Multidimensional modeling and simulation of diesel engine combustion using multi-pulse injections by CFD.

Showry, Konkala Bala ; Raju, A.V.S.

Introduction

Engine experiments have shown that, with high pressure multiple injections reduces NOx-Soot trade off curves of a diesel engine can be shifted to the origin[4] than those with the conventional single pulse injections reducing NOx and soot significantly. Computational fluid dynamics helps in analyzing the various parameters without expensive experimental setup. Using high pressure multiple injection higher efficiency and NOx can be reduced as temperature gets reduced. For an optimum dwell the performance (for number of pulses) of diesel engine increases [2]. Tanin studied that high pressure is very effective in single cylinder of heavy duty diesel engine. They found that particulate emissions decreased significantly with increased boost pressure due to increased available air for soot to oxidation at elevated intake pressure while holding NOx constant [6]. Small advance of the start of combustion (two or three crank angle degrees) was enough to reduce particulate by a factor of six[1]. Nemer and Reitz Experimentally investigated the effect of double pulse split injection on soot and NOx emissions using single cylinder caterpillar engine, they varied the amount of fuel injected in the first pulse from 10 to 75 percent of the fuel and found split injection affected soot-NOx trade off [4]. Tow continued the study of Nehmer and Reitz using same engine for different dwells between pulses in triple injection and they found at high engine load particulate could be reduced by factor of three [4].

In the present study triple injection has been carried out. High pressure injection with multi-pulse injection (three pulses per cycle) has been carried out, and performance of engine and emissions were studied. This study focuses mainly on p-[theta] curve, temperature [v.sub.s]. crank angle, enthalpy, turbulent kinetic energy, mass fractions, and tangential velocity, NOx, Sox, and soot during the combustion process.

Nomendature: Percent of fuel injected in each pulse

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Methodology

Model formulation

The computer code used in this study was FLUENT. The code can solve unsteady, compressible turbulent flows with combustion and fuel spray, and have been used for the computations of various internal combustion engines The code uses a finite volume methodology to solve discretized Navier-strokes equations. RNGK-[??] was used in this study. It could predict more realistic large scale flame structures compared with the K-[??] model. The RNG K-[??] model is formulated as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Where [C.sub.3] = [-1 + [2 [C.sub.1] - 3m(n - 1)] + [(-1) [delta] [square root of 6] [C.sub.[mu]] [C.sub.[eta]] [eta]]]/3 (3)

[delta] = 1; if [nabla] x u < 0

[delta] = 0; if [nabla] x u > 0

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In equation (1)-(3) k and e are turbulent kinetic energy and its dissipation rate respectively. [rho],u,[tau] and [mu] are density, velocity, stress tensor and effective viscosity respectively. [eta] is the ratio of the turbulent--to mean--strain time scale. S is the magnitude of the mean strain. m=0.5, and n =1.4. The [C.sub.3] term accounts for the nonzero velocity dilatation which is closed.

Governing Equations

The governing equations of gas flow consist of mass, momentum and energy conservation equations turbulence equations, gas state relation equations. To take care of physical modeling k-[epsilon] turbulence model is employed. The various equations, which are solved:

Continuity [partial derivative]p/[partial derivative]t + [nabla]([partial derivative]U) = 0

Momentum [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Turbulence Model

K-Equation

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

s-Equation

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The quantities c[[epsilon].sub.1] c[[epsilon].sub.2], [[epsilon].sub.3] [pr.sub.[epsilon]], [pr.sub.k] are constants whose values are determined from experiments and some theoretical considerations, a feature that establishes certain universality. Standard values of these constants are often used in engine calculations as given below. c[[epsilon].sub.1] = 1.44 c[[epsilon].sub.2] = 1.92 c[[epsilon].sub.3] = -1, [pr.sub.k] = 1.0, [pr.sub.[epsilon] = 1.3

Mathematical models

Spray model

Spray models used in this study is WAVE break up model suggested by Reitz and could be summarized as follows. [9]

Liquid break up is modeled by postulating the new drops are formed (with drop radius r) from a parent drop or blob (with radius a) with stripping.

[r.sub.new] = [B.sub.0] x [LAMBDA] [4]

Where [B.sub.0] = 0.61 is a constant, the value of which is fixed. The rate of change of drop radius in apparent parcel due to drop breakup is described by using the rate expression;

dr/dt = [r - [r.sub.new]]/[[tau].sub.bu], [[tau].sub.bu] = 3.788 r/[LAMBDA][OMEGA] [5]

The spray--wall interaction model used in the simulations is based on the spray--wall impingement model descried in [8]. The model assumes that a droplet, which hits the wall is affected by rebound or reflection based on the Weber number. The Dukowicz model was applied for treating he heat--up and evaporation of the droplet which is described in [10]. This model assumes a uniform droplet temperature. In addition the rate of droplet temperature change is determined by the heat balance which states that that heat convection from the gas to the droplet ether heat up the droplet or supplies heat for vaporization.

With higher droplet densities and relative velocities droplet collisions occur. High droplet densities are restricted to the spray kernel. High relative velocities can especially be seen at the tip of the spray, where preceding droplets are decelerated by the gas. Depending on the droplet collision conditions various effects like elastic droplet bouncing, droplet coalescence and droplet atomization are observed.

Ignition and combustion models

The shell auto ignition model was used for modeling of the auto ignition [9].In this mechanism species for hydrogen fuel, oxidizer, total radical pool, branching agent, intermediate species and products were involved. In addition the important stages of auto ignition such as initiation propagation, branching and termination were presented by generalized reactions described in [9].

The combustion model used in this study is of the turbulent mixing controlled verity as described by Magnusson and Hjertager [10]. This model assumes that in premixed turbulent flames, the reactions (fuel, oxygen) are contained in the same eddies and are separated from eddies containing hot combustion products. The chemical reactions usually have time scales that are very short compared to the characteristics of the turbulent transport processes. Thus it can be assumed that the rate of combustion is determined by the rate of intermixing on a molecular scale of the eddies containing reactants and those containing hot products in other words by the rate of dissipation of these eddies.

NOx and soot Formation Models

The reaction mechanism of Nox formation is expressed in terms of the extended a Zeldovich mechanism.

N2+O [left and right arrow] NO+N [6]

N+O2 [left and right arrow] NO+O [7]

N+OH [left and right arrow] NO+H [8]

From the fact that in most stoichiometric and fuel--lean flames, the occurring OH concentration very small, the third reaction of the Zeldovich mechanism can be neglected. For the formation of thermal Nox, the partial equilibrium approach can be used and the equilibrium of the first two reactions result in one global reaction as follows; N2+O2 [left and right arrow] 2NO [9]

The chemical species appearing in this global reaction are used in the giver single-step fuel conversion equation via:

d[NO]/dt = 2[k.sub.f] [[N.sub.2]I[O.sub.2]] = 2kf [N2/O2] [10]

Where only the forward reaction is considered and the reaction rate [k.sub.f] is given as

Kf = A/[square root of T] exp (-E.sub.a]/RT) [11]

The soot formation model currently implemented in fluent is based upon a combination of suitably extended and adapted joint chemical/physical rate expressions for the representation of the processes of particle nucleation, surface growth and oxidation.

[dm.sub.soot]/dt = [dm.sub.form]/dt - [dm.sub.axid]/dt [12]

[dm.sub.form]dt = [A.sub.f] [m.sub.fv] [p.sup.0.5] exp (-[E.sub.a]/RT) [13]

[dm.sub.soot]/dt = 6[M.sub.c]/[[rho].sub.s][d.sub.s] [m.sub.2][R.sub.tot] [14]

Numerical model

The numerical method used in this study is a segregated solution algorithm with a finite volume-based technique. The segregated solution is chosen is due to the advantage over the alternative method of strong coupling between the velocities and pressure. This can help to avoid convergence problems and oscillations in pressure and velocity fields. This technique consists of an integration of the governing equations of mass, momentum species, energy and turbulence on the individual cells within the computational domain to construct algebraic equations for each unknown dependent variable. The pressure and velocity are coupled using the SIMPLE algorithm which causes a guess and correct procedure for the calculation of pressure on the staggered grid arrangement. It is more economical and stable compared to the other algorithms. The upwind scheme is always bounded and provides stability for the pressure correction equation. The CFD simulation convergence is judged upon the residuals of all governing equations. This scaled residual is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where [phi]p is a general variable at a cell p, [a.sub.p] is the center coefficient, [a.sub.nb] are the influence coefficients for the neighboring cells and b is the contribution of the constant part of the source term. The results reported in this paper are achieved when the residuals are smaller than 1.0 x 10-4.

Turbulent dispersion of particles

Dispersion of particles due to turbulent fluctuations in the flow can be modeled using either

Stochastic tracking (discrete random walk)

Particle cloud model

Turbulent dispersion is important because it is more realistic, enhances stability by smoothing source terms and eliminating local spikes in coupling to the gas phase.

Engine and injector specification

Results

Contour of static pressure at different crank angles

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Contours of NOX

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Contours of particulate matter

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Conclusions

1. NOx levels of simulation were compared to experimental results from SAE technical series 950217 and found very good agreement.

2. P-e curve have also shown good agreement.

3. Soot levels are very low.

4. Multiple injections with secondary injections following the main injection were found to be most effective in reducing particulate.

Appendix

BTDC Bottom dead center

ATDC After top dead enter

CA Crank angle

SOI Start of injection

DOI Duration of injection

References

[1] D.A. Pierpont, D.T. Montgomerry, and R.D. Reitz Reducing NOx using multiple Injections and EGR in a D.I. Diesel engine 950217.

[2] Internal combustion fundamentals by J.B. Heywood.

[3] T.C. Tow, D.A. Pier Pont, and R.D. Reitz Reducing particulate and NOx Emissions by using Multiple injections in a Heavy duty D.I. Diesel Engine S.A.E Paper 940897.

[4] Zhiyu Han, AN Uludogan, Gregory J. Hampson, and Rolf D. Reitz Mechanism of soot and NOx Emission Reduction Using Multiple-injection in a Diesel Engine SAE Paper 960633.

[5] Taewon Lee and Rolf D. Reitz The Effects of Split Injection and Swirl on a HSDI Engine E quipped With a Common Rail Injection System SAE Paper 2003-01-0349.

[6] K.V. Tanin, D.D. Wickman, D.T. Mantgomery, S. Das, and R.D. Reitz The influence of boost pressure on emission and fuel consumption of a heavy duty single cylinder diesel Engine SAE paper 1999-01-0840.

[7] Chengxin Bai and A.D. Gosman Development of methodology for spray impingement simulation. SAE paper 950283.

[8] Naber JD and Reitz R.D "Modeling Engine Spray wall impingement" SAE 880107

[9] Liu, A.B. and Reitz R.D. "Modeling the Effects of Drop Drag and Break-up on Fuel sprays SAE 930072.

[10] Dukowicz, J.K "Quasi steady droplet change in the presence of convection Informal report Los Alamos Scientific Laboratory" LA 7997-MS.

Konkala Bala Showry (1) and A.V.S. Raju (2)

(1) Professor, CMR Technical Education Society, Hyderabad A.P India Corresponding Author balakshowry@yahoo.com

(2) Professor, JNTUCEH Hyderabad A.P. India

Table 1

No of cylinder 1 No of Nozzles 6

Cylinder bore 137.2mm Nozzle diameter 0.26mm
Spray included 140 Fuel N-heptane
 angle
Stroke length 165.1mm Piston Deep bowl
displacement 2.44lt Injection pressure 1200 bar
Fuel injection Common rail Injection approach La Grangian
 system
Connecting rod 298.5mm Turbulence model RNGK-[epsilon]
 length
Engine speed 2100 rpm Atomization Pressure swirl
Swirl ratio 2.0
Atomizer 6 deg
 dispersion angle

Table 2

Dwell 20deg
Start of injection 20[degrees]BTDC
Duration of injection 24[degrees]
Half cone angle 20
Fuel n-heptane
Mass flow rate 0.00356 kg/sec
Time step /deg 6.6666e-5
Pressure 120 MPa