Abstract
Many models for the prediction of emissions and combustion based on the phenomenology of spray combustion for DI diesel engines are available in the literature. All of them utilized empirical heat transfer correlation, which is mass averaged. Experimental observations from modern diesel engines of heavy-duty application showed that NOx formation suppresses at higher loads although favourable conditions exist. A new phenomenological model for NOx emission is developed based on mixing-controlled combustion incorporating localized wall heat transfer. In this work, a phenomenological model for heat transfer from wall–spray is also proposed which is employed along with the heat release model to account for the effect of localized heat transfer. A simple geometrical relation is employed for the spray–wall interaction and subsequent turbulence structure for spray developed earlier by the authors. This model is one-dimensional and does not need any engine-specific tuning. The newly evolved NOx model takes into consideration all the engine operating parameters, viz. engine speed, fuel injection pressure, intake air pressure, temperature and swirl number, etc. The effects of exhaust gas recirculation and biodiesel on NOx formation are also incorporated in this model. The new model was validated by conducting experimental investigations on 6 engines at different operating conditions with widely varying features.
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Abbreviations
- A s :
-
Surface area (m2)
- C f :
-
Concentration of fuel vapour (–)
- δ :
-
Virtual source = 2.3 de (m)
- d :
-
A distance from the nozzle tip (m)
- \(C_{f_{{\text{noz}}} }\) :
-
Vapour concentration at the nozzle (–)
- \(C_f \left( {r, y} \right)\) :
-
Vapour concentration at any position in free spray (–)
- \(C_{f_{{\text{wall}}} }\) :
-
Vapour concentration along wall–spray (–)
- \(C_{f_x }\) :
-
Vapour concentration along the axis of free spray (–)
- EGR:
-
% Of exhaust gas recirculated (%)
- EOC:
-
End of combustion for each volume (CA deg)
- EOC:
-
End of combustion (CA deg)
- F :
-
Equivalence ratio (–)
- h c :
-
Heat transfer coefficient (W/(m2K))
- N o :
-
Number of holes (–)
- \({\text{NO}}_{x_{{\text{wall}}} } ,{\text{NO}}_{x_{{\text{free}}} } ,{\text{NO}}_{x_{{\text{cycle}}} }\) :
-
NOx formed in free and wall–sprays are summed up to arrive at cycle NOx (kg)
- \({\text{NO}}_{x_{{\text{cycle}}} }\) :
-
Cycle averaged NOx (ppm)
- Q wall :
-
Heat transfer to the wall (J)
- r s :
-
Radius of spray (m)
- S :
-
Distance from the mouth of the nozzle (m)
- S liq :
-
Liquid core = 7 de (m)
- SOC:
-
Start of combustion for each volume (CA deg)
- SOI:
-
Start of injection (CA deg)
- SWI:
-
Start of wall impingement (CA deg)
- T cyl :
-
Cylinder gas temperature (K)
- t dur :
-
Combustion duration (s)
- t flame , T flame :
-
Flame temperature (K)
- T fllame corrected :
-
Corrected flame temperature (K)
- T wall :
-
Piston wall temperature (K)
- V free :
-
Free spray volume (m3)
- V free_corr :
-
Corrected free spray volume (m3)
- V spray :
-
Spray volume (m3)
- V wall :
-
Sectional volume of wall–spray volume (m3)
- V wall-corr :
-
Corrected wall–spray volume (m3)
- Φ :
-
Equivalence ratio, the ratio of chemically correct (stoichiometric) fuel–air ratio to actual fuel–air ratio (–)
- \(\frac{{{\text{d}}m_f }}{{{\text{d}}\theta }}\) :
-
Rate of injection (mm3/deg)
References
Aghav YV, Lakshminarayanan PA, Babu MKG, Thatte V, Kumar MN (2008) Phenomenological modelling of NOx under mixing controlled combustion in DI eiesel engines. J Therm Sci
Deshmukh BS, Aghav YV, Gokhale NP, Kumar MN, Ramesh A, Babu MKG (2008) An innovative EGR admission concept for heavy-duty diesel engine. In: SAE international mobility conference
Deshmukh BS, Aghav YV, Gokhale NP, Kumar MN, Ramesh A (2007) EGR mal-distribution analysis for DI diesel engines using AVL Boost. In: AVL users international conference, Graz
Lakshminarayanan PA, Dent JC (1983) Interferometric studies of vapourising and combusting sprays. SAE 830244
Uyehara OA (1980) Effect of burning zone A/F, fuel H/C on soot formation and thermal efficiency. SAE 800093
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Lakshminarayanan, P.A., Aghav, Y.V. (2022). Oxides of Nitrogen from Direct Injection Diesel Engines. In: Modelling Diesel Combustion. Mechanical Engineering Series. Springer, Singapore. https://doi.org/10.1007/978-981-16-6742-8_14
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DOI: https://doi.org/10.1007/978-981-16-6742-8_14
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