Part 1: Influence of scaling on a turbocharged 4 stroke direct

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Part 1: Influence of scaling on a turbocharged 4 stroke direct
Part 1: Influence of scaling on a turbocharged 4 stroke direct common rail diesel injection engine
and the potential of opposed piston design.
by Marcel R. de la Fonteijne, DLF Sustainable, June 2011
In order to investigate several engine design methodologies we developed a software simulation
program in Matlab. This program is calculating the thermo dynamic cycle and will result in a pV
diagram.
The following options are available:
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several mechanical system: off axis, opposed piston, variable compression and expansion
cv en cp and k of gasses temperature dependent.
Cylinder Heat Transfer Model: Woschni or Hohenberg
Heat Release model: multiple Wiebe function
fuel injection adjustable
optimization of injection timing
CO2 emission calculation
fuel consumption calculation with respect to EG standard regulation
max. cylinder pressure and temperature
cylinder pressure limitation option
water/steam injection
EGR option, power and engine speed dependent
Turbo, power and engine speed dependent
Adjustable valve timing
More than 100 adjustable parameters
Besides a pV diagram more than 60 graphic plots like torque, engine power are generated
As a start we consider a 4 cylinder 4 stroke direct common rail 1998 cc diesel injection engine
running at 1800 rpm (for detailed specification see appendix 1). The first exercise is a geometric
scaling with s and a power scaling with s3 to maintain a AFR of 21.3. As a result the effective valve
area is scaled with s2. The calculated MEP (fuel, exhaust, cylinder heat transfer, pumping, brake) is
shown in graphic 1. The fuel power is ranging from 114 kW up to 114 MW, corresponding with s
being 10. Due to the higher content to surface ratio you expect the cylinder heat transfer MEP to
decrease. And indeed it starts to act like this, but then due to that same ratio the pumping MEP is
increasing until s=5 approx. and after that surprisingly resulting in a higher cylinder heat transfer MEP
and much higher exhaust MEP.
We noticed however that with s>2 the AFR is rapidly decreasing and the scaling of the power with s3
is realistic in order to keep the AFR constant. So the graph becomes unreliable with s>2. In fact there
is not sufficient air sucked into the engine.
In order to keep the pumping MEP the same, we now scale the effective valve area with s3. The result
is shown in graphic 2. Because the pumping MEP will remain the same the cylinder heat transfer MEP
will keep on decreasing when s increases. This will now result in a continuous increase of the Brake
MEP and thus power output.
At maximum engine speed this motor is running 3540 rpm which is approximately twice the speed
we used in our calculations, so we can expect a limitation due to pumping effect around this
maximum speed. This also explain that up to s=2 there is a not so tremendous negative effect on the
Brake MEP.
From here we could examine the effect of opposed piston mechanics, but for that we need a
concrete mechanical design and an estimate of change (increase) in friction MEP. If we estimate the
potential gain to be 40 % of the cylinder heat transfer loss (MEP), then the Brake MEP can increase
from 12 to 5 percent over the scaling range, resulting in a Brake MEP of 52 to 55 percent over the
scaling range. We conclude with the statement: The balance between friction, pumping and cylinder
heat transfer to consider opposed piston design is an interesting topic to examine in more detail in a
future exercise with our program.
percentage of Fuel MEP
MEP, scaling of eff. valve area with s2
60
50
40
30
20
10
0
exhaust
cyl. heat
pumping
friction
brake
0
2
4
6
8
10
12
scale s
net
percentage of Fuel MEP
MEP, scaling of eff. valve area with s3
60
50
40
30
20
10
0
exhaust
cyl. heat
pumping
friction
brake
0
2
4
6
scale s
8
10
12
net
Power in kW
Fuel and Brake Power
120000
100000
80000
60000
40000
20000
0
power fuel
Brake power, valve area s^2
Brake power, valve area s^3
0
2
4
6
8
10
12
scale s
Appendix 1
Here you find all parameters of the engine under consideration. In plot 30a you find a pV diagram of
the initial situation.
********************************************************************
********************************************************************
Simulatie Ford Mondeo 66 kW
Tddi 2.0 2001
Max torque 245 Nm at 1900 rpm
Marcel de la Fonteijne, DLF Sustainable
********************************************************************
********************************************************************
Specific air gas constant
Pressure surrounding p_surr
Temperature surrounding T_surr
Temperature surrounding T_surr
287 [J.kgK]
1.01 [bar]
20 [degrees C]
293 [K]
Relative humidity
50.0 [percent]
Max. amount water vapor in air at T_surr
13.2 [g/kg dry air]
Amount of water vapor in air at T_surr
6.6 [g/kg dry air]
Volume water vapor in air
0.008 [m3/kg air] equal to
1.1 [vol. percent]
Volume air
0.773 [m3/kg air] equal to
98.9 [vol. percent]
Specific air density 0 degr. C and 1 bar
1.293 [kg/m3]
Volume fraction of oxygen in air
0.210 []
Volume fraction of nitrogen in air
0.780 []
Volume fraction of argon in air
0.010 []
Mass fraction of oxygen in air
0.232 []
Mass fraction of nitrogen in air
0.754 []
Mass fraction of argon in air
0.014 []
Number of cylinders in engine
4 []
Number of strokes in thermodynamic cycle
4 []
Compression ratio geometric
Number of revolutions per thermo cycle
Specific air density
19.2 []
2 []
1.293 [kg/m3]
Cylinder wall temperature
120 [degrees C]
Cylinder wall temperature
393 [K]
Cylinder wall temperature Stirling 1
120 [degrees C]
Cylinder wall temperature Stirling 1
393 [K]
Cylinder wall temperature Stirling 2
120 [degrees C]
Cylinder wall temperature Stirling 2
393 [K]
Bore cylinder a
86.0 [mm]
Crank arm cylinder a
43.0 [mm]
Piston rod length cylinder a
172.0 [mm]
Offset cylinder a to crank
Bore cylinder b
86.0 [mm]
Crank arm cylinder b
Piston rod length cylinder b
Offset cylinder b to crank
Ratio speed crank b/ speed crank a
Difference in fase
0.0 [mm]
(crank a - crank b)
Stroke of piston
Ratio of stroke/bore
0.0 [mm]
172.0 [mm]
0.0 [mm]
0.50 []
90 [CA cyl b]
86 [mm]
1.0 []
Cylinder area a
5809 [mm2]
Cylinder area b
5809 [mm2]
Volume stroke per cylinder
Volume stroke in engine
Pressure limit in cylinder
Spring constant
Angle for TDC in cylinder a
Volume in cylinder minimum Vd
Volume in cylinder maximum
LHV Fuel
Density of Fuel
Price of Fuel
Price of man hour and additional
Weight factor alfa1 in Wiebe function 1
500 [cc]
1998 [cc]
500 [bar]
0.000 [m/bar] not in use
-0 [CA a]
27.448 [cc]
527.005 [cc]
42.5 [MJ/kg]
850 [kg/m3]
1.50 [€/l]
25.00 [€/l]
0.10 []
t_sigma1 in Wiebe function 1
1 [ms]
t_delay1 in Wiebe function 1
1 [ms]
Power parameter n in Wiebe function 1
2.0 []
Factor parameter a in Wiebe function 1
6.0 []
t_sigma1_acc in Wiebe function 1
0 [ms]
Weight factor alfa2 in Wiebe function 2
0.80 []
t_sigma2 in Wiebe function 2
4 [ms]
t_delay2 in Wiebe function 2
1 [ms]
Power parameter n in Wiebe function 2
2.0 []
Factor parameter a in Wiebe function 2
6.0 []
t_sigma2_acc in Wiebe function 2
Weight factor alfa3 in Wiebe function 3
2 [ms]
0.10 []
t_sigma3 in Wiebe function 3
8 [ms]
t_delay3 in Wiebe function 3
1 [ms]
Power parameter n in Wiebe function 3
2.0 []
Factor parameter a in Wiebe function 3
6.0 []
t_sigma3_acc in Wiebe function 3
Maximal ignition shift
Standard deviation of add. noise in HR
Efficiency of irreversible combustion
Fuel injection max length at n_max
3 [ms]
-40 [CA]
0 [part of signal]
1.00 []
40 [CA]
Engine Speed n max
3540 [rpm]
Power output crank desired
66.0 [kW]
Power fuel at max injection and n_max
224.7 [kW]
Engine efficiency desired
0.294 []
Air to Fuel Ratio AFR desired
22.0 []
Fuel consumption desired
288.4 [g/kWh]
Max CO2 production desired
906.4 [g/kWh]
Engine efficiency desired
0.294 []
Air to Fuel Ratio AFR desired
22.0 []
Volume efficiency VE
0.90 []
p loss compressor to compr. inlet
0.10 [bar]
p loss compressor to inletmanifold
0.20 [bar]
Heat transfer model 0=C 1= Woschni 2=H
2 []
Heat coefficient constant
1500 [W/m2K]
Heat factor Woschni
10.0 []
Heat factor Hohenberg
1.0 []
Parameter C1 Hohenberg
130.0 []
Parameter C2 Hohenberg
1.4 []
Effective area of inlet valve
350 [mm2]
Effective area of outlet valve
200 [mm2]
Angle exhaust valve start opening
140 [CA]
Exhaust valve opening duration
20 [CA]
Angle inlet valve start opening
350 [CA]
Inlet valve opening duration
Angle exhaust valve start closing
Exhaust valve closing duration
Angle inlet start closing=start calc
Inlet valve closing duration
20 [CA]
350 [CA]
20 [CA]
-140 [CA]
20 [CA]
p loss turbo inlet
0.10 [bar]
p loss turbo outlet
0.10 [bar]
Pressure inlet manifold
1.80 [bar]
Pressure outlet manifold
2.35 [bar]
Engine speed where turbo starts
1100 [rpm]
Engine speed where turbo is max at Pmax
1710 [rpm]
Turbo factor in turbo model
p loss exhaust
4 []
0.10 [bar]
Temperature outlet manifold
600 [degrees C]
Temperature outlet manifold
873 [K]
Temperature inlet manifold
25 [degrees C]
Temperature inlet manifold
298 [K]
Specific Friction in cylinder
925 [N/m]
Friction in cylinder
250 [N]
Number of step in numerical proces
4000 []
Car speed actual
90.0 [km/h]
Car speed max
177.0 [km/h]
Speed wheel actual
756 [rpm]
Engine speed actual in gear 1
9231 [rpm]
Engine speed actual in gear 2
5143 [rpm]
Engine speed actual in gear 3
3186 [rpm]
Engine speed actual in gear 4
2368 [rpm]
Engine speed actual in gear 5
1800 [rpm]
Mass car
1540 [kg]
Roll coefficient of car
Steepness of road Ramp
0.0110 []
1:ramp
0 []
Accelaration of car
0.00 [m/s2]
Gravity earth
9.81 [m/s2]
Front surface area of car
2.33 [m2]
Air resistance coefficient of car cw
0.30 []
Transmission losses
0.11 []
Power roll
4.2 [kW]
Power air
6.6 [kW]
Power up hill
0.0 [kW]
Power accelaration
0.0 [kW]
Power at wheel needed
10.7 [kW]
Power at crank needed
12.1 [kW]
Percentage Power roll
38.7 [percent]
Percentage Power air
61.3 [percent]
Percentage Power height
0.0 [percent]
Percentage Power accelaration
0.0 [percent]
Fuel consumption
3.7 [l/100km]
CO2 production
98.4 [g/km]
Fuel consumption
27.2 [km/l]
R size tire
16 ["]
B width of tire
205 [mm]
H height of tire in percentage of width
55 [procent]
Circumference of tire
1985 [mm]
Max speed of car in gear 1 at n_1_max
39.0 [km/h]
Max speed of engine in gear 1 n_1_max
4000 [rpm]
Speed of tire in gear 1 at max car speed
Gear ratio gear 1
327 [rpm]
0.082 []
Max speed of car in gear 2 at n_2_max
70.0 [km/h]
Max speed of engine in gear 2 n_2_max
4000 [rpm]
Speed of tire in gear 2 at max car speed
588 [rpm]
Gear ratio gear 2
0.147 []
Max speed of car in gear 3 at n_3_max
113.0 [km/h]
Max speed of engine in gear 3 n_3_max
4000 [rpm]
Speed of tire in gear 3 at max car speed
949 [rpm]
Gear ratio gear 3
0.237 []
Max speed of car in gear 4 at n_4_max
152.0 [km/h]
Max speed of engine in gear 4 n_4_max
4000 [rpm]
Speed of tire in gear 4 at max car speed
1276 [rpm]
Gear ratio gear 4
0.319 []
Max speed of car in gear 5 at n_5_max
177.0 [km/h]
Max speed of engine in gear 5 n_5_max
3540 [rpm]
Speed of tire in gear 5 at max car speed
1486 [rpm]
Gear ratio gear 5
Speed stationair of engine
Water_injection
Enthalpy of water injected
Water mass injected between theta h-l
0.420 []
850 [rpm]
0 [weight percent] of fuel mass
1016900 [J/kg]
0.000 [g/cycle]
Theta_water_inj_compr_laag
-140.0 [CA]
Theta_water_inj_compr_hoog
-25.0 [CA]
********************************************************************
********************************************************************
Power Fuel desired
224.7 kW
Power output desired
66.0 kW
Specific Power output desired
33.0 kW/l
Motor torque
178.0 Nm
Revolutions per minute max
3540 rpm
Air to Fuel ratio AFR desired
22.0
Cilinder fill efficiency
0.90
Fuel usage desired
288.4 g/kWh output
Fuel needed
5.287 g/s
Motor efficiency
29.4 percent
Fuel MEP
38.12 bar
Brake MEP
11.20 bar
Compression ratio real
15.5
Air flow required for air intake
0.116 kg/s
Corrected Air flow req. on Garrett map
14.175 lb/min
Manifold air pressure required
2.20 bar
p loss compr outlet to inlet manifold
0.20 bar
Compressor discharge pressure estimate
2.40 bar
Compressor discharge pressure atc
2.00 bar
p loss surrounding to compressor inlet
0.10 bar
Compressor inlet pressure
0.91 bar
Pressure ratio to search for turbo est.
2.63
Pressure ratio to search for turbo actual
2.19
Temp. end compressor before intercooler
367 K
Power Pi_compr compressor req. actual
8.5 kW
********************************************************************
********************************************************************
Power fuel begin
225 kW equal to
100 percent of Power Fuel max
Power fuel end
225 kW equal to
100 percent of Power Fuel max
Number of intervals
0
Motor speed begin interval
1800 rpm
Motor speed end interval
3540 rpm
Number of intervals
0
********************************************************************
Power fuel in at max rpm
224.7 kW
Energy fuel W per cylinder
1.90 kJ
Engine speed in rpm
1800 rpm
Height in cylinder in common
0.0 mm
Height of V minimum in cylinder
4.7 mm
V_stroke compression
499.6 cc
V_stroke expansion
499.6 cc
ratio V_stroke expansion/compression
Fuel injection start at t
1.0
-2.3 ms before CA=0
Begin of fuel injection
-25.2 CA
Theta max of fuel injection advance
-40.0 CA before CA=0
Duration of fuel injection
20.3 CA
End of fuel injection
-4.9 CA
Delta theta parameter in Wiebe function 1
10.8 CA
Pressure at begin of injection
Tau ignition delay
Theta ignition delay
p,phi,T
p,phi,T
32.25 bar
1.70 ms
18.33 CA
Temperature at begin of injection
672 K
Pressure inlet manifold absolute
1.80 bar
Pressure outlet manifold absolute
2.35 bar
EGR in wt percent of air inlet
0.0 percent
Volume in cil. when inlet valve is total closed
481.6 cc
Volume O2 in cil. when inlet valve is total closed
101.1 cc
Mass O2 per cylinder when inlet valve closed total
0.221 g
Cyl. pressure when inlet valves total closed
2.04 bar
Cyl. pressure when exhaust valves start opening
6.07 bar
Turbo begin pressure
2.25 bar
Turbo begin volume (slag) motor
2.0 liter
Turbo begin temperature
1016 K
Turbo end pressure
1.21 bar
Turbo end volume (slag) motor
3.2 liter
Turbo end temperature
348 K
Power turbo from exhaust
3.9 kW
Fuel Power max stochiometric
164.4 kW
Motor Power max stochiometric
48.3 kW
Motor torque max stochiometric
256.2 Nm
Air to Fuel ratio stochiometric AFR
14.8
Fuel usage max stochiometric, eta desired
288.4 g/kWh
Mass fuel per cylinder stochiometric
0.064 g
Mass CO2 per cylinder stochiometric
0.203 g
Fuel MEP max stochiometric
54.86 bar
Brake MEP max stochiometric
16.11 bar
Fuel MEP
Exhaust MEP
38.12 bar equal to 100.0 percent
9.83 bar equal to
25.8 percent
10.89 bar equal to
28.6 percent
Pumping MEP
0.57 bar equal to
1.5 percent
Friction MEP
1.72 bar equal to
4.5 percent
15.12 bar equal to
39.7 percent
Indicated MEP=B MEP + F MEP 16.84 bar equal to
44.2 percent
Heat Transfer cil. MEP
Brake MEP
Mass air per cylinder when inlet valve closed total
0.953 g
Mass gas per cylinder when inlet valve closed total
0.953 g
Mass flow air motor actual
0.057 kg/s
H2O injected in percentage of fuel injected
0.0 percent
Mass H2O per cylinder injected
0.000 g
Mass fuel per cylinder injected
0.045 g
Mass O2 per cylinder available
0.220 g
Mass CO2 per cylinder produced
0.141 g
Mass flow fuel injected in motor actual
2.688 g/s
Mass CO2 motor actual
8.449 g/s
Power Fuel actual
114.3 kW
Motor Power actual
45.3 kW
Power Turbo
3.9 kW
Power Compressor
4.3 kW
Motor Power Net
44.9 kW
Motor efficiency fuel to crank Net
39.3 percent
Energy exhaust minus P turbo
25.6 kW
Motor torque actual
240.5 Nm
Revolutions per minute actual
1800 rpm
Air to Fuel ratio actual AFR
21.3
Lambda desired
1.49
Lambda phi base
1.44
Lambda O2 base
1.43
Equivalence Ratio=1/lambda
0.69
Equivalence Ratio=1/lambda O2 base
0.70
Fuel usage actual
213.5 g/kWh
CO2 actual
671.1 g/kWh
Motor efficiency fuel to crank
39.7 percent
Fuel MEP max actual
38.12 bar
Brake MEP max actual
15.12 bar
p max actual
Theta at p max actual
146.98 bar
9.6 CA
T max actual
1958 K
Theta at T max actual
23.1 CA
********************************************************************
********************************************************************
Optimization by hand of max Torque and max Power and AFR desired
Max Torque actual
weight
1.0
0.0 Nm compared to torque desired
Max Power actual at n_toer_eind
weight
1.0
45.3 kW compared to Power output desired
AFR actual at n_toer_eind
weight
1.0
Value of functional to minimize
21.26
compared to AFR desired
245.0 Nm
66.0 kW
22.0
1099225
Elapsed time is 44.302272 seconds.
********************************************************************
********************************************************************
Simulatie Ford Mondeo 66 kW
Tddi 2.0 2001
Max torque 245 Nm at 1900 rpm
Marcel de la Fonteijne, DLF Sustainable
********************************************************************
********************************************************************
Specific air gas constant
Pressure surrounding p_surr
Temperature surrounding T_surr
Temperature surrounding T_surr
287 [J.kgK]
1.01 [bar]
20 [degrees C]
293 [K]
Relative humidity
50.0 [percent]
Max. amount water vapor in air at T_surr
13.2 [g/kg dry air]
Amount of water vapor in air at T_surr
6.6 [g/kg dry air]
Volume water vapor in air
0.008 [m3/kg air] equal to
1.1 [vol. percent]
Volume air
0.773 [m3/kg air] equal to
98.9 [vol. percent]
Specific air density 0 degr. C and 1 bar
1.293 [kg/m3]
Volume fraction of oxygen in air
0.210 []
Volume fraction of nitrogen in air
0.780 []
Volume fraction of argon in air
0.010 []
Mass fraction of oxygen in air
0.232 []
Mass fraction of nitrogen in air
0.754 []
Mass fraction of argon in air
0.014 []
Number of cylinders in engine
4 []
Number of strokes in thermodynamic cycle
4 []
Compression ratio geometric
Number of revolutions per thermo cycle
Specific air density
19.2 []
2 []
1.293 [kg/m3]
Cylinder wall temperature
120 [degrees C]
Cylinder wall temperature
393 [K]
Cylinder wall temperature Stirling 1
120 [degrees C]
Cylinder wall temperature Stirling 1
393 [K]
Cylinder wall temperature Stirling 2
120 [degrees C]
Cylinder wall temperature Stirling 2
393 [K]
Bore cylinder a
86.0 [mm]
Crank arm cylinder a
43.0 [mm]
Piston rod length cylinder a
Offset cylinder a to crank
Bore cylinder b
0.0 [mm]
86.0 [mm]
Crank arm cylinder b
Piston rod length cylinder b
Offset cylinder b to crank
Ratio speed crank b/ speed crank a
Difference in fase
172.0 [mm]
(crank a - crank b)
Stroke of piston
Ratio of stroke/bore
0.0 [mm]
172.0 [mm]
0.0 [mm]
0.50 []
90 [CA cyl b]
86 [mm]
1.0 []
Cylinder area a
5809 [mm2]
Cylinder area b
5809 [mm2]
Volume stroke per cylinder
500 [cc]
Volume stroke in engine
Pressure limit in cylinder
Spring constant
Angle for TDC in cylinder a
Volume in cylinder minimum Vd
Volume in cylinder maximum
LHV Fuel
Density of Fuel
Price of Fuel
Price of man hour and additional
Weight factor alfa1 in Wiebe function 1
1998 [cc]
500 [bar]
0.000 [m/bar] not in use
-0 [CA a]
27.448 [cc]
527.005 [cc]
42.5 [MJ/kg]
850 [kg/m3]
1.50 [€/l]
25.00 [€/l]
0.10 []
t_sigma1 in Wiebe function 1
1 [ms]
t_delay1 in Wiebe function 1
1 [ms]
Power parameter n in Wiebe function 1
2.0 []
Factor parameter a in Wiebe function 1
6.0 []
t_sigma1_acc in Wiebe function 1
Weight factor alfa2 in Wiebe function 2
0 [ms]
0.80 []
t_sigma2 in Wiebe function 2
4 [ms]
t_delay2 in Wiebe function 2
1 [ms]
Power parameter n in Wiebe function 2
2.0 []
Factor parameter a in Wiebe function 2
6.0 []
t_sigma2_acc in Wiebe function 2
Weight factor alfa3 in Wiebe function 3
2 [ms]
0.10 []
t_sigma3 in Wiebe function 3
8 [ms]
t_delay3 in Wiebe function 3
1 [ms]
Power parameter n in Wiebe function 3
2.0 []
Factor parameter a in Wiebe function 3
6.0 []
t_sigma3_acc in Wiebe function 3
3 [ms]
Maximal ignition shift
Standard deviation of add. noise in HR
Efficiency of irreversible combustion
Fuel injection max length at n_max
-40 [CA]
0 [part of signal]
1.00 []
40 [CA]
Engine Speed n max
3540 [rpm]
Power output crank desired
66.0 [kW]
Power fuel at max injection and n_max
224.7 [kW]
Engine efficiency desired
0.294 []
Air to Fuel Ratio AFR desired
22.0 []
Fuel consumption desired
288.4 [g/kWh]
Max CO2 production desired
906.4 [g/kWh]
Engine efficiency desired
0.294 []
Air to Fuel Ratio AFR desired
22.0 []
Volume efficiency VE
0.90 []
p loss compressor to compr. inlet
0.10 [bar]
p loss compressor to inletmanifold
0.20 [bar]
Heat transfer model 0=C 1= Woschni 2=H
2 []
Heat coefficient constant
1500 [W/m2K]
Heat factor Woschni
10.0 []
Heat factor Hohenberg
1.0 []
Parameter C1 Hohenberg
130.0 []
Parameter C2 Hohenberg
1.4 []
Effective area of inlet valve
350 [mm2]
Effective area of outlet valve
200 [mm2]
Angle exhaust valve start opening
140 [CA]
Exhaust valve opening duration
20 [CA]
Angle inlet valve start opening
350 [CA]
Inlet valve opening duration
Angle exhaust valve start closing
Exhaust valve closing duration
Angle inlet start closing=start calc
Inlet valve closing duration
20 [CA]
350 [CA]
20 [CA]
-140 [CA]
20 [CA]
p loss turbo inlet
0.10 [bar]
p loss turbo outlet
0.10 [bar]
Pressure inlet manifold
1.80 [bar]
Pressure outlet manifold
2.35 [bar]
Engine speed where turbo starts
1100 [rpm]
Engine speed where turbo is max at Pmax
1710 [rpm]
Turbo factor in turbo model
p loss exhaust
4 []
0.10 [bar]
Temperature outlet manifold
600 [degrees C]
Temperature outlet manifold
873 [K]
Temperature inlet manifold
25 [degrees C]
Temperature inlet manifold
298 [K]
Specific Friction in cylinder
925 [N/m]
Friction in cylinder
250 [N]
Number of step in numerical proces
4000 []
Car speed actual
90.0 [km/h]
Car speed max
Speed wheel actual
177.0 [km/h]
756 [rpm]
Engine speed actual in gear 1
9231 [rpm]
Engine speed actual in gear 2
5143 [rpm]
Engine speed actual in gear 3
3186 [rpm]
Engine speed actual in gear 4
2368 [rpm]
Engine speed actual in gear 5
1800 [rpm]
Mass car
1540 [kg]
Roll coefficient of car
0.0110 []
Steepness of road Ramp
1:ramp
0 []
Accelaration of car
0.00 [m/s2]
Gravity earth
9.81 [m/s2]
Front surface area of car
2.33 [m2]
Air resistance coefficient of car cw
0.30 []
Transmission losses
0.11 []
Power roll
4.2 [kW]
Power air
6.6 [kW]
Power up hill
0.0 [kW]
Power accelaration
0.0 [kW]
Power at wheel needed
10.7 [kW]
Power at crank needed
12.1 [kW]
Percentage Power roll
38.7 [percent]
Percentage Power air
61.3 [percent]
Percentage Power height
0.0 [percent]
Percentage Power accelaration
0.0 [percent]
Fuel consumption
3.7 [l/100km]
CO2 production
98.4 [g/km]
Fuel consumption
27.2 [km/l]
R size tire
B width of tire
H height of tire in percentage of width
16 ["]
205 [mm]
55 [procent]
Circumference of tire
1985 [mm]
Max speed of car in gear 1 at n_1_max
39.0 [km/h]
Max speed of engine in gear 1 n_1_max
4000 [rpm]
Speed of tire in gear 1 at max car speed
Gear ratio gear 1
327 [rpm]
0.082 []
Max speed of car in gear 2 at n_2_max
70.0 [km/h]
Max speed of engine in gear 2 n_2_max
4000 [rpm]
Speed of tire in gear 2 at max car speed
588 [rpm]
Gear ratio gear 2
0.147 []
Max speed of car in gear 3 at n_3_max
113.0 [km/h]
Max speed of engine in gear 3 n_3_max
4000 [rpm]
Speed of tire in gear 3 at max car speed
949 [rpm]
Gear ratio gear 3
0.237 []
Max speed of car in gear 4 at n_4_max
152.0 [km/h]
Max speed of engine in gear 4 n_4_max
4000 [rpm]
Speed of tire in gear 4 at max car speed
1276 [rpm]
Gear ratio gear 4
0.319 []
Max speed of car in gear 5 at n_5_max
177.0 [km/h]
Max speed of engine in gear 5 n_5_max
3540 [rpm]
Speed of tire in gear 5 at max car speed
1486 [rpm]
Gear ratio gear 5
Speed stationair of engine
Water_injection
Enthalpy of water injected
Water mass injected between theta h-l
0.420 []
850 [rpm]
0 [weight percent] of fuel mass
1016900 [J/kg]
0.000 [g/cycle]
Theta_water_inj_compr_laag
-140.0 [CA]
Theta_water_inj_compr_hoog
-25.0 [CA]
********************************************************************
********************************************************************
Power Fuel desired
224.7 kW
Power output desired
66.0 kW
Specific Power output desired
33.0 kW/l
Motor torque
178.0 Nm
Revolutions per minute max
3540 rpm
Air to Fuel ratio AFR desired
22.0
Cilinder fill efficiency
0.90
Fuel usage desired
288.4 g/kWh output
Fuel needed
5.287 g/s
Motor efficiency
29.4 percent
Fuel MEP
38.12 bar
Brake MEP
11.20 bar
Compression ratio real
15.5
Air flow required for air intake
0.116 kg/s
Corrected Air flow req. on Garrett map
14.175 lb/min
Manifold air pressure required
2.20 bar
p loss compr outlet to inlet manifold
0.20 bar
Compressor discharge pressure estimate
2.40 bar
Compressor discharge pressure atc
2.00 bar
p loss surrounding to compressor inlet
0.10 bar
Compressor inlet pressure
0.91 bar
Pressure ratio to search for turbo est.
2.63
Pressure ratio to search for turbo actual
2.19
Temp. end compressor before intercooler
367 K
Power Pi_compr compressor req. actual
8.5 kW
********************************************************************
********************************************************************
Power fuel begin
225 kW equal to
100 percent of Power Fuel max
Power fuel end
225 kW equal to
100 percent of Power Fuel max
Number of intervals
0
Motor speed begin interval
1800 rpm
Motor speed end interval
3540 rpm
Number of intervals
0
********************************************************************
Power fuel in at max rpm
224.7 kW
Energy fuel W per cylinder
1.90 kJ
Engine speed in rpm
1800 rpm
Height in cylinder in common
0.0 mm
Height of V minimum in cylinder
4.7 mm
V_stroke compression
499.6 cc
V_stroke expansion
499.6 cc
ratio V_stroke expansion/compression
1.0
Fuel injection start at t
-2.3 ms before CA=0
Begin of fuel injection
-25.2 CA
Theta max of fuel injection advance
-40.0 CA before CA=0
Duration of fuel injection
20.3 CA
End of fuel injection
-4.9 CA
Delta theta parameter in Wiebe function 1
10.8 CA
Pressure at begin of injection
Tau ignition delay
p,phi,T
Theta ignition delay
p,phi,T
32.25 bar
1.70 ms
18.33 CA
Temperature at begin of injection
672 K
Pressure inlet manifold absolute
1.80 bar
Pressure outlet manifold absolute
2.35 bar
EGR in wt percent of air inlet
0.0 percent
Volume in cil. when inlet valve is total closed
481.6 cc
Volume O2 in cil. when inlet valve is total closed
101.1 cc
Mass O2 per cylinder when inlet valve closed total
0.221 g
Cyl. pressure when inlet valves total closed
2.04 bar
Cyl. pressure when exhaust valves start opening
6.07 bar
Turbo begin pressure
2.25 bar
Turbo begin volume (slag) motor
2.0 liter
Turbo begin temperature
1016 K
Turbo end pressure
1.21 bar
Turbo end volume (slag) motor
3.2 liter
Turbo end temperature
348 K
Power turbo from exhaust
3.9 kW
Fuel Power max stochiometric
164.4 kW
Motor Power max stochiometric
48.3 kW
Motor torque max stochiometric
256.2 Nm
Air to Fuel ratio stochiometric AFR
14.8
Fuel usage max stochiometric, eta desired
288.4 g/kWh
Mass fuel per cylinder stochiometric
0.064 g
Mass CO2 per cylinder stochiometric
0.203 g
Fuel MEP max stochiometric
54.86 bar
Brake MEP max stochiometric
16.11 bar
Fuel MEP
Exhaust MEP
38.12 bar equal to 100.0 percent
9.83 bar equal to
25.8 percent
10.89 bar equal to
28.6 percent
Pumping MEP
0.57 bar equal to
1.5 percent
Friction MEP
1.72 bar equal to
4.5 percent
15.12 bar equal to
39.7 percent
Indicated MEP=B MEP + F MEP 16.84 bar equal to
44.2 percent
Heat Transfer cil. MEP
Brake MEP
Mass air per cylinder when inlet valve closed total
0.953 g
Mass gas per cylinder when inlet valve closed total
0.953 g
Mass flow air motor actual
0.057 kg/s
H2O injected in percentage of fuel injected
0.0 percent
Mass H2O per cylinder injected
0.000 g
Mass fuel per cylinder injected
0.045 g
Mass O2 per cylinder available
0.220 g
Mass CO2 per cylinder produced
0.141 g
Mass flow fuel injected in motor actual
2.688 g/s
Mass CO2 motor actual
8.449 g/s
Power Fuel actual
114.3 kW
Motor Power actual
45.3 kW
Power Turbo
3.9 kW
Power Compressor
4.3 kW
Motor Power Net
44.9 kW
Motor efficiency fuel to crank Net
39.3 percent
Energy exhaust minus P turbo
25.6 kW
Motor torque actual
240.5 Nm
Revolutions per minute actual
1800 rpm
Air to Fuel ratio actual AFR
21.3
Lambda desired
1.49
Lambda phi base
1.44
Lambda O2 base
1.43
Equivalence Ratio=1/lambda
0.69
Equivalence Ratio=1/lambda O2 base
0.70
Fuel usage actual
213.5 g/kWh
CO2 actual
671.1 g/kWh
Motor efficiency fuel to crank
39.7 percent
Fuel MEP max actual
38.12 bar
Brake MEP max actual
15.12 bar
p max actual
146.98 bar
Theta at p max actual
9.6 CA
T max actual
1958 K
Theta at T max actual
23.1 CA
********************************************************************
********************************************************************
Optimization by hand of max Torque and max Power and AFR desired
Max Torque actual
weight
1.0
Max Power actual at n_toer_eind
weight
1.0
AFR actual at n_toer_eind
weight
1.0
Value of functional to minimize
Elapsed time is 44.302272 seconds.
0.0 Nm compared to torque desired
45.3 kW compared to Power output desired
21.26
1099225
compared to AFR desired
245.0 Nm
66.0 kW
22.0
specific fuel consumption in [g/kWh output]
fig.1 Fuel comsumption as a function of the engine efficiency with par. LHV Fuel in MJ/kg
600
30.0
550
32.5
35.0
500
37.5
40.0
450
42.5
45.0
400
47.5
50.0
350
52.5
300
55.0
42.5
250
200
150
100
0.2
0.25
0.3
0.35
0.4
0.45
engine efficiency
0.5
0.55
0.6
0.65
fig. 9a Specific heat of air at constant pressure as a function of temperature
c p lucht [J/kgK]
2500
1000
air
N2
O2
CO2
H2O
Argon
mix
3000
3500
1000
air
N2
O2
CO2
H2O
Argon
mix
3000
3500
2000
1500
1000
500
0
500
1500
2000
2500
temp [K]
fig. 9b Specific heat of air at constant volume as a function of temperature
c v lucht [J/kgK]
2000
1500
1000
500
0
0
500
1500
2000
temp [K]
2500
fig. 10a Adiabatic index of air as a function of temperature
1.8
air
N2
O2
CO2
H2O
Argon
mix
1.7
kappa lucht []
1.6
1.5
1.4
1.3
1.2
1.1
0
500
1000
1500
2000
temp [K]
2500
3000
3500
fig. 66a Adiabatic index of air as a function of CA
1.4
1.38
kappa gas mix []
1.36
1.34
1.32
1.3
1.28
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 66b Specific Gas constant of mixture in cylinder as a function of CA
288.5
specific gas constant R mix [J/kgK]
288.45
288.4
288.35
288.3
288.25
288.2
288.15
288.1
288.05
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 64 Max and actual water vapor in air as a function of temperature
1200
water vapor [g/kg air]
1000
800
600
400
200
0
0
10
20
30
40
50
temp [degrees C]
60
70
80
90
fig. 11 Valves timing diagram
1
0.9
0.8
kleppen diagram
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-200
-100
0
100
200
300
theta in CA of cil 1
400
500
600
fig. 12 Piston speed as a function of CA
10
8
6
Piston speed [m/s]
4
2
0
-2
-4
-6
-8
-10
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 13 Relative Heat Release as a function of CA
1
mass water injection rel.
mass fuel injection rel.
Wiebe 1 heat release
Wiebe 2 heat release
Wiebe 3 heat release
Wiebe heat release
Relative Heat release,injection curve [/CA]
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
heat release,inj. curve,burn rate, heat transf. to cil., friction heat and tot. heat in [J/CA]
fig. 14a Fuel Injection and Heat Release as a function of CA
80
fuel injection curve
gross fuel heat release
Wiebe heat release
cylinder heat transfer
friction loss
net heat release
70
60
50
40
30
20
10
0
-10
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 14b Heat Release as a function of CA
Power heat release,injection curve, burn rate in [J/CA]
80
fuel injection curve
gross fuel heat release
Wiebe heat release
70
60
50
40
30
20
10
0
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 14c Friction power
0.2
friction loss
0.18
0.16
friction heat [J/CA]
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
500
600
fig. 15a Heat Release coëfficient as a function of CA
3500
Heat coeefficient h in [W/m2K]
3000
2500
2000
1500
1000
500
0
-200
-100
0
100
200
300
angle theta [degrees CA]
400
-4
6
fig. 16 Cilinder Volume as a function of CA
x 10
5
a
V en V dapt [m3]
4
3
2
1
0
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 17 Work per cylinder generated as a function of CA
25
20
15
dW [J/CA]
10
5
0
-5
-10
-15
-20
-25
-100
0
100
200
300
400
angle theta [degrees CA]
500
600
700
V [m3]
npoly []
W wrijving [J/CA] dWi [J/CA]
dWi2 [J/CA]
dW [J/CA]
mass in volume [g]
V [m3]
-3
-3
fig. 18 xCilinder
Volume as a function of timefig. 19x Cilinder
Volume as a function of CA
10
10
1
1
0.5
0.5
0
0
0
0.02
0.04
0.06
0.08
-200
0
200
400
600
time [s]
angle theta [degrees CA]
fig. 20 Mass in Cilinder Volume as a function
fig. 21
of Work
CA per cylinder generated as a function of CA
2
20
1
0
-20
0
-200
0
200
400
600
0
200 400 600
angle theta [degrees CA]
angle theta [degrees CA]
fig. 22 Indicator Work Wi per cylinder generated
fig. 23as
Indicator
a function
Work
of CA
Wi2 per cylinder generated as a function of CA
20
20
0
0
-20
-20
0
200 400 600
0
200 400 600
angle theta [degrees CA]
angle theta [degrees CA]
fig. 24 Friction Loss per cylinder generated as a function
fig. 25 Polynome
of CA
coëfficient as a function of CA
0
2
-0.1
0
-2
-0.2
-200
0
200
400
600
0
200 400 600
angle theta [degrees CA]
angle theta [degrees CA]
fig. 26 Pressure in cylinder as a function of CA
150
p
p max
T max
water injection start
water injection end
fuel injectection start
fuel injection end
p [bar]
100
50
0
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 27 Temperature in cyl. and T cyl. wall as a function of CA
2000
T cylinder
T cylinder wall
p max
T max
water injection start
water injection end
fuel injectection start
fuel injection end
1800
1600
T in [K]
1400
1200
1000
800
600
400
200
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
500
600
fig. 28a Mass in Cilinder Volume as a function of CA
1.4
1.2
mass in volume [g]
1
0.8
0.6
0.4
0.2
0
-200
-100
0
100
200
300
angle theta [degrees CA]
400
fig. 28b Mass flow out of exhaust as a function of CA
0
-0.004
-0.006
-0.008
-0.01
-0.012
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
fig. 28c Mass of gas components in Cilinder Volume as a function of CA
0.8
N2
O2
Argon
H2O
CO2
0.7
0.6
mass in volume [g]
mass in volume [g/s]
-0.002
0.5
0.4
0.3
0.2
0.1
0
-0.1
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
mass in volume [percent]
fig. 28d Relative Mass of gas components in Cilinder Volume as a function of CA
80
N2
70
O2
Argon
H2O
60
CO2
50
40
30
20
10
0
-10
-200
-100
0
100
200
300
angle theta [degrees CA]
400
500
600
500
600
fig. 29 Net Heat Release as a function of CA
70
60
50
q net [J/CA]
40
30
20
10
0
-10
-200
-100
0
100
200
300
angle theta [degrees CA]
400
fig. 30a pV diagram
150
pV
exhaust open
exhaust open total
inlet open
inlet open total
exhaust close
exhaust close total
inlet close
inlet close total
intersection
p max
T max
water injection start
water injection end
fuel injectection start
fuel injection end
p [bar]
100
50
0
0
1
2
3
V adapt [m3]
4
5
6
-4
x 10
fig. 30b pV diagram
2.2
pV
exhaust open
exhaust open total
inlet open
inlet open total
exhaust close
exhaust close total
inlet close
inlet close total
intersection
p max
T max
water injection start
water injection end
fuel injectection start
fuel injection end
2
1.8
log(p) [bar]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
2
3
V adapt [m3]
4
5
6
-4
x 10
fig. 31 TS diagram
2000
ST
exhaust open
exhaust open total
inlet open
inlet open total
exhaust close
exhaust close total
inlet colse
inlet close total
intersection
intersection
p max
T max
water injection start
water injection end
fuel injectection start
fuel injection end
1800
1600
T in [K]
1400
1200
1000
800
600
400
200
0
200
400
600
S [J/kgK]
800
1000
1200

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