Mathematical Modeling of the Dual Fuel Engine Cycle Joshi Anant, Poonia M.P., Jethoo A.S
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1 Mathematical Modeling of the Dual Fuel Engine Cycle Joshi Anant, Poonia M.P., Jethoo A.S Abstract The main aim of this paper is to investigate the combustion and performance characteristics of a single cylinder LPG diesel dual fuel engine. A computer simulation program has been developed to model the experimental data assuming the constituents in the cylinder during the combustion process consist of air, LPG, residual gas and injected pilot diesel fuel. The physical process such as atomization of fuel into droplets, fuel spray penetration, vaporization of fuel and mixing of diesel fuel with air and gas in spray zone, collectively known as preparation of fuel has been calculated. It is assumed that the mixture of air and LPG that is entrained during the preparation phase, releases heat with diesel after completion of delay period. The pilot fuel spray tip penetration can be obtained as a function of the difference in pressure between the fuel injection and the engine cylinder pressure. In the present analysis, the fuel injection pressure is assumed to be constant during the fuel injection period. A reasonably good prediction of engine performance and combustion characteristics was obtained by computation covering the entire range of engine operating conditions. Index Terms Duel Fuel Engine, Mathematical Modeling. I. INTRODUCTION In a dual fuel engine, two fuels are used simultaneously. Primary fuel that is usually gaseous forms the major content of the total energy supplied to the engine. After the compression of the primary fuel air mixture, small quantity of pilot diesel initiates the combustion near top dead center. The pilot diesel auto ignites first and works as an intense ignition source after which combustion of the inducted fuel occurs. A mathematical model of the dual fuel engine cycle processes can be helpful in gaining a better understanding of various cycle processes, particularly the combustion process which is a complex combination consisting of combustion initiation by compression ignition of diesel fuel, diffusion burning of the diesel and entrained gaseous fuel and finally premixed burning of remaining gaseous fuel by flame propagation. It is seen from the literature that whereas considerable work has been done on modeling of diesel engine combustion [1], [2] and Spark Ignition (S.I.) engine combustion. The available apparent heat release models for dual fuel engines are either based on the experimental cylinder pressure diagrams that are applicable only to a particular engine or involve complex simultaneous chain reactions and hence are complicated in nature and require large computer time. Further, the pilot fuel spray geometry that is an essential aspect of fuel-air mixing calculations has not been taken into account in dual fuel combustion modeling in past. Many combustion simulation of dual fuel engine have used multi zones models to analyze the combustion [3], [4], [5]. Further improvement on computer simulation ability enables us to use increasingly multi-dimensional models to analyze the dual fuel engine combustion. Early CFD studies have used global reaction model to predict the combustion process [6]. Gharehghani [7] in his work has used a reduced detailed chemical kinetics mechanism, to predict knock in the dual fuel engine. Also, partially stirred combustion model has been used in KIVA3V2 for simulation of turbulence and investigation of fuels interactions and found the effect of intake temperature and pressure on engine performance and knock occurrence, effect of initial swirl ratio on combustion phenomena. V. Pirouzpanah and R. Khoshbakhti Saray [8] work on quasi-dimensional model, combined with the detailed chemical kinetic scheme has investigated the combustion phenomena with the help of the methods like advancement of injection timing, increasing pilot fuel quantity, intake air throttling etc. Donepudi Jagadish [9] has carried out zero dimensional combustion model simulation in his work to predict the single cylinder constant speed diesel engine performance and predicted the performance of the given constant speed engine, as an alternate to a complex methodology of multidimensional modeling. Moranahalli Ponnusamy Sudeshkumar [10]had developed a two zone simulation model for ignition improver blend with diesel fuel to predict the combustion, performance and engine emissions characteristics in direct injection compression ignition engines. The operational range of the model is wide and computational run time is short, thus making the simulation model suitable for use with thermodynamically based cycle simulations in compression ignition engines running with ignition improver blend and diesel fuel. Cheikh Mansour [11] has developed a computer program to model the experimental data using a chemical kinetic reaction mechanism of the gas-diesel (dual-fuel) combustion, to investigate the emission and performance characteristics of a commercial diesel engine (Deutz FL8 413F) used natural gas with pilot diesel using chemical kinetic reaction mechanisms to predict NOx formation with reasonable accuracy. Cheikh Mansourhas suggested that the application of such kinetic models is reasonable when the object is the prediction of engine performance trends [11]. Good agreement between a model and experiment cannot be considered as a verification of the validity of the approximate model. Instead, such good agreement between model and experiment should be regarded as a verification of the utility of the model for prediction under the same conditions as used in the experiment. 19
2 PRESENT MODEL Sufficient experimental data on the combustion characteristics including heat release, delay period, rate of pressure rise, peak cycle pressure, etc. has been obtained during the present work for the dual-fuel operation (Using LPG and diesel) under wide range of operating parameters. Combining the insight obtained from present experimental investigations and the features of diffusion and premixed flame combustion, an attempt has been made to synthesize a simple cycle simulation to predict the performance of dual fuel engine. The system considered is a direct injection compression ignition engine, in which the gaseous fuel LPG is supplied through the inlet manifold whilst the diesel fuel is fed through the normal fuel injection system. The salient features of the model are described below. analysis, the fuel injection pressure is assumed to be constant during the fuel injection period. Jet break-up is almost instantaneous when it enters the chamber. Ignition originates, however not at the fringe, but somewhere between the core and the fringe. It is interpreted that the fringe, being the earliest part of the fuel injected, has the longest time for mixing and hence becomes too lean for ignition to take place. The probable ignition centers are shown in Fig 3[12]. The first visible flame does appear at the mixing part as shown in Fig 1, that is the remainder of the length L p of the penetration part and L s of the initial part. II. COMBUSTION MODEL FOR DUAL FUEL OPERATION In the present combustion model, the constituents in the cylinder during the combustion process consist of air, LPG, residual gas and injected pilot diesel fuel. It is assumed that the LPG-air mixture supplied during the suction stroke and residual gases are present as homogeneous mixture, surrounding fuel spray. The physical process such as atomization of fuel into droplets, fuel spray penetration, vaporization of fuel and mixing of diesel fuel with air and gas in spray zone, collectively known as preparation of fuel has been calculated. It is assumed that the mixture of air and LPG that is entrained during the preparation phase, releases heat with diesel after completion of delay period. In the first stage, the mixture preparation rates are calculated for the diesel fuel. Whitehouse and Way [13] have proposed relation for calculating the rate of preparation of fuel as (1) The mass of injected fuel M i could be obtained from the injection rate diagram. Typical values of the constants are a 1 = 1/3, a 2 = 2/3, m = 0.4 and C = It must be stated that the value of C needs to be adjusted to match the specific engine. The total mass of prepared fuel is added till the completion of delay period. In the first stage of combustion the prepared diesel and entrained gas are assumed to be burnt. The entrained gas is calculated on the basis of actual spray geometry till the end of delay period as shown in Fig. 1. In the second stage of combustion, it is necessary to determine the mass of diesel and LPG that is unburned. Heat release model taken for diesel burning was the simple Wiebe sfunction [2], whereas for gas burning, spherical pattern of flame front movement was assumed as shown in Fig 2. The heat release by both the fuels is finally calculated by adding the heat release rates. A. Fuel spray tip penetration The pilot fuel spray tip penetration can be obtained as a function of the difference in pressure between the fuel injection and the engine cylinder pressure. In the present Fig 1 Spray Geometry The flame never goes in the initial part during the injection [14]. The air is entrained into the spray in the initial and mixing part of the spray due to the lower static pressure in the spray at these regions. At the moment of ignition, the premixed combustible mixture is considered to be bounded by the lean limit of combustion at the outer edges of the spray and the rich limit near the core. The jet velocity till the jet break-up is obtained from the following relationship: (2) Where: C = coefficient of discharge of the nozzle ΔP = pressure difference across the nozzle (Pa) ρ L = liquid fuel density (kg/m3 U F0 =initial jet velocity (m/sec) Transient time from injection start to jet break-up is obtained from (3) D n = diameter of nozzle orifice (mm) t b = time from fuel injection to break up (sec) The spray tip penetration can be calculated by Hiroyasu s formula as 0 < t<t b, t >t b, 20
3 The spray cone angle is given by ISSN: (5) µ a = coefficient of viscosity of air (Pa.s) 2θ = cone angle The break up length is nearly constant and is little influenced by the pressure. The relations between the length XL P and the spray tip penetration Xs is as follows: (6) (7) The spray tip penetration Xs and spray cone angle θ s can be modified by influence of the swirl as follows. X S1 = (1 + П.N.Xs/30.U FO.) -1 Xs (8) θ S =(1+.N.Xs/30.U FO ) 2.θ (9) N = swirl number (rpm) (4) Fig 2: Complete Picture of Filling the Cylinder by Flame value of 5 is added in the value of spray angle. Spray cone angle is usually of the order of 10 at atmospheric conditions. By knowing the mass of diesel prepared till the end of delay period, mass of diesel vapor, air and LPG entrained into the fuel spray s mixing zone, the heat release rates in the first phase could be determined by assuming heat release at constant volume in this phase. The following steps have been visualized for calculating the heat release: 1. To calculate actual geometry of the spray. 2. To calculate the mass of the air and gas entrained with the diesel in the mixing zone leaving the rich zone boundary. 3. The initial radius of the flame is calculated by calculating the entrained or ready to burn volume by equating it to the volume of a sphere. It is assumed that this sphere lies somewhere in the center of the mixing part. 4. Initial rate of heat release is assumed at constant volume. Remaining mass fraction burnt in second phase of combustion in the case of pilot fuel has been characterized by the well-known semi empirical burning law in dimension less form (Wiebe s function) as follows in a very small time: (10) Where: y = dimension less time function = (Crank angle at that point - Angle of injection) / (Duration of combustion) a and m are the adjustable constants Burning velocity of homogeneous mixture is calculated by empirical relations given by Thomas and Samuel [15]. Since velocity of flame is known and density of charge at each step is being calculated, hence mass burning rate can be calculated. 5. At every step burnt volume is calculated by assuming one spray and propagates spherically in the outward direction. III. GOVERNING EQUATIONS FOR ENGINE CYLINDER The basic governing equations defining the small change in cylinder gas temperature, pressure and its composition are derivable from the equation of state. The general quasi-steady flow energy equation in differential form for any control volume is given by, Fig 3: Injection of a Fuel Jet, Schematic Diagram Spray equivalent spray cone angle (θ S ) and the spray angle (θ) is functions of the initial pressure and specific weight of the charge. For calculating the equivalent angle, a constant (11) Assuming negligible change in kinetic and potential energy of the streams and zero shaft work, the energy equation can be written as: (12) By using equation of state and expressing internal energy 21
4 u as a function of temperature and composition, the rate of change of temperature with respect to crank angle θ is given by, (13) The equation (13) is valid for all quasi-steady, control volumes. A. Instantaneous Cylinder Volume, Flame Volume And Volume Change The instantaneous cylinder volume measured from BDC position, which is a function of the crank-angle and the geometry of tile slider-crank, can be expressed as. (14) S = stroke length X n = ratio of connecting rod-to-crank length θ r = crank angle expressed in radian V cl = clearance volume A P = piston or cylinder area of cross-section By differentiating the equation (14), the rate of change of cylinder volume with crank angle is given by, (15) Considering the actual geometry of the combustion chamber having a bowl in the piston, the volume and surface area of the flame at any instant is calculated with the help of standard geometrical relations as the flame propagates in a spherical manner. B. Model for Ignition Delay Period Ole et.al conducted series of experiments on a single cylinder diesel engine to investigate the effect of various parameters such as compression ratio, angle of injection, engine speed, mass of pilot fuel and intake temperature on delay period [16]. Considering these experimental results and present investigations on LPG fuel, an equation for delay period has been obtained by the method of least squares that can take into account compression ratio, nature of the fuel, angle of injection and relative fuel air ratio. This equation is valid for different fuels namely Methane, Natural Gas LPG and Bio-gas. The developed delay period equation is given below: (16) DP = delay period in deg. Crank angle SP = mean piston speed XMF = mass of pilot fuel in kg/cycle TIN = intake temperature in K PHI = equivalence ratio AN = compression index AINJ angle of injection This equation is applicable up to 0.8 relative fuel-air ratio, which is also approximately the combustion limit of gaseous fuels, beyond this in actual practice, engine operation becomes difficult. C. Heat transfer The heat transfer rate from the cylinder or to the cylinder at any instant can be determined by: (17) dq/dθ = heat transfer rate h = gas side heat transfer coefficient T g = mean bulk temperature of the gases T w = effective wall surface temperature A w = total surface area exposed to gases at any instant A number of correlations are available to estimate the gas side heat transfer coefficient in cylinder. In present study Woschni s relation has been used to calculate the gas side heat transfer coefficient. Heat transfer area is given by the relation: (18) A fix is the area when piston is at TDC. Fixed area components are inlet and exhaust valve, cylinder head, piston crown and combustion chamber surface. For considering the temperature of various component surfaces for calculating heat transfer it is assumed that cyclic variations in the component temperatures are negligible.a var is the variable area of the cylinder due to piston movement. The average wall temperature can be calculated by the relation; (19) D. Calculation of Mass Flow Rate through Valves The instantaneous mass flow rate through the inlet and exhaust valves can be calculated by using the one-dimensional compressible, adiabatic flow relations. The mass flow rate is given by, (20) Where: A eff = effective valve area at any given instant P 01, T 01 = up-stream stagnation pressure and temperature. Putting in terms of crank angle, N E = engine speed, rev/mm. IV. RESULTS AND DISCUSSIONS (21) The results obtained from the simulation model including the comparison with experimental results obtained in diesel and dual fuel mode can be categorized in three groups. They 22
5 are: 1. Program development results 2. Results for validation of the model, and 3. Parametric study results The results obtained are for a single cylinder, four stroke, direct injection Kirloskar diesel engine used for experimental work using diesel and LPG. A. Results of Developmental Runs To develop the simulation model for acceptable accuracy of prediction several trials to choose appropriate step size, coefficients for the semi-empirical correlation s used for heat release, flame propagation and heat transfer were made. The outcomes of these developmental trials are presented in the following paragraphs. B. Heat Release Model Heat release pattern for the homogeneously mixed fuel is based on the rate of flame movement through the combustion chamber. The existing correlation s are for calculating laminar burning velocity in the combustion chamber. Considering the experimental data developed during the present study, multiplying factors for actual turbulent velocity calculations were determined for LPG. The total heat release duration has been divided in three parts based on the actual heat release patterns obtained during the present investigations. The values of the constants are given in table 1. The rate of preparation was calculated by the Whitehouse and way model assuming the same constants suggested by them. The coefficients finally adopted for heat release rate and heat transfer in the present simulation are as given in table 1 Table 1: Coefficients for the Semi-Empirical Correlation s Coefficient Coefficients of Wiebe s function s of Whitehouse and Way model Coefficients of flame velocity Coefficients of heat transfer Woschni s eqn.c1=6.18 during gas exchange=2.2 C1= , 8.0 and 8 during a1=1/3 ln(fidp) 2.0(assumin comp. and a2= 2/3 C2= 0.4 A/F g three exp. without m=0.4 FIDP=(DP/DINJ) different firing C= * XMF stages) C2 =3.24*1.e+03 rn/sec K during Combustion Fig 4 depicts the heat release pattern obtained experimentally as well as using cycle simulation in dual fuel mode at 80% load and optimum pilot (5.9 mg/cyc1e) obtained from previous studies. Fig 4: Comparison between Experimental and Computed Heat Release Patterns C. Results for validation of the model Some typical results of the simulation model developed as above have been compared with the corresponding experimental results to demonstrate the validity of the model in the present form. The comparisons presented include different engine load and different pilot fuel quantities in dual fuel mode correspond to 20% and 80% load at compression ratio Figs.5 show the comparison between computed and measured pressure-crank angle diagrams for dual fuel operation at 80% load using optimum pilots 5.9 mg/cycle. A satisfactory comparison between the predicted and experimentally obtained pressure crank angle diagram can be observed. Effect of load on computed cylinder gas temperature is shown in Fig 6. The maximum cylinder gas temperature may reach up 1850 K at 100% load. Figs 7&8 show the effect of load on cylinder peak cycle pressure and IMEP As could be seen from the graphs that the trends obtained from the model are closely following the experimental trends. Fig 5: Comparison between Experimental and Computed P-θ Diagrams 23
6 Fig 6: Computed Cylinder Gas Temperature at Different Loads and 4, parameters of interest were altered, keeping other parameters constant. In all these cases intake temperatures was chosen as 34 C and 80% load. Table 2 shows the effect of compression ratio on performance parameters at optimum pilot of 5.9 mg/cycle obtained during the present study at 80% load. The brake thermal efficiency of the engine increases, with increase in compression ratio up to Compression ratio 19.0 gives the maximum brake thermal efficiency but very high rate of pressure rise and hence higher peak pressures are observed. Table 3 shows the effect of engine speed on engine performance at 80% load. At speeds higher than 1500 rev/mm., the brake thermal efficiency obtained is poor due to longer ignition delay and increased friction losses. Maximum efficiency was obtained at 1250 rev/mm. Due to more time available near TDC at the time of combustion, the efficiency in the case of dual fuel engine is observed to be higher at lower engine speeds Table 2: Effect of compression ratio on engine performance at 80% load in dual fuel mode at Engine speed = 1500 rev/mm.injection timing = 27.4 crank angle BTDC, Pilot = 5.9 mg/cycle, Intake temperature = 34 C, Injector opening pressure = 150 bar Compres sion ratio BHP IHP DP (deg.) B.Th Eff. (%) IMEP Peak press ure TEX ( C) Fig 7: Effect of Load on Peak Cylinder Pressure and IMEP Fig 8: Effect of Load on Peak Cylinder Pressure and IMEP These validation results show a close comparison (within accuracy %) between presently computed and experimentally obtained results. Predicted delay period from the developed relation during present work, closely follow the experimental data. Parametric study results After ensuring the validity of the model, to realize its capability for simulating the engine, the model was used over wide range of operating parameters. As shown in table 2, 3 Table 3: Effect of engine speed on engine performance at 80% load in dual fuel mode at Compression ratio= 15.0Injection timing = 27.4 crank angle BTDC, Pilot = 5.9 mg/cycle, Intake temperature = 340 C, Injector opening pressure= 150 bar Engin espee d (rev/ mm.) BHP IHP Delay Perio d (deg.) Brahe Ther mal Effici ency IMEP Peak press ure Exha ust Temp eratur e ( C)
7 V. SUMMARY/CONCLUSION The cycle simulation model presently developed attempts to incorporate the simultaneous combustion of the two fuels (pilot and gas burning) in a simple but fairly representative manner. The pilot diesel fuel spray geometry, rate of fuel preparation and mass of gaseous fuel in prepared diesel have been calculated. The point of start of combustion has been traced. The Wiebe s function type of representation has been retained for burning of pilot diesel. The heat release of the gaseous fuel has been calculated on the basis of spherical flame propagation in the combustion chamber by taking into consideration the geometry of the combustion chamber. The predicted value of peak cylinder gas pressure, IMEP, brake power, brake thermal efficiency and ignition delay period was observed to be within the accuracy of 0.2 to 2.5%. The model can be used for optimization of a number of design parameters of a dual fuel engine for any application. [10] Moranahalli Ponnusamy Sudeshkumar, G. D. (2011). Development of a simulation model for compression ignition engine running with ignition improved blend. Thermal science. [11] Cheikh Mansour, A. B. (2001). Gas-Diesel (dual-fuel) modeling in diesel engine environment. international Journal of Thermal Science, [12] W.T., L. (1970). The Spectrum of Diesel Combustion Reaserch. Proc. Instt. of Mech Engg., 184, [13] Whitehouse N D, W. R. (1996). Rate of Heat Release in Diesel Engine and its Corelation With Fuel Injection Data. Proc. Institute of Mechanical Engineering, 184(70). [14] Fujimoto, H. T. (1982). Investigations on the Charactrsticts of Diesel Spray. Bulletin of Japan Society Mechanical Engineering (JSME), 25(200). [15] Thomas W, S. S. (1980). The Laminar Burning Velocity of Iso-octane, n-haptane, Methanol, Methane and Propane at Elevated Temprerature and Pressure in the Presence of Diluent. SAE: [16] Ole, B. a. (1980). Ignition Dealy in Dual Fuel Engine. SAE: Author s Profile REFERENCES [1] Ramos, J. (1989). Internal Combustion Engine Modeling. Hemisphere Publishing Corporation. [2] Gaurr, R. (1977). Digital Simulation of Four Stroke High Speed Diesel Engine With Turbocharger For wide Range Matching And Optimization. Ph. D. Thesis, Department of Mechanical Engineering, Indian Institute of Technology, Delhi. [3] Karim, G. (1991). An Examination of Some Measures for Improving the Performance of Gas Fuelled Diesel Engines at Light Load. SAE Paper [4] Z. Liu, a. K. (1994). An analytical examination of the pre ignition processes within homogeneous mixtures of a gaseous fuel and air in a motored engine. SAE Paper [5] Hountalas, D. a. (2000). Development of a Simulation Model for Direct Injection Dual Fuel Diesel-Natural Gas Engines. SAE [6] Hiroyasu H, K. T. (1979). Combustion and Simulation of Emission on Diesel engine. Japan Society Mechanical Engineering and Japan Society Automobile Engineering Symposium of Combustion, Emission and Fuel Consumption on IC Engine, 37. [7] Gharehghani, A. (2010). Numerical and Experimental Investigation on Performance of Dual Fuel D87 Engine. ASME 2010 International Mechanical Engineering Congress. [8] V. Pirouzpanah and R. Khoshbakhti Saray. (2005). A predictive model for the combustion process in dual fuel engines at part loads using a quasi dimensional multi zone model and detailed chemical kinetics mechanism. [9] Donepudi Jagadish, R. K. (2011). Zero Dimensional Simulation of Combustion Process of a DI Diesel Engine Fuelled With Biofuels. World Academy of Science, Engineering and Technology, 80, Joshi Anant(Bikaner, May 16, 1988) is an M Tech Scholar of Energy Engineering at Malaviya National Institute of Technology, Jaipur, Rajasthan, India. He has earned his Bachelor s Degree (B Tech) in Mechanical Engineering in 2010 from Rajasthan Technical University, Rajasthan, India. He has worked with CADD Centre Training Services Pvt. Ltd. As ENGINEER BUSINESS SUPPORT in Rajasthan. He has presented four papers in national conferences in the field of energy conservation. Mr. Joshi is a student member of ASME (American Society of Mechanical Engineers) and ISHRAE (Indian Society of Heating, Refrigerating and Air Conditioning Engineers). 25
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