CASE STUDY: Effect of Fuel Burn Rates on Engine Performance Of A 6-Cyl-Turbocharged-DI Engine Using A Non-predictive Combustion model (DI WIEBE)


CASE STUDY: Effect of Burn Rate on engine performance Of A 6-Cyl-Turbocharged-DI Engine Using A Non-predictive Combustion model (DI WIEBE)

Abstract: Analytical functions approximating the burn rate in internal combustion engines are useful and cost-effective tools for engine cycle simulations. Most functions proposed todate are based on the law of normal distribution of a continuous random variable. The best known of these is the Wiebe function, which is used to predict the burn fraction and burn rate in internal combustion engines operating with different combustion systems and fuels. These include direct injection (DI) and indirect injection (IDI) diesel engines, classical spark ignition (SI) engines and gasoline direct injection (GDI) engines, engines with homogeneous charge compression ignition (HCCI) and premixed charge compression ignition (PCCI).

Literature Review Of Ivan Ivanovitch Wiebe

The use of continuous mathematical functions provides a fast and cost-effective technique for the prediction of the burn rate and performance of internal combustion engines. These functions are usually derivatives of the normal distribution of a continuous random variable and the best known among them is the Wiebe function. The function has now become so common that researchers in many parts of the world have stoped citing the source(s) from which it originates, and there is still some confusion about whether it should be referred to as the Wiebe, Weibe, Vibe, or Viebe function. An interesting example of this confusion can be found in a Russian translation of an SAE paper [1] where the function is referred to by its literal English/German variant ‘VIBE’ instead of its original Cyrillic spelling ‘B e’. For such a widely used and cited function, little is known about the man behind its introduction, Ivan Ivanovitch Wiebe. Ivan Wiebe was a Russian engineer
and scientist from the Urals of German descent. He was born in the Ukraine in 1902, finished his undergraduate studies in 1926 while simultaneously working as a mechanic, then enrolled in the postgraduate programme at the Leningrad Engineering Institute of Civil Aviation where he was awarded the degree of ‘Candidate of Technical Sciences’ (equivalent to engineering doctorate) in 1932 for his thesis titled Theoretical investigation of the processes in diesel engines with solid-injection. Wiebe published a monograph  detailing the results of his work on the development of the combustion function bearing his name while working at the Chilyabinsk Politechnic Institute (currently known as the South Ural State University) where he also briefly headed the department of internal combustion engines, before his death in 1969


Combustion:   Combustion in GT-Power is refered as the instantaneous rate of air-fuel mixture and their associated enthalpies transfered from unburned to burned zone in the cylinder. The release of chemical energy stored in the fuel into  thermal energy. The types of Combustion model available in GT-Power. 




GT-Suite is one of the most popular engine simulation software developed by Gamma Technologies. It is predominantly a 1D simulation tool with many sub programs with their own area of expertise.

GT-Power is used to study the gas exchange and combustion simulations from an overall system perspective. The solver is based on 1D unsteady, nonlinear Navier-Stokes equation. It contains thermodynamic and phenomenological models to capture the effects of combustion, heat transfer, evaporation, turbulence, tailpipe out emissions, etc.

There are two kinds of combustion models in GT-Power:

  1. Non predictive combustion model.
  2. Predictive Combustion model.
  • Non-predictive Combustion Model:

In a Non predictive combustion model as the name suggests the burn rate is imposed and does not depend on the in cylinder conditions to characterize the combustion and emission related parameters . The major benefit of this model is fast simulation time and is useful for evaluating concepts which do not have an impact on the burn rate characteristics . For example, this kind of model can be used to study the wave dynamics, boosting concepts and exhaust configurations to name a few. However it would not be accurate to study phenomenon such as EGR, injection timing, etc.

  • Predictive Combustion Model:

In a predictive combustion model, the burn rate is calculated for each cycle based on the in cylinder conditions. This leads to a longer simulation time compared to the non-predictive model however, it is useful to study the concepts that have an impact on the burn rate such as different injection timings, EGR and various injection profiles (GT-Suite, 2013). In order to obtain accurate predictions, the model must be calibrated initially against test data. Phenomenological predictive combustion models make use of a concept known as zone modelling in which, the combustion is modelled to take place in single or multiple zones

Types of Combustion models on the basis of Zones:

  • One-Zone Combustion Model: A combustion model consisting of only a single overall zone. 'EngCylCombHCCI' is the only one-zone combustion model.
  • Two-zone Combustion Model: A combustion model with two distinct zones – unburned and burned. All combustion models in GT-POWER are two-zone except for 'EngCylCombHCCI', 'EngCylCombDIPulse' and 'EngCylCombDIJet'. The two zones are normally modeled with a separate temperature for each zone, but can optionally be specified to have the same temperature.
  • Multi-Zone Combustion Model: A combustion model with several unburned and burned zones, each with a separate temperature. The predictive diesel model 'EngCylCombDIPulse' employs 3 zones: the main unburned zone, the spray unburned zone, and the spray burned zone. The predictive diesel model 'EngCylCombDIJet' employs up to 500 main zones. Each of these main zones contains three sub-zones for unburned liquid fuel, unburned air-fuel mixture, and burned gas.

Two-Zone Combustion Methodology

  • This section will provide details on the combustion calculations that occur during two-zone combustion.
  • Two-zone combustion applies to all GT-POWER combustion models except for 'EngCylCombHCCI' and the predictive diesel models 'EngCylCombDIPulse' and 'EngCylCombDIJet'.

The combustion in GT-power takes place in the following manner:-

  1. At the start of combustion or at the start of fuel injection in CI engine,the cylinder is divided into two zones: an unburned zone and a burned zone. All of the contents of the cylinder at that time start in the unburned zone.
  2. At each time step, a mixture of fuel and air is transferred from the unburned zone to the burned zone. The amount of fuel-air mixture that is transferred to the burned zone is defined by the Burn rate. This  burn rate is calculated in combustion process.
  3. Once the unburned fuel and associated air has been transferred from the unburned zone to the burned zone in a given time step, a chemical equilibrium calculation is carried out for the entire "lumped" burned zone. This calculation takes into account all of the atoms of each species (C, H, O, N, S, Ar) present in the burned zone at that time, and obtains from these an equilibrium concentration of the 13 products of combustion species (N2, O2, H2O, CO2, CO, H2, N, O, H, NO, OH, SO2, Ar). The equilibrium concentrations of the species depend strongly on the current burned zone temperature and to a lesser degree, the pressure.
  4. Once the new composition of the burned zone has been obtained, the internal energy of each species is calculated. Then, the energy of the whole burned zone is obtained by summation over all of the species. Applying the principle that energy is conserved, the new unburned and burned zone temperatures and cylinder pressure are obtained.

The Energy conservation equation is given as:


Similarly, for the BURNED ZONE:

"b" subscript means burned zone.


Non-predictive Combustion Model  (DI WIEBE):

  • The non-predictive combustion model used for the case study is  "DI Wiebe"
  • Direct-Injection Diesel Wiebe Model:
  • In this model, Heat input is taken as constant, not affected by any other parameters like rail pressure, injected fuel mass etc. It uses 3-term Wiebe function (the superposition of three normal Wiebe curves). These Wiebe curves approximate the "typical" shape of a DI compression ignition, single main injection burn rate. The purpose of using three functions is to make it possible to model the premixed and diffusion portions of the combustion process.
  • This combustion model should be used only when the injection is done directly into the cylinder.

The WIEBE equation is given below as:


  1. SOI    = Start Of Injection.
  2. ID      = Ignition Delay.
  3. D(p)   = Pre-Mix Duration.
  4. D(m)  = Main Duration.
  5. D(T)   = Tail Duration.
  6. F(p)    =  Pre-Mix Fraction.
  7. F(T)    =  Tail Fraction.
  8. E(p)    =  Premix -Exponent.
  9. E(M)    =  Main Exponent.
  10. E(T)    =  Tail Exponent.
  11. CE      =  Fraction Of Fuel Burned (" Combustion Effeciency").


Calculated Constants:

Burn Rate Calculation:




1-D model Of 6-Cyl-Turbocharged-DI-Engine In GT-Power


A Brief Description Of The Above Model:


  1. It is a 4-stroke, 6-stroke and 11.7L with trubocharged configuration Engine.
  2. Per cylinder has 3-ports( 1-Inlet and 2-exhaust).
  3. The engine runs at "Speed" mode to achieve a desired power requirement.
  4. The Combustion Model used here is a "Non-predictable (DI WIEBE)") model.
  5. The Heat transfer model used is "Woschni GT" model and the in-cylinder temperature are predefined.
  6. Emission Models are ignored.
  7. The simulation will run till it attains the convergence value within maximum simulation cycles.
  8. The Convergence criteria is set to RLT target value of "MAX_BRAKE_POWER" which is  defined for each cases. The simulation will try to converge the "RLT variable" by constantly checking with Target steady state RLT convergence value along with other convergence criteria within the maximum simulation time period.
  9. The steady state Tolerance is set to 0.2%. 
  10. The solver type used is " Explicit Runge-Kutta of 5th order approximation" is used.
  11. The solution Matrix optimization algorithm used is " Cuthill-Mckee".
  12. The fuel injection is controlled using an injection controller.


  1. The inlet system is set to ambient pressure and temperature (1bar & 298K) before entering the Turbocharger.
  2. It uses a smooth 'Bellmouth' orifice in which both the forward and backward coefficient of discharge is set to('def = 1').


  1. A "Radial" type compressor is used to model the turbocharger in which the reference temperature and pressure is set to ambient inlet condition.
  2. The compressor is of fixed geometry i.e.,( rack position = 1).The compressor map contains the datas (arrays) regarding different pressure ratios and efffeciencies at diffferent mass flow rate and compressor speed corrosponding for a particular rack position.
  3. Similary, the turbine is also of fixed geometry i.e.,(rack position = 1) where  the turbine characteristics (datas) are mapped  using "TURBOSAE"


TEST DATA for Apparent BURN RATE (Default experimental data in  GT-Suite)

Experimental Values  
THETA Burn Rate
-109.990 0.000
-108.977 0.000
-107.961 0.000
-106.948 0.000
-105.936 0.000
-104.915 0.000
-103.883 0.000
-102.852 0.000
-101.820 0.000
-100.789 0.000
-99.758 0.000
-98.728 0.000
-97.697 0.000
-96.677 0.000
-95.669 0.000
-94.660 0.000
-93.649 0.000
-92.637 0.000
-91.624 0.000
-90.610 0.000
-89.595 0.000
-88.580 0.000
-87.564 0.000
-86.547 0.000
-85.528 0.000
-84.508 0.000
-83.486 0.000
-82.462 0.000
-81.436 0.000
-80.409 0.000
-79.379 0.000
-78.349 0.000
-77.327 0.000
-76.315 0.000
-75.312 0.000
-74.317 0.000
-73.330 0.000
-72.347 0.000
-71.369 0.000
-70.395 0.000
-69.426 0.000
-68.462 0.000
-67.501 0.000
-66.544 0.000
-65.589 0.000
-64.637 0.000
-63.688 0.000
-62.742 0.000
-61.799 0.000
-60.862 0.000
-59.929 0.000
-59.000 0.000
-58.075 0.000
-57.153 0.000
-56.235 0.000
-55.320 0.000
-54.408 0.000
-53.499 0.000
-52.593 0.000
-51.689 0.000
-50.785 0.000
-49.883 0.000
-48.980 0.000
-48.078 0.000
-47.176 0.000
-46.272 0.000
-45.367 0.000
-44.459 0.000
-43.547 0.000
-42.631 0.000
-41.710 0.000
-40.785 0.000
-39.855 0.000
-38.922 0.000
-37.983 0.000
-37.041 0.000
-36.093 0.000
-35.139 0.000
-34.180 0.000
-33.252 0.000
-32.322 0.000
-31.392 0.000
-30.459 0.000
-29.526 0.000
-28.592 0.000
-27.656 0.000
-26.720 0.000
-25.782 0.000
-24.842 0.000
-23.901 0.000
-22.957 0.000
-22.010 0.000
-21.060 0.000
-20.105 0.000
-19.146 0.000
-18.180 0.000
-17.209 0.000
-16.232 0.000
-15.250 0.000
-14.263 0.000
-13.272 0.000
-12.278 0.000
-11.281 0.000
-10.281 0.000
-9.279 0.000
-8.274 0.000
-7.268 0.000
-6.261 0.000
-5.253 0.000
-4.245 0.000
-3.236 0.000
-2.228 0.000
-1.221 0.000
-0.214 0.000
0.792 0.000
1.797 0.000
2.803 0.006
3.808 0.009
4.813 0.007
5.817 0.007
6.821 0.008
7.825 0.010
8.830 0.012
9.835 0.014
10.348 0.015
11.354 0.016
12.360 0.018
13.366 0.020
14.371 0.021
15.376 0.022
16.380 0.024
17.384 0.025
18.388 0.026
19.395 0.027
20.403 0.027
21.414 0.028
22.427 0.028
23.442 0.029
24.459 0.029
25.477 0.029
26.496 0.029
27.515 0.029
28.536 0.028
29.558 0.028
30.582 0.027
31.608 0.026
32.635 0.025
33.663 0.024
34.692 0.023
35.722 0.022
36.754 0.021
37.787 0.020
38.822 0.019
39.858 0.018
40.896 0.017
41.938 0.016
42.982 0.015
44.030 0.013
45.066 0.012
46.090 0.011
47.107 0.011
48.120 0.010
49.129 0.009
50.135 0.008
51.139 0.007
52.141 0.007
53.144 0.006
54.148 0.005
55.153 0.005
56.159 0.004
57.167 0.004
58.175 0.004
59.180 0.003
60.184 0.003
61.185 0.003
62.186 0.002
63.186 0.002
64.185 0.002
65.184 0.002
66.182 0.001
67.180 0.001
68.179 0.001
69.178 0.001
70.178 0.001
71.178 0.001
72.180 0.001
73.182 0.001
74.185 0.001
75.189 0.001
76.195 0.000
77.203 0.000
78.213 0.000
79.226 0.000
80.244 0.000
81.265 0.000
82.292 0.000
83.324 0.000
84.364 0.000
85.412 0.000
86.468 0.000
87.532 0.000
88.604 0.000
89.681 0.000
90.761 0.000
91.845 0.000
92.931 0.000
93.959 0.000
94.973 0.000
95.983 0.000
96.990 0.000
97.995 0.000
98.999 0.000
100.001 0.000
101.003 0.000
102.005 0.000
102.982 0.000
103.960 0.000
104.938 0.000



  • CASE-1

  • CASE-2








A convergence plot of ACTUAL BRAKE POWER [KW] , TARGET BRAKE POWER [KW] and FUEL RATE [mg/cycle]




  • Higher the ignition delay, the more the pre mix fuel will get accumulated and hence will result into higher uncontrolled combustion. Uncontrolled combustion ( Pre-mix combustion will lead to detonation  in the cylinder and might damage the engine cylinders.
  • More pre-mix fuel fraction leads to higher pre-mix combustion.
  • However, if the pre-mix duration is increased than the value of pre-mix combustion also decreases because it gives more time for proper A/F mixture.
  • Decreasing Main-exponent skews the diffusion combustion curve toward left. Hence from case 3 and 4 it is evident that more brake power is generated as diffusion combustion is achieved at lower crank angle i.e., when piston is very near to TDC.
  • Lower BSFC at higher brake power is obtained in case 3 and 4.
  • However, in case 3 more engine detonation will occur as the premix combustion is higher. But in case 4, due to lower premix combustionlower BSFC, more diffused combustion and higher Brake power  it is more for the engine durability as well as performance.
  • Increasing tail duration increases the time duration for the left over unburnt fuel to undergo combustion.
  • The exhaust temperature for case 3 is slightly lower than the rest of the cases. 



  • DI WIEBE Combustion model can only be used to understand the dynamics of other IC engine components like Turbocharger but cannot be used to study other critical paramater like emissions because the of constant burn rate.
  • For CI engines, detonation (Uncontrolled Combustion) which is a major durability issue. It is mainly affected by IGNITION DELAY , premix duration and premix fraction which needs to calibrated accordingly to avoid any material failure.
  • Other parameters like decreasing "main duration"  skews the diffusion combustion curve towards left, which means combustion takes place when piston is very close to TDC thus, more power is obtained.
  • Hence, For the above case study case-4 seems to be more suitable configuration providing a good balance between power and reliability


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The End