CI Engine Case Study [Tractor Application]
Accurate analysis and modeling have been conducted on a tractor engine for use in India. Starting from the target values, given by the challenge, two cases were analyzed: intermediate case (which corresponds maximum torque) and rate case (which corresponds maximum power).
RATE CASE INTERMEDIATE CASE
rpm: 2200 rpm: 1300
Maximum Power: 56 kW=75 HP Power: 40 kW=53.6 HP
*Torque: 243 Nm **Maximum Torque: 292 Nm
BSFC: 210 g/kWh BSFC: 210 g/kWh
A/F: 25 A/F: 22
* Torque at the "Rate case" was calculated in this way:
P: power; T: torque; ω: angular speed; n: rpm
P=T⋅ωT⋅ω
T=Pω=P⋅602⋅π⋅nT=Pω=P⋅602⋅π⋅n
**Maximum Torque at the "Intermediate case"
This value was calculated as suggested from the challenge: maximum torque is around 20% more than rated torque.
To reach target values, different models were implemented, following these steps:
1) Naturally aspirated CI engine, SOHC, 4 in-line cylinders, 4 strokes, direct injection;
2)Naturally aspirated CI engine, DOHC, 4 in-line cylinders, 4 strokes, direct injection;
3) Turbocharged CI engine; DOHC; 4 in-line cylinders, 4 strokes, direct injection.
Let's analyze all these steps and how to reach target values.
STEP 1) Naturally aspirated CI engine, SOHC, 4 in-line cylinders, 4 strokes, direct injection
The building of the final model started from the one found in the following directory of the software: "Tutorials" - "Modeling_Applications" - "Engine_Performance" - "01-1cylDIorSI"-"1cylDI-final".
Immediately the model was modified, considering 4 cylinders with only one intake-valve and exhaust-valve for each one, obtaining the following configuration:
The environment inlet and outlet conditions were the same:
From the beginning of the building of the model, the length intake and exhaust ducts were not chosen accurately, without trying to increase the volumetric efficiency with the resonance effect of the fluid, with the awareness that the engine would be turbocharged in the final model, losing all the resonance effect linked to the length of the ducts. For this reason, looking at different GTP models of the software, arbitrary lengths were chosen.
One of the most important parts of the model was the "engine". In fact, cylinder geometry was accurately analyzed: starting from the equation of power, and based on the max torque condition, the total displacement of the engine was calculated
V=P⋅60⋅ε⋅αρ⋅n⋅λ⋅Hi⋅ηg=3880cm3V=P⋅60⋅ε⋅αρ⋅n⋅λ⋅Hi⋅ηg=3880cm3
where:
V: total displacement of the engine;
P: Power=40 kW
ε: number of the rounds that the crank-shaft must complete for a thermodynamic cycle of the engine. In this case, considering a 4 stroke engine, this value is 2
α: air to fuel ratio=22
ρ: density of the ambient air 1.225kgm31.225kgm3
n: speed of the engine =1300 rpm
λ: volumetric efficiency=0.95
Hi: lower calorific power =44.4MJKg44.4MJKg (Diesel)
ηg: global efficiency of the engine=38.6%
Global efficiency of the engine was calculated considering the following expression:
ηg=Hi⋅BSFCηg=1Hi⋅BSFC
Considering a naturally aspirated engine, BMEP must be controlled. In fact, this value should not exceed 8 bar. So, considering the value of total displacement obtained by the past equation, BMEP was calculated:
BMEP=2⋅π⋅ε⋅MV=9.4barBMEP=2⋅π⋅ε⋅MV=9.4bar
For a naturally aspirated engine, this value was too high and for this reason, the total displacement of the engine was recalculated, starting from the last equation and considering a BMEP=8 bar.
V=2⋅π⋅ε⋅MBMEP=4586cm3V=2⋅π⋅ε⋅MBMEP=4586cm3
So, after calculations, a new value of total displacement of the engine and global efficiency were found:
Total displacement: 4.586 L
Global efficiency: 34.27 % (acceptable value for CI tractor engine)
After that, was necessary to define the geometry of cylinders. Generally, this type of engine is characterized by low BSFC, so high global efficiency, high thermal efficiency, and very high torque, even at low loads. Starting from these considerations, the best type of engine for this application is an undersquare engine, having a stroke bigger than the bore. After different researches on the web, one of the most used Stroke/Bore ratio is 1.2, for tractor engines. In this way, considering the following equations, the cylinder geometry was defined:
Single displacement=1.14668 L
So:
V=π⋅c⋅D24cD=1.2{V=π⋅c⋅D24cD=1.2
Obtaining:
D=106.755 mm
c=128.106 mm
To complete the cylinder geometry, the compression ratio and the connecting rod length were defined.
For the first one a value of 18:1 was chosen, considering that's a CI engine and reading different articles on the web.
In the end the "connecting rod length" was chosen, generally considered as two times the stroke, to allow the connecting rod could move inside a little angle θθ around the axis parallel to the stroke.
The last part of the model analyzed was injectors. To define the pressure profile of the fuel injected inside the cylinders was chosen a different GTP object, called: "InjProfileConn". For both cases analyzed, the mass flow injected was calculated and used in the model:
Intermediate case
1300 rpm = 21.6 rps
fuel mass flow rate = Power*BSFC = 8.4kgh8.4kgh= 2.333⋅10−32.333⋅10-3(kg)/s`
⋅106⋅106 = 2333.33 mg/s
:rps=108.024mground:rps=108.024mground
*2 = 216.049 mg/cycle
:4=54.012mgcyl:4=54.012mgcyl
So, the injected fuel mass is: 54.01 mg
Considering an A/F ratio of 22, the corresponding air mass flow rate is:
air mass flow rate = (A/F ratio)*fuel mass flow rate = 22*8.4 kg/h =184.8 kg/h
As the previous case, the same passages were followed for the rate case:
2200 rpm = 36.66 rps
fuel mass flow rate = Power*BSFC = 11.76kgh11.76kgh = 3.266⋅10−33.266⋅10-3(kg)/s`
⋅106⋅106 = 3266.66 (mg)/s`
:rps=89.107mground:rps=89.107mground
⋅2=178.214mgcyc≤⋅2=178.214mgcyc≤
:4=44.553mgcyl:4=44.553mgcyl
So, the injected fuel mass is: 44.553 mg
Considering an A/F ratio of 22, the corresponding air mass flow rate is:
air mass flow rate = (A/F ratio)*fuel mass flow rate = 25*11.76 kg/h =315 kg/h
For both the following pressure profile of the injected fuel was considered:
Then to maximize the air mass flow that enters inside cylinders, a totally new lift law for the inlet and exhaust valve was defined. To value the correct timing and lift law of the valves, in GT-POST the "valve mass flow and lift" was analyzed, obtaining the following improvements in terms of air trapped inside the cylinder:
1300 rpm - too much reflux of air at the end of the intake phase
1300 rpm - very low reflux of the air at the end of the intake phase
2200 rpm - too much reflux of air at the end of the intake phase
2200 rpm - very low reflux of the air at the end of the intake phase
Below is reported the new crank angle array for the lift used to obtain the improvements shown on the air mass flow rate trapped inside cylinder:
Intake Exhaust
| -161 | -136 |
| -159 | -134 |
| -157 | -132 |
| -155 | -130 |
| -153 | -128 |
| -151 | -126 |
| -149 | -124 |
| -147 | -122 |
| -145 | -120 |
| -143 | -118 |
| -141 | -116 |
| -139 | -114 |
| -137 | -112 |
| -135 | -110 |
| -133 | -108 |
| -131 | -106 |
| -129 | -104 |
| -127 | -102 |
| -125 | -100 |
| -123 | -98 |
| -121 | -96 |
| -119 | -94 |
| -117 | -92 |
| -115 | -90 |
| -113 | -88 |
| -111 | -86 |
| -109 | -84 |
| -107 | -82 |
| -105 | -80 |
| -103 | -78 |
| -101 | -76 |
| -99 | -74 |
| -97 | -72 |
| -95 | -70 |
| -93 | -68 |
| -91 | -66 |
| -89 | -64 |
| -87 | -62 |
| -85 | -60 |
| -83 | -58 |
| -81 | -56 |
| -79 | -54 |
| -77 | -52 |
| -75 | -50 |
| -73 | -48 |
| -71 | -46 |
| -69 | -44 |
| -67 | -42 |
| -65 | -40 |
| -63 | -38 |
| -61 | -36 |
| -59 | -34 |
| -57 | -32 |
| -55 | -30 |
| -53 | -28 |
| -51 | -26 |
| -49 | -24 |
| -47 | -22 |
| -45 | -20 |
| -43 | -18 |
| -41 | -16 |
| -39 | -14 |
| -37 | -12 |
| -35 | -10 |
| -33 | -8 |
| -31 | -6 |
| -29 | -4 |
| -27 | -2 |
| -25 | 0 |
| -23 | 2 |
| -21 | 4 |
| -19 | 6 |
| -17 | 8 |
| -15 | 10 |
| -13 | 12 |
| -11 | 14 |
| -9 | 16 |
| -7 | 18 |
| -5 | 20 |
| -3 | 22 |
| -1 | 24 |
| 1 | 26 |
| 3 | 28 |
| 5 | 30 |
| 7 | 32 |
| 9 | 34 |
| 11 | 36 |
| 13 | 38 |
| 15 | 40 |
| 17 | 42 |
| 19 | 44 |
| 21 | 46 |
| 23 | 48 |
| 25 | 50 |
| 27 | 52 |
| 29 | 54 |
| 31 | 56 |
| 33 | 58 |
| 35 | 60 |
| 37 | 62 |
| 39 | 64 |
| 41 | 66 |
| 43 | 68 |
| 45 | 70 |
| 47 | 72 |
| 49 | 74 |
| 51 | 76 |
| 53 | 78 |
| 55 | 80 |
| 57 | 82 |
| 59 | 84 |
| 61 | 86 |
| 63 | 88 |
| 65 | 90 |
| 67 | 92 |
| 69 | 94 |
| 71 | 96 |
| 73 | 98 |
| 75 | 100 |
| 77 | 102 |
| 79 | 104 |
| 81 | 106 |
| 83 | 108 |
| 85 | 110 |
| 87 | 112 |
| 89 | 114 |
| 91 | 116 |
| 93 | 118 |
| 95 | 120 |
| 97 | 122 |
| 99 | 124 |
| 101 | 126 |
| 103 | 128 |
| 105 | 130 |
| 107 | 132 |
| 109 | 134 |
| 111 | 136 |
| 113 | 138 |
| 115 | 140 |
| 117 | 142 |
| 119 | 144 |
| 121 | 146 |
| 123 | 148 |
| 125 | 150 |
| 127 | 152 |
| 129 | 154 |
| 131 | 156 |
| 133 | 158 |
| 135 | 160 |
| 137 | 162 |
| 139 | 164 |
| 141 | 166 |
| 143 | 168 |
| 145 | 170 |
| 147 | 172 |
| 149 | 174 |
| 151 | 176 |
After all these changes from the first model considered, was necessary to change injection timing and the values of the "combustion object" inside the cylinders, as shown below:
(all these values were obtained after different and different simulations)
Injection timing
Nozzle hole diameter and number of holes per nozzle
Combustion object
So, after the definition of every single parameter of this first model, the results obtained were:
Intermediate case - 1300 rpm
The percentage differences from the target values are:
Brake Power: 37.5−4037.5[kW]⋅100=−6.66%37.5-4037.5[kW]⋅100=-6.66%
Brake Torque: 275.8−292275.8[Nm]⋅100=−5.8%275.8-292275.8[Nm]⋅100=-5.8%
Air flow rate: 168.8−184.8168.8[kgs]=−9.47%168.8-184.8168.8[kgs]=-9.47%
Fuel flow rate: 8.4−8.48.4⋅100=0%8.4-8.48.4⋅100=0%
BFSC: 224.4−210224.4⋅100=+6.41%224.4-210224.4⋅100=+6.41%
A/F ratio: 20.03−2220.03=−9,83%20.03-2220.03=-9,83%
Rate case - 2200 rpm
The percentage differences from the target values are:
Brake Power: 53.3−5653.3[kW]⋅100=−5.06%53.3-5653.3[kW]⋅100=-5.06%
Brake Torque: 231.4−243231.4[Nm]⋅100=−5.01%231.4-243231.4[Nm]⋅100=-5.01%
Air flow rate: 291.7−315291.7[kgs]=−7.98%291.7-315291.7[kgs]=-7.98%
Fuel flow rate: 12.6−11.7612.6⋅100=6.66%12.6-11.7612.6⋅100=6.66%
BSFC:BSFC:(236.4-210)/(236.4)*100=11.04%`
AFratio:AFratio:(23.15-25)/(23.15)=-7.99%`
This could be considered as a very good simulation because every percentage difference is under 15%, always under 10% except for one parameter in one case. But improving this model is possible to reach the target values of the challenge.
STEP 2) Turbocharged CI engine, DOHC, 4 in-line cylinders, 4 strokes, direct injection
To reach the targets the model has been improved with different new elements. At first, to increase the air mass flow rate entering inside cylinders the nature of the engine changed, passing from "naturally aspirated" to "turbocharged", and so using a DOHC system. For this reason, the inlet environment condition (so the condition of the air after the compressor) and the outlet environment condition (condition of the exhaust gases before entering into the turbine) changed, and an intercooler was added, to cool the inlet air after the compression, and so to increase its density. Below that's the complete model:
Inlet environment parameters:
Outlet environment parameters:
Case setup, in which were defined: inlet pressure, outlet pressure, injected fuel mass and brake torque target for every case runned.
To control the quantity of fuel to obtain exactly the target values of torque and power, an "injector controller" was added to the model. In this using as input parameter the rpm of the engine, the inlet air mass flow, and the brake torque target value, it was possible to control the exact quantity of fuel to inject in every cylinder.
So, the results obtained are presented below:
Intermediate case - 1300 rpm
The percentage differences from the target values are:
Brake Power: 39.8−4039.8[kW]⋅100=−0.5%39.8-4039.8[kW]⋅100=-0.5%
Brake Torque: 292.1−292292.1[Nm]⋅100=0.03%292.1-292292.1[Nm]⋅100=0.03%
Air flow rate: 204.6−184.8204.6[kgs]=9.67%204.6-184.8204.6[kgs]=9.67%
Fuel flow rate: 8.4−8.48.4⋅100=0%8.4-8.48.4⋅100=0%
BSFC:BSFC:(212-210)/(212)*100=0.94%`
AFratio:AFratio:(24.27-22)/(24.27)=9.35%`
Rate case - 2200 rpm
The percentage differences from the target values are:
Brake Power: 56−5656[kW]⋅100=0%56-5656[kW]⋅100=0%
Brake Torque: 243−243243[Nm]⋅100=0%243-243243[Nm]⋅100=0%
Air flow rate: 312.8−315312.8[kgs]=−0.70%312.8-315312.8[kgs]=-0.70%
Fuelflowrate:Fuelflowrate:(11.5-11.76)/(11.5)*100=-2.26%`
BSFC:BSFC:(204.5-210)/(204.5)*100=2.68%`
AFratio:AFratio:(27.32-25)/(27.32)=8.49%`
So it's possible to define that target values were reached, considering that the maximum error is 9.67%.
STEP 3) Turbocharged CI engine, DOHC, 4 in-line cylinders, 4 strokes, direct injection, with cooled EGR
The last part of the challenge asked to use a cooled EGR in the model. The EGR is acronymous of "exhaust gas recirculation", and it's an operation used to reduce one of the most important pollutants: a family called NOx. These elements could generate in two different ways: the first one is called "prompt NOx", and the formation of this pollutant derives from the oxygen and nitrogen present in the inlet air; the second one is called "thermal" and defines that this pollutant borns at the higher temperature, in which oxygen and nitrogen are very reactive, and they create NOx. The EGR is a very useful technique because thanks to the recirculation of a part of the exhaust gases, used as inlet air inside the cylinder, is possible to decrease the combustion temperature and so the formation of NOx. In the model, an EGR circuit has been used. In particular an "EGR valve controller" was used to control the opening of this valve, to permit only a certain quantity of exhaust to recirculate. The system is very simple because it doesn't use a pump, but gases are recirculated only using a delta pressure between exhaust gases and inlet air.
and after different simulations, an EGR value was chosen for every studied case:
1300 rpm - 15% of EGR
2200 rpm - 25% of EGR
Obtaining the following results, compared to the previous model without EGR:
Intermediate case - 1300 rpm
NO EGR
WITH EGR
Rate Case - 2200 rpm
NO EGR
WITH EGR
So, it's visible that using the EGR inside the model the maximum temperature inside cylinders decreases, and that's a decreasement of the NOx, as expected.