Application of Space-time Conservation Element and Solution Element Method in Intake and Exhaust Flows of High Power Density Diesel Engine

Guo-dong YOU*,Chun-long XU,Jun-feng XUMing ZHUZeng-qun WANG

Application of Space-time Conservation Element and Solution Element Method in Intake and Exhaust Flows of High Power Density Diesel Engine

Guo-dong YOUa,*,Chun-long XUb,Jun-feng XUa,Ming ZHUa,Zeng-quan WANGb

aSchool of Mechatronics Engineering,North University of China,Taiyuan 030051,ChinabChina North Engine Research Institute,Datong 037036,China

A one-dimensional pipe f l ow model of single-cylinder diesel engine is established to investigate the intake and exhaust f l ow characteristics of diesel engine in the condition of high power density(HPD).A space-time conservation element and solution element(CE/SE)method is used to derive the discrete equations of the partial differential equation for the intake and exhaust systems.The performance parameters of diesel engine with speed of 2100 r/min are simulated.The simulated results are in accordance with the experimental data.The effect of increased power density on charging coeff i cient is analyzed using a validated model.The results show that the charging coeff i cient is slowly improved with the increase in intake pressure,and is obviously reduced with the increase in engine speed.

Copyright?2013,China Ordnance Society.Production and hosting by Elsevier B.V.All rights reserved.

Power machinery and engineering;HPD diesel engine;Intake and exhaust system;CE/SE method;Charging coeff i cient;Numerical simulation

1.Introduction

As the global demand for energy conservation and emission reduction is getting more and more attention,the development trend of diesel engine is to reduce its displacement and improve its power density[1-5].The basis characteristics of HPD diesel engine are high speed and high boost pressure, which makes the research on exhaust process of HPD diesel engine different from the traditional research.The gas f l ow states of intake and exhaust systems have great inf l uence on the power,fuel economy and emission performances of engine.The research on engine intake and exhaust f l ow has been always a project of particular interest to the researchers[6]. Currently,the fi nite volume method is a main numerical method for simulating the intake and exhaust systems of diesel engine[7-10].

The CE/SE method is a new numerical method,which was originally proposed by S.C.Chang from NASA Lewis Research Center in the 1990s.It treats the space and time fl uxes uniformly,establishes the conservation and solution elements based on the principle of conservation of space fl ux and time fl ux,and ensures the conservation of the format in local and global.It needs no other numerical approximation technique except simple Taylor expansion,and does not need toapplyanymonotonicityrestrictionorcharacteristic computing technology.Therefore,the method has the advantages of simple structure,convenient calculation and high accuracy of shock wave-capturing calculation,etc[11-16].

In the paper,the CE/SE method is used to simulate the intake and exhaust processes of a HPD single-cylinder diesel engine,test and verify the applicability of the method in the one-dimensional unsteady fl ow simulation,and provide the reliable bases for the design and experiment of engine intake and exhaust systems in HPD diesel engine.

2.Governing equations and algorithm

2.1.Governing equations

Under the conditions of variable section,wall friction,heat transfer or combustion and gradually changing entropy,the variation of parameters when f l uid f l ows through a pipe with length of dx is shown in Fig.1.

In Fig.1,x is the inf l ow section;u,ρ,p and F are the f l ow velocity,density,pressure and section area,respectively.The fundamental equation of unsteady f l ow in the intake and exhaust pipes of internal combustion engine is derived according to the law of conservation of mass,the momentum theorem,and the law of conservation of energy.

By introducing state vector w,f l ow vector f and source vector s,the above fundamental equation can be rewritten to a uniform conservation equation

where c1(w)is a term caused by variation of delivery pipe section,and c2(w)is a term caused by friction and heat transfer.

2.2.Derivation of discrete equation based on CE/SE

method

Let x1=x and x2=t represent two coordinates in twodimensional Euclidian space E2.By introducing vector hm=(fm,wm),m=1,2,3,and divergence operator?= (?/?x，?/?t),the governing equation can be rewritten to where S(V)is the closed surface of any area V in space E2.In Eq.(3),obviously the space and time are unif i ed to treat.

Fig.1.Control volume of non-isentropic f l ow with variable section.

Fig.2.Time-space staggered grid of SE/CE.

In the staggered grid shown in Fig.2(a),there is a corresponding CE/SE for every grid point(e.g.A,C and F).A solution is approximately given in CE,satisfying the conservation law in SE.As shown in Fig.2(b),SE(j,n+1/2) corresponding to the grid point A(xj，tn+1/2)is a diamond area BDFG surrounded by dashed lines,while CE(j,n+1/2)is a rectangle area BCEF surrounded by solid lines.

For any point(x，t)∈SE(xj，tn),wmand fmcan be approximately calculated by f i rst order Taylor expansion,and the source item smcan be approximately calculated by zero order Taylor expansion.In this way,if wmt,fm,fmx,fmtand smare treated as the functions of wmand wmx,and every explicit scheme of CE(j,n+1/2)is derived,Eq.(4)can be simplif i ed tocondition of pipe end to obtain the values of(wm)njon the boundary.

Fig.3.Simulation model of single-cylinder diesel engine.

3.Validation of simulation model

3.1.Simulation model

Most of intake and exhaust systems of engines are the pipe fl ow systems.Since the fl ow area of the diesel exhaust valve changes rapidly,a unstable fl ow is caused by heat exchange when the working fl uid fl ows through the valve.The unstable fl ow is assumed to be the adiabatic and isentropic quasi-steady fl ow for simplifying the calculation,and the fl ow control equations are solved by using CE/SE method.

Based on the actual working conditions of single-cylinder diesel engine,an one-dimensional thermal power model has been established for performance simulation,as shown in Fig.3.

3.2.Experimental conditions and methods

In the experiment,a single-cylinder four-stroke direct injectiondieselengineisused.Itsboreis132mm,thestrokeis145mm, thelengthofconnectingrodis262mm,andthecompressionratio is17.Ahighpressurecommonrailisusedforfuelsupply,thefuel injection advance angle is15°,the opening and closing anglesof intake valve are 27°CA BTDC and 40°CA ABDC,respectively, and the opening and closing angles of exhaust valves are 58°CA BBDC&25°CA ATDC,respectively.

The measured Hg pressure is used as test intake pressure pin,and the average value from the pressure sensor of the combustion analyzer is used as test exhaust pressure pex.The simulation boundary conditions are that the intake pressure is 0.3 MPa,the intake temperature is 333 K;the exhaust pressure is 0.15 MPa,the exhaust temperature is 523 K;the combustion model is double Vibe model,and the heat transfer model is Woschni1978 model.

3.3.Analysis of experimental results

According to the principle of that the simulation parameters corresponds with the experimental parameters,the effective power Pe,peak f i ring pressure Pmax,fuel consumption beand other performance parameters of diesel engine are compared at the engine speed of 2100 r/min.The deviation between the simulated values and the experimental results is minimized,asshown in Table 1.The simulated main performance parameters are in good agreement with the experimental results,and the maximum error of effective fuel consumption is up to 3.18%.

Fig.4 shows the pressure f l uctuation curves of singlecylinder diesel engine.It can be seen from Fig.4 that the experimental results are in good agreement with the simulated values,and the correlation coeff i cient of the two curves is 0.99.The phases of their peak pressures are approximately the same,but the simulated value is 0.4 MPa larger than the experiment value.

The pressure curves of exhaust duct outlet at the measuring point MP2 are shown in Fig.5.Fig.5 shows the variations of phases obtained from the experimental results and simulated values are the same,the peak values are relatively close to each other,and the correlation coeff i cients of the two curves are 0.89.Thus it can be seen that CE/SE method is very applicable to the unsteady f l ows of intake and exhaust pipes of diesel engine.The model can be used to analyze the charging coeff i cient in next step.

The outlet pressure of exhaust duct at the measuring point MP2 is simulated by using f i nite volume method.The results are shown in Fig.6.The exhaust pressure f l uctuation obtained by the experimental and simulated results has a signif i cant phase difference,a larger non-physical oscillation partially appears in the calculated result,the deviation of the peak value is high,and the correlation coeff i cient of the two curves is 0.58.It indicates that the f i nite volume method has obvious disadvantages in simulating the exhaust system of HPD diesel engine in which the shock f l ow exists.

Table 1Performance parameters and deviation of diesel engine

4.The inf l uence of improved power density on charging coeff i cient

The inf l uence of improved rotational speed and exhaust pressure on the charging coeff i cient of single-cylinder diesel engine is analyzed by using a calibration model and CE/SE method.When the rotational speed is improved,the excess air coeff i cient remains unchanged,and the fuel delivery per cycle is adjusted according to inf l ow air mass.Fig.7 shows the variation of charging coeff i cient with intake pressure.It can be seen from Fig.7 that the experimental result is relatively close to the simulated result.The charging coeff i cient slowly increases with the increase in intake pressure.

Fig.4.Pressure f l uctuation of single-cylinder diesel engine.

Fig.5.Experimental and calculated pressures of exhaust port at MP2 at 2 100 r/min.

Fig.6.The experimental and calculated pressures of exhaust port at MP2 obtained by f i nite volume method at 2100 r/min.

Fig.7.Variation of charging coeff i cient with intake pressure.

Fig.8 shows the variation curve of charging coeff i cient with engine speed.It can be seen from Fig.8 that theexperimental result is relatively close to the simulated result. With the increase in engine speed,the charging coeff i cient obviously reduces.

Fig.8.Variation of charging coeff i cient with engine speed.

5.Conclusions

(1)CE/SE method is used for the discrete governing equations.The program for the simulation of intake and exhaust f l ows of HPD diesel engine is simpler and more applicable.

(2)The simulated results of diesel engine exhaust process show that the simulated main performance parameters are in good agreement with the experimental results at the engine speed of 2100 r/min,the maximum error of effective fuel consumption is up to 3.18%;the simulation curve of pressure f l uctuation at the exhaust duct outlet is in good agreement with the experimental curve,and the correlation coeff i cient is 0.94.

(3)CE/SE method can be used to ref l ect the intake and exhaust f l ow characteristics of HPD diesel engine.A solution is provided to multi-component mixed f l ow issue or other issues of other systems of engine.It can also provide more accurate initial conditions for in-cylinder multidimensional simulation.

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20 August 2012;revised 22 April 2013;accepted 2 July 2013 Available online 3 October 2013

*Corresponding author.

E-mail address:ygdnuc@163.com(G.D.YOU).

Peer review under responsibility of China Ordnance Society

Production and hosting by Elsevier

2214-9147/$-see front matter Copyright?2013,China Ordnance Society.Production and hosting by Elsevier B.V.All rights reserved.

http://dx.doi.org/10.1016/j.dt.2013.09.018