Research for the turbulent two-phase flow governing equations in direct- injection engine/Turbulentinio dvieju faziu sriauto tiesioginio ipurskimo variklyje svarbiausiuju lygybiu tyrimas.
Liu, Y. ; Yang, J. ; Qin, J. 等
1. Introduction
In the last years a considerable improvement of High Speed Direct
Injection (HSDI) Diesel Engine technology has occurred, with a strong
increase of fuel economy and a remarkable reduction of emissions and
combustion noise [1]. However, more stringent regulations are forcing
manufactures of automotives and power plants to reduce pollutant
emissions, for the sake of our environment. Turbulent two-phase flow in
diesel engine is far from being fully understood; it is probably the
most significant unsolved problem in classical physics. Since the flow
is turbulent in nearly all engineering applications, the urgent need to
resolve engineering problems has led to preliminary solutions based on
the Navier-Stokes equations up to a certain point, but then they
introduce closure hypothesis that rely on dimensional arguments and
require empirical input [2]. This semiempirical nature of turbulence
models puts them into the category of an art rather than a science. In
the standard KIVA-code, the Taylor Analogy Breakup (TAB) model,
originally proposed by Amsden is used to describe droplet breakup. The
TAB-model is based on an analogy between a droplet and an oscillating
spring-mass system [3]. The external force, the restoring force and the
damping forces are analogous to the droplet aerodynamic drag, the liquid
surface tension and the liquid viscous forces, respectively. A novel
feature of the model is claimed to be its absence of a critical Weber
number, for which breakup occurs. Instead, breakup is governed by the
droplet oscillation history. A second advantage is that the spray angle
is automatically determined, since the product droplets have velocities
normal to the respective paths of the parent droplets [4]. However, in
applying the model to the spray produced by a high-pressure common-rail
system breakup was seen to occur extremely rapidly, which led to a
significant under prediction of the liquid and vapor penetration
lengths. The TAB-model was found to be appropriate for injection
pressure up to around 400 bar, which was also observed by Tanner et al.
In the paper, the governing equations for the turbulent reacting
two-phase flow solved in the KIVA-3V fluid dynamics code are presented.
An Extended TAB-model (TP) model is proposed and used to calculate
cylinder pressure and corresponding heat release rates. One of the
features of this model is to equip droplets at the exit nozzle with a
deformation velocity such that their lifetime is extended to match
experimentally observed jet breakup lengths.
2. Gas phase equations
Applying Favre-averaging and some assumptions to be discussed
later, the governing equations for the gas phase can be cast in the
following form.
Continuity
[partial derivative][bar.[rho]]/[partial derivative]t + [partial
derivative]/[partial derivative][x.sub.i] [bar.[rho]] [[??].sub.j] =
[??] (1)
Momentum in i-direction
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
is the Favre-averaging of the viscous stress tensor.
[[delta].sub.ij] is the Kronecker symbol, [[delta].sub.ij] = 1 for i = j
and [[delta].sub.ij] = 0 for i [not equal to]. Specific internal energy,
E
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Turbulent kinetic energy, k
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
Turbulence dissipation, [epsilon]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where double indicates denote summation, thus e.g.
[[??].sub.ij] [partial derivative][[??].sub.i]/[partial derivative]
[x.sub.j] corresponds to the tensor product [??][gradient][??] x
[bar.[rho]] is the Reynolds-averaged density and [[??].sub.i], is the
i-th component of the volume-averaged velocity. P is the pressure,
which, for the cases considered in this thesis, is assumed to be
spatially uniform according to the low Mach-number limit, [??],[??],
[??],[??], are the Favre-average of the turbulent kinetic energy, its
dissipation, the specific internal energy and the i-th component of the
heat flux vector, respectively. [[??].sub.ij] has been defined above,
and u is the dynamic viscosity, which has two contributions
u = [u.sub.air] + [C.sub.u] [[??].sup.2]/[epsilon] (7)
[u.sub.air] is the laminar contribution and is calculated according
to a Sutherland formula
[u.sub.air] = [A.sub.1][T.sup.3/2]/[[A.sub.2]+T] (8)
where [A.sub.1] = 1.457 x [10.sup.-5] and [A.sub.2] = 111. The
second term in the expression for the viscosity is the turbulent eddy
viscosity, which is calculated from equations (5) and (6). In flows with
high Reynolds number [u.sub.air] is very small compared to the eddy
viscosity. [C.sub.1], [C.sub.2], [C.sub.3], [Pr.sub.k],
[Pr.sub.[epsilon]] are constants resulting from a combination of
theoretical considerations and empiricism. Their values for the
k-[epsilon] turbulence model employed in this work are given in Table 1.
In addition, the constant [C.sub.s] is set equal to 1.5. The term [??]
in the energy equation is the source term due to chemical heat release.
For the cases studies here, buoyancy effect can be neglected, so no
terms containing the gravity have been retained in the equations.
Eqs. (1) and (2) result from the Favre-averaging of the
Navier-Stokes equations, which fully describe the fluid flow. As a
result of the averaging, unclosed terms appear which require modeling.
In order to close the turbulent Reynolds stress tensor in the momentum
equations, the so-called Boussinesque-approximation, which is based on
an analogy between molecular diffusion and diffusion turbulent eddies,
has been employed. It reads
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where [u.sub.t] is the turbulent eddy viscosity as given by the
second term on the right-hand side of Eq. (7). An important implication
of introducing a turbulent viscosity of the kind describes here is that
the model is incapable of accounting for anisotropy of turbulence.
Regarding the small scales, this is not a serious limitation, since they
tend to dissipate energy without any directional preference. Large
turbulent structures, on the other hand, are clearly anisotropic, which
poses a significant constraint for the applied turbulence model.
3. Treatment of the liquid phase
In addition to the solution of the fluid dynamics of the gas phase,
modeling the physical processes occurring in a DI diesel engine also
requires an adequate treatment of the liquid phase. Current approaches
are generally based on a statistical description of the spray. The spray
equation [5] describes the evolution of the droplet probability density
function (PDF). This PDF has a number of independent variables in
addition to time, defined by the amount of statistical information
needed. The spray equation has two source terms, one due to droplet
breakup (increases the number of droplets) and the other due to droplet
coalescence (decreases the number of droplets). The breakup model, which
is the subject of the current discussion, should ideally be able to
describe primary (atomization) as well as secondary breakup. In the
standard KIVA-code, the Taylor Analogy Breakup (TAB) model, originally
proposed by Amsden [6] is used to describe secondary droplet breakup.
The TAB--model is based on an analogy between a droplet and an
oscillating spring-mass system. A novel feature of the model is claimed
to be its absence of a critical Weber number, for which breakup occurs.
Instead, breakup is governed by the droplet oscillation history. A
second advantage is that the spray angle is automatically determined,
since the product droplets have velocities normal to the respective
paths of the parent droplets. However, in applying the model to the
spray produced by a high-pressure common-rail system breakup was seen to
occur extremely rapidly, which led to a significant under prediction of
the liquid and vapor penetration lengths. The TAB-model was found to be
appropriate for injection pressure up to around 400 bar, which was also
observed by Tanner et al [7, 8]. An Extended TAB-model (TP) model is
proposed and used to calculate cylinder pressure and corresponding heat
release rates. One of the features of this model is to equip droplets at
the exit nozzle with a deformation velocity such that their lifetime is
extended to match experimentally observed jet breakup lengths. Being
somewhat related to the TAB-model, the wave-breakup model assumed that
breakup is caused by instabilities on the droplet surface. A major
advantage of the approach is that the model treats atomization and
secondary breakup as indistinguishable processes. Hence, no information
of the droplet size distribution at the nozzle exit is needed.
Cylindrical blobs with a diameter equal to that of the nozzle exit are
injected into the computational domains.
4. Experiment set-up
In the process of engine bench tests, the cylinder pressure must be
strictly monitored for the various tanks, therefore, the cylinder head
design needs to be modified with the four warm-plugs and the cylinder
pressure sensor is installed on the transition casing. Fig. 1 is the
cylinder pressure sensor design and structure. The in-cylinder pressure
was measured using a flush mounted quartz sensor from Kistler (type
6061B) order to assess the performance of the model in terms of
predicting cylinder pressure, heat release over a wide range of part
load conditions an extensive parameter study varying injection timing,
EGR (exhaust gas recirculation)-rate and rail pressure, has bee
conducted. First, boundary conditions required for the calculations as
well as the operating points investigated are discussed. Next, the basis
for the numerical analysis is outlined. Thereafter, the results of the
simulations and the measured data are compared. Following this, the
results obtained are reflected upon qualitatively in order to assemble a
picture of how combustion in a small bore DI diesel engine featuring
relatively high swirl proceeds.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
The pressure transducer is very accurate on a relative basis but
does not directly yield absolute values. In this measurement, the
reference was taken to be atmospheric pressure and it had to be
corrected for the applied boost pressure. The peak motored cylinder
pressure is extremely sensitive to small changes in the pressure at
intake valve closing (IVC).
In Table 2 some data on the engine is summarized. The multicylinder
equivalent of the investigated single-cylinder test engine is the four
cylinders. The injection system is a first generation Bosch Common-Rail
featuring a maximum injection pressure of 1350 bar.
5. Results and discussions
For each of the simulations cylinder pressure and heat release rate
are compared with measured values. Fig. 2 shows the cylinder pressure
traces and corresponding heat release rates for the measured and
simulated parameter study varying the work conditions. As can be seen in
Fig. 2, the overall agreement in both ignition delay and peak cylinder
pressure are excellent. For 2200 r/min 64 Nm, the cylinder pressure is
changed quickly when it is 20[degrees]CA (Crank angle) BTDC (before top
dead center). So the ignition delay time is 12[degrees]CA. The biggest
experimental pressure is 5800 kPa, which is near to TP model (5820 kPa)
and far from KIVA original model (6020 kPa). The heat release rates are
similar between TP model (45 J/[degrees]CA) and experiment (42
J/[degrees]CA), but in the original KIVA model it is 55 J/[degrees]CA.
This is due to fact the TP model is a multistep chemistry model and KIVA
is a one step model. But the difference between the original model and
the improved model decreases with the fuel injection quantity, because
as the fuel injection quantity increases, power increases, the cylinder
temperature and pressure increase and the difference between the
multistep and one step models decreases. The cylinder pressures are well
fitted between simulation and experiment for all other work conditions.
The simulation heat release rates are higher than the experiments
because of different calculation steps, but the errors are small and the
TP model can be used for simulating a real diesel engine.
6. Conclusion
1. The Navier-Stokes equations are closed if turbulent kinetic
energy k equation and turbulent dissipation e equation are added.
2. The calculation applying PDF and experiments of cylinder
pressure and the corresponding heat release rates in DI diesel engine
are fitted well.
http://dx.doi.org/ 10.5755/j01.mech.18.1.1283
Acknowledgment
The study was sponsored by the Beijing Natural Science Foundation
(3102011), China and Beijing University of Civil Engineering and
Architecture Ph.D foundation (101001604) and Funding Project for
Academic Human Resources Development in Institutions of Higher Learning
under the Jurisdiction of Beijing Municipality (PHR (IHLB) 201008370,
201106125).
References
[1.] Graedel, T. 2002. Industrial ecology and the automobile,
Prentice-Hall, New Jeasey, 243-256.
[2.] Janulevicius, A.; Juostas, A.; Pupinis, G. 2010. Engine
working modes during tractors operational period, Mechanika 3(83):
58-63.
[3.] Kellaci, A.; Mazouzi, R.; Khelidj, B.; Bounif, A. 2010. The
effect of lubricant rheology on piston skirt/cylinder contact for an
internal combustion engine, Mechanika 1(81): 30-36.
[4.] Liu Yongfeng; Pei Pucheng. 2005. Analysis on ignition and
extinction of n-heptane in homogeneous systems, Science in China 10:
556-569.
[5.] Carl-Anders Hergart. 2001. Modeling combustion and soot
emissions in a small-bore direct-injection diesel engine, Shaker Verlag,
Aachen, 10-22.
[6.] Liu Yongfeng; Pei Pucheng. 2006. Asymptotic analysis on
autoignition and explosion limits of hydrogen-oxygen mixtures in
homogeneous systems, International Journal of Hydrogen Energy 31(5):
639-647. http://dx.doi.org/10.1016/j.ijhydene.2005.05.005
[7.] Liu Yongfeng. 2011. A Phenomenological model for prediction
auto-ignition and soot formation of turbulent diffusion combustion in a
high pressure common rail diesel engine, Energies 4: 894-912.
http://dx.doi.org/10.3390/en4060894
[8.] Liu Yongfeng. 2010. Optimization research for a high pressure
common rail diesel engine based on simulation, International Journal of
Automotive Technology 11(5): 625-636.
http://dx.doi.org/10.1007/s12239-0100075-4
Y. Liu, Beijing University of Civil Engineering and Architecture,
Beijing 100044, China, E-mail: liuyongfeng@bucea. edu. cn
J. Yang, Beijing University of Civil Engineering and Architecture,
Beijing 100044, China, E-mail: yangjianwei@bucea.edu.cn
J. Qin, Beijing University of Civil Engineering and Architecture,
Beijing 100044, China, E-mail: qinjianjun@bucea.edu.cn
A. Zhu, Beijing University of Civil Engineering and Architecture,
Beijing 100044, China, E-mail: zhuaihua@bucea.edu.cn
Received March 23, 2011
Accepted February 02, 2012
Table 1
k-[epsilon] turbulence model constants
[C.sub.I] [C.sub.2] [C.sub.3] [Pr.sub.k] [Pr.sub.[epsilon]]
1.44 1.92 -1.0 1.0 1.3
Table 2
k-[epsilon] turbulence model constants
Displacement 300 cc
Bore 70.0 mm
Stroke 78.0
Connecting tod 132.6 mm
Combustion chamber Omega-shape bowl
Injector nozzle 6-hole
Nozzle hole diameter 0.124 mm
Injector protrusion 1 mm