Fast discrete resolution of combustion process in diesel engine based on cylinder pressure parameter

With the increasing concern over world energy resources and worldwide environmental issues, regulations for fuel efficiency and emissions on current engines are becoming more and more stringent. Closed-loop control is an effective method to precisely control fuel injection. Current diesel engines are controlled based on the rotational speed, which is an open loop control to combustion process because there is not a feedback parameter from combustion condition. Combustion information is key to condition flag of engine control, there is different gaining method of combustion information, cylinder combustion is treated by severval method to meet different calculation aim. Thermal-dynamic method is early calculation for combustion process, for instant, Austen-Lyn triangle menthod, White house single area method, this calculation result is rough to description of cylinder combustion, overall parameters, such as temperature and pressure of in-cylinder. Partion area calculation is relative progresss in contrast to thermaldynamic method, because chamber space is divides into several areas according to time change, Cummins company Lyn combustion model of gas-phase fuel spray and combustion model of fuel drop evaporation are typical calculation method and applies widely. Three-dimension calculation is an accuracy method for fine model of fuel injection and fuel–air mixture and so on, its model calculation result is more suitable to real cylinder condition. FIRE, STAR– CD and KIVA software are current popular calculation means, its calculation result, such as portion temperature, emission NOx and PM, is precise, but its disadvantage is long calculation time, these are difficult to measure in real time. How to select simple easy-detection parameter is important to engine control. Cylinder pressure directly reflects combustion process in contrast with temperature and releasing heat, also includes combustion information. Introducing cylinder pressure into electronic controlled system can provide feedback of combustion process [1]. To abstract pressure characteristic index from in-cylinder pressure curve has become a key point of electronic control engine. In order to get combustion information quickly and apply it into engine control, an effective path is to obtain combustion characteristic parameter from cylinder pressure curve directly. Powell presented control spark timing by location of peak pressure (LPP) in spark ignition (SI) engine in order to make air-fuel ratio (AFR) to object value [2]. Mateunas et al presented a method of pressure ratio (PR) to obtain character of cylinder pressure curve, in order to made cylinder combustion to be best by mediating ignite timing in minimum spark timing for the best torque (MBT) [3]. Leondhart provided another method of forming dynamic injection quantity and injection advance angle by cylinder pressure, so that monitoring injection parameter is performed [4]. With the development of electronic control and sensor technology, it is possible to optimize combustion process by pressure information.


Introduction
With the increasing concern over world energy resources and worldwide environmental issues, regulations for fuel efficiency and emissions on current engines are becoming more and more stringent.Closed-loop control is an effective method to precisely control fuel injection.Current diesel engines are controlled based on the rotational speed, which is an open loop control to combustion process because there is not a feedback parameter from combustion condition.Combustion information is key to condition flag of engine control, there is different gaining method of combustion information, cylinder combustion is treated by severval method to meet different calculation aim.Thermal-dynamic method is early calculation for combustion process, for instant, Austen-Lyn triangle menthod, White house single area method, this calculation result is rough to description of cylinder combustion, overall parameters, such as temperature and pressure of in-cylinder.Partion area calculation is relative progresss in contrast to thermaldynamic method, because chamber space is divides into several areas according to time change, Cummins company Lyn combustion model of gas-phase fuel spray and combustion model of fuel drop evaporation are typical calculation method and applies widely.Three-dimension calculation is an accuracy method for fine model of fuel injection and fuel-air mixture and so on, its model calculation result is more suitable to real cylinder condition.FIRE, STAR-CD and KIVA software are current popular calculation means, its calculation result, such as portion temperature, emission NOx and PM, is precise, but its disadvantage is long calculation time, these are difficult to measure in real time.How to select simple easy-detection parameter is important to engine control.Cylinder pressure directly reflects combustion process in contrast with temperature and releasing heat, also includes combustion information.Introducing cylinder pressure into electronic controlled system can provide feedback of combustion process [1].To abstract pressure characteristic index from in-cylinder pressure curve has become a key point of electronic control engine.In order to get combustion information quickly and apply it into engine control, an effective path is to obtain combustion characteristic parameter from cylinder pressure curve directly.Powell presented control spark timing by location of peak pressure (LPP) in spark ignition (SI) engine in order to make air-fuel ratio (AFR) to object value [2].Mateunas et al presented a method of pressure ratio (PR) to obtain character of cylinder pressure curve, in or-der to made cylinder combustion to be best by mediating ignite timing in minimum spark timing for the best torque (MBT) [3].Leondhart provided another method of forming dynamic injection quantity and injection advance angle by cylinder pressure, so that monitoring injection parameter is performed [4].With the development of electronic control and sensor technology, it is possible to optimize combustion process by pressure information.

Combustion process calculation analysis
For four-stroke engine, one working cycle is made up of intake, compression and combustion working and emission stages, combustion process is happened in fixed stage in continuous working cycle, so combustion parameter changes with time, it belonged to continuous process.In the combustion process, combustion parameter variation is in high speed.Obvious character of combustion process in diesel engine is inhomogeneous distribution of working medium in cylinder, in the fuel spray formed by injector, distribution condition of fuel, air and combustion production is not only varied from time change, but also from different space position.Combustion process is un-linearity and transient change in several microseconds.

Combustion thermal process
In order to analyze changed condition and character condition, thermal process is a basic character in the complex physics and chemical change, when cylinder is regarded as thermal system, boundary is made up of piston top, cylinder cover and cylinder inter surface, as showed in Fig. 1, a typical thermal approach is used to describe condition change with pressure, temperature, mass and gas, thermal simulation equations are as followed.

Condition conservation equation
Energy conservation equation Mass conservation equation where i E is energy exchanged with system boundary, j m is mass exchanged with system boundary [5].This three equations are formed to resolve pressure, temperature and mass.In the four stroke diesel engine, mass conservation and energy conservation is followed with differential equation.
Intake process Combustion process Releasing heat ( ) Exhaust process 4 4 where message of all kind of above variable is listed in material [6] in detail.

Traditional resolution method of comsution process
For combustion process equation, there are three methods to resolve the in-cylinder parameter.Zerodimensional model is simple method, it is called single area model or thermal model.All of parameters is purposed to only change with time and is neglected change with position, so there is only one independent variable time t.In the zero dimensional model, invariable differential equation groups are used to calculate temperature and pressure in cylinder.Quasidimensional model divided combustion chamber space into several areas, in the each area, multi differential equation groups are used to calculate temperature and pressure in cylinder, in order to predict emission character, as part temperature and air-fuel ratio are different in different position of combustion chamber, considered from combustion, ignite mixture forming and flame spread, partition model is developed.Multidimensional model is most complex treatment to thermal system, time, position, space of combustion chamber is considered, such as gas flow motion, mass and motion energy and energy transmission and conversion, is included, fuel injection, atomization and evaporation and fuel gas mixture forming, ignition and combustion, and heat transmission, gas matter and boundary motion (piston and gas valve) is described as submodel, so all energy conservation equation and submodel of turbulent flow, chemical reaction and boundary character are combined together, with suitable boundary condition, numerical method is used to resolve.Detail information of gas flow speed, temperature and composition in combustion chamber are provided, this model is relative fine one.
Time t is replaced with crankshaft angle θ in the differential equation groups, small fixed step Δθ is set, by means of numerical calculation method, iteratedinterpolation calculation type and calculation precision is given, resolution of differential equation is obtained, in sum, this calculation time is from several seconds to several hours.

Combustion pressure index
Based on real measurement cylinder pressure, releasing heat index can be obtained from releasing heat rate or mass fraction burned by thermal dynamic calculation from cylinder pressure [7].Calculation accuracy of the former method is determined by transient specific heat volume γ whose average value is usually given in the compression and expand stroke respectively, so calculation result is varied from different given value.This method requires high calculation configure, long calculation time and high demand for cylinder pressure sensor.The method based on mass fraction burned directly calculates cylinder pressure curve, which can decrease personal factor.
Pressure difference method invented by Bosch Company was used to analyze combustion condition.It is obtained by subtracting motor pressure from combustion pressure in the same work cycle, as shown in Fig. 2 is pressure difference curve represents results from fuel combustion injected into cylinder.Integral to pressure difference from commence angle to some angle after top dead center (TDC) represents combustion quantity.In the pressure difference curve, positions of combustion commencement point, maximal burst pressure and its angle are obviously identified.The method can decrease calculation quantity effectively and structural effects of different engines.

Fig. 2 Cylinder pressure curve
Mass fraction burned (MFB) is easy to calculate by pressure difference.Combustion process is indicated by dynamic thermal formula.Energy equilibrium of working medium in cylinder followed the first law of dynamic thermal mechanism where dW is work done by piston ( dW PdV = ), dU is internal energy of work mass, and dQ is addition heat.
Addition heat quantity in combustion chamber is where H u is lower heat quantity of fuel, m b is fuel mass burned, and Q wi is heat exchange with chamber walls.Relation equations of an ideal gas are where C v is specific heat of given volume, C p is specific heat of given pressure, and R is constant of ideal air.dW, dU and dQ in Eq. ( 1) are replaced by cylinder pressure P and volume V and addition heat to yield following equation.
[ ] When the differentials are expressed as derivatives with respect to crankshaft rotational angle, this equation represents a first order liner differential equation with following solution, cylinder pressure ( ) p θ is expressed by motor pressure ( ) mot P θ in a given crankshaft angle θ.
where ( ) V θ is cylinder volume of crankshaft angle θ, 0 V is combustion chamber volume.
By defining a term of the total heat of combustion, H u , fuel injection m f , and factoring it from within the integral, Eq. ( 1) may be rewritten In the preceding equation, INT2 is the integral from ignition commencement angle θ fi to combustion end angle θ fe of the following expression In integral INT2, the following terms apply, mass rate burned ' ( ) b m θ and heat exchange rate The terms in Eq. ( 15) represents the mass fraction of fuel burned at any crankshaft angle, while the term in Eq. ( 16) represent the wall heat transfer as a fraction of total fuel energy.
Recognizing that the mass m of the combustion chamber content is the sum of intake air m a , intake fuel m f , and residual gasses m r , the following equation applies This allows Eq. ( 11) to be rewritten The factor A1 depends primarily on the mass of fuel relative to the mass of diluents, decreasing with greater dilution.The term A2 depends on the time of for combustion and the timing of combustion in the cycle along with the wall-loss rate.
Derivation process is not listed in the paper due to the limit of page number.Final derivation result is written as  20).In each crankshaft angle, MFB is a ratio of pressure difference and motor pressure.So there is a relationship between releasing heat and MFB.

Combustion characteristic parameter
Combustion pressure data are mainly used for design purpose and combustion analysis.Releasing heat indexes obtained by thermal dynamic calculation based on cylinder pressure are used to evaluate combustion reasonableness [8].As combustion process repeats in periodic work cycles, we introduced phase and intensity of physical parameter in periodical motion to describe combustion process.Combustion character parameter covers combustion phase, combustion intensity and releasing heat prompting in cylinder.It includes combustion commencement and end position, maximum burst pressure, maximal pressure rising rate and its angle, 50% MFB, 95% MFB and maximum releasing heat quantity.The parameters reflecting combustion phase include maximum burst pressure angle, maximum pressure rising rate angle and 50% MFB angle.Maximal burst pressure, maximal pressure rise rate and 50% MFB reflect combustion intensity.Among these combustion parameters, character parameters used for combustion control must be comprehensively described character for combustion process.They must not only reflect combustion commencement position, intensity and releasing heat quantity, but also be accurate and need less acquirement time.
Pressure difference curve is an approximate smooth Gauss curve.Its geometry character covers start point, maximal top point, shape factor, bar-center point, first order derivative, and second order derivative.Among these character points, calculation quantity is different.To reduce calculation time, the geometry characteristic indexes of pressure difference curve are used to describe the combustion process (Fig. 3) such as maximal pressure difference ΔP max and its angle Δθ Pmax , bar-center point (ΔP C , Δθ C ), combustion commencement and angle difference of fixed pressure.Above analysis is made from the viewpoint of math and physics, since in-cylinder combustion is not only physical and chemical process, but thermal dynamic process, and is in nonlinearity complex change, it is needed to find the relation of engine input and character index.Cylinder pressure under the different condition of injection time and injection quantity is analyzed, due to limited experimental data, it can not meet requirement of acquisition analysis data in any profile, by means of GTpower simulation software, YN4100 diesel engine is selected as calculation object, its specification is followed: bore/stroke 100/105 mm, cylinder number 4, compression ratio 18.5, swirl ratio 2.5, rated power 70 kW, maximal torque/rotation speed 185 Nm/2200 r/min.Its combustion simulation model of is structured, one dimension simulation calculation is made, simulation model is shown in Fig. 4.
Model calculation accuracy is verified by experimental data, cylinder pressure, engine torque, engine power and fuel consumption is selected to evaluated index, in order to verify simulation model precise.Cylinder pressure of calculation and real measurement in the profile of engine rotational speed 2200 r/min is compared in Fig. 5. Seen from Fig. 4, the two curve trends are correspond in the most range though there is a little difference in small position, it is shown that engine combustion process and selected parameter is reasonable.It is chosen some profiles in the model calculation, which is rotation speed 1200, 1400, 1800, 2200, 2600, 3000 r/min, engine load 50%, 80%, 100% respectively, performance parameter of diesel engine is calculated by simulation model, output torque, output power and fuel consumption of calculation and real measurement are compared in Fig. 6.Comparison results in Fig. 6 indicate that calculation error for each parameter of calculation and real measurement is in less 5%.All this is shown that simulation model can reflect real combustion condition and model calculation precision is reasonable.
With above simulation model, some calculation point is chosen when engine rotation speed is set as 2200 r/min, its given parameter of simulation calculation is shown in Table 2, pressure character index of pressure difference is calculated in the different injection timing and injection quantity.

Combustion characteristic parameter
To verify the effectiveness of the method, we use a DC motor as the controlled object to simulate in As engine combustion begins with drastic increase of cylinder pressure in cylinder pressure curve, pressure rise point before TDC is regard as fuel ignite position in the pressure difference curve, based on cylinder pressure calculated by simulation model, combustion commence angle calculated from pressure difference curve is shown in Table 3. Ignition commence angle is different from injection timing, and its position is related with injection quantity, this varying regularity is fit combustion rule.Change of pressure character index under different injection timing and injection quantity is shown in Figs.7 and 8. From Fig. 7, maximal pressure difference ΔP max and its angle Δθ Pmax was mapping one by one with each injection time and injection quantity, both of them did not exist intercrossing and overlapping.Maximal pressure difference ΔP max was direct proportion to injection quantity and its angle Δθ Pmax was constant in the same injection timing.10.From Fig. 10, at same rotational speed, when engine load increased, NOx concentration basically increased with maximum value of pressure difference.When injection quantity was enlarged, maximal burst pressure increased with injection quantity.In the range of engine load 50%, 80%, increasing argument of maximal pressure difference is much more so that NOx concentration produced more, but in high engine load 80~100%, increment of maximum pressure difference was not more, and NOx concentration produced less.

Jun Wang, Youtong Zhang FAST DISCRETE RESOLUTION OF COMBUSTION PROCESS IN DIESEL ENGINE BASED ON CYLINDER PRESSURE PARAMETER
S u m m a r y Combustion information is needed to apply engine control system, current calculation methods for combustion process are analyzed briefly, cylinder pressure difference method was introduced to study combustion condition.Cylinder pressure is used to be combustion indication flag in order to meet combustion information requirement, based on cylinder pressure parameter, by means of pressure difference method, math algorithm of fast dispersed resolution to combustion process by pressure difference is presented.Combustion intensity, phase and heat-releasing rate are provided to describe combustion condition.Ignition commencement angle, maximal burst pressure and its angle, and bar-center point in pressure difference curve are selected as character parameters to specialize overall combustion character.Combined with cylinder pressure of real engine, relation of pressure character index with injection timing and injection quantity was resolved by simulation and measurement of pressure data, and change trend of each pressure character index with diesel engine emission NOx based on experimental data was analyzed.The results indicated that fast discrete resolution for combustion process with pressure parameter was effective and pressure character index could reflect combustion character.
Received February 10, 2011 Accepted December 05, 2011 the preceding equation, INT1 is the integral from ignition commencement angle θ fi to combustion end angle θ fe of the following expression

Fig. 7
Fig. 7 Trend of maximal pressure difference index in different injection parameters

Fig. 9
Fig. 9 Change of pressure difference ΔPc and torque Nitric oxide (NOx) and particulate matter (PM) are main emissions of diesel engine.NOx was initially selected as representative emission of diesel engine on preliminary stage.Changes of rotational speed and fuel injection timing could directly affect NOx production.ΔP max could reflect variety of injection timing and position relation between maximal burst pressure and TDC.Due to coming time of maximal temperature lagging to that of

Fig. 10
Fig. 10 Change of pressure ΔP max and NOx

Table 1
Physical meaning covered by pressure parameter

Table 2
Simulation calculation point parameter

Table 3
Ignition commencement angle change, °CA