsfc.
Locating the turbocharged engine operating points at suitable position on the map of compressors (far enough from surge–choke lines) was also an important constraint in
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turbocharger selection procedure. Furthermore, other constraints such as maximum cylinder pressure, maximum exhaust temperature and compressor to turbine diameter ratio were also used in turbocharger selection procedure. The method narrows the number of candidate turbochargers which really match to an engine and decreases the number of experimental tests seriously. Thus, by primary selection of HP and LP turbochargers (HP and LP compressors and turbines) and following a modifying approach to reach better selections, a faster (than trial-and-error) procedure for optimum turbocharger selection was reached.
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Nomenclature
a Hydraulic perimeter, m A Area, m2 A/F Air to fuel ratio, – A/R Turbine area to radius ratio, – b Width, m bmep Brake mean effective pressure, Pa bsfc Brake specific fuel consumption, g/kWh b* Ratio of the diffuser inlet width to impeller exit width, – cP Specific heat at constant pressure, J/kgK cv
Specific heat at constant volume, J/kgK C Velocity, m/s Cback Impeller back plate clearance, m Cf Skin friction coefficient, – Cmod Model constant, J/kg.degree D Diameter, m Df Diffusion factor, – e Loss coefficient, – E Energy, J f Loss coefficient, – f1 Function, – f2 Function, – h Specific enthalpy, J/kg H Height, m Kt
Density of turbulent kinetic energy, J/kg L Mean value of blade tip radius at the impeller inlet and exit, m LHV Lower heating value, J/kg Lb Impeller flow length, m m Mass, kg
m Mass flow rate, kg/s
mep Mean effective pressure, Pa N Rotational speed; Number of blades, rev/min; – OF Objective function, – P Pressure, Pa Q Heat transfer, J r Radius, m R Gas constant, Radius, J/kgK; m Re Reynolds number, – rpm Revolutions per minute, min–1 SCI Surge Choke Index
A new method for optimum selection of two-stage turbocharger 71
Sp Average blade spacing between inlet and exit, m T Temperature, K U Rotor tip speed, m/s V Volume, m3 w Weighting factor W Work; Velocity relative to blade, J; m/s
W Power, W
Greek α Angle, degree
β Angle, degree
γ Ratio of specific heats (cp/cv); –
ε Effectiveness; Wake fraction of blade-to-blade space, –; –
εc Clearance gap, m
ζ Loss coefficient, –
η Efficiency, –
ηv Volumetric efficiency, –
θ Angle, degree
µ Dynamic viscosity, N.s/m2
ρ Density, kg/m3
σ Slip factor, –
ω Rotational speed, rad/s
Subscripts a Air amb Ambient b Blade bld Blade loading loss br Brake c Coolant cl Clearance loss com Compressor comb Combustion cor Corrected mass flow rate cyl Cylinder d Displacement df Disk friction loss ex Exit Eu Euler’s turbomachinery equation f Fuel h Hot fluid, Hub
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hyd Hydraulic in Inlet inc Incidence loss inj Injection is Isentropic lk Leakage loss m Meridional direction mech Mechanical min Minimum mix Mixing loss n Nozzle r Rotor, Rotor kinetic energy loss, Radial rc Recirculation loss s Stator, Stator kinetic energy loss, Engine rotational speeds sf Skin friction loss st Stoichiometric sur Surge t Tip tot Total tur Turbine x Axial
