Multidimensional modeling of the effect of fuel injection ... - Core

Propulsion and Power Research 2013;2(2):162–175 http://ppr.buaa.edu.cn/

Propulsion and Power Research www.sciencedirect.com

ORIGINAL ARTICLE

Multidimensional modeling of the effect of fuel injection pressure on temperature distribution in cylinder of a turbocharged DI diesel engine Sajjad Emamia,n, Samad Jafarmadarb a

Young Researchers and Elite Club, Khoy Branch, Islamic Azad University, Khoy, West Azerbaijan 58159 -15149, Iran Mechanical Engineering Department, Technical Education Faculty, Urmia University, Urmia, West Azerbaijan 57561-15311, Iran

b

Received 3 August 2012; accepted 16 January 2013 Available online 6 June 2013

KEYWORDS Injection pressure; Indicated power; Temperature contour; Equivalence contour; Soot; NOx; Combustion modeling

Abstract In this study, maintaining a constant fuel rate, injection pressure of 275 bar to 1000 bar (275 102 kPa to 1000 102 kPa), has been changed. Effect of injection pressure, the pressure inside the cylinder on the free energy, power, engine indicators, particularly indicators of fuel consumption, pollutants and their effects on parameters affecting the output of the engine combustion chamber have been studied in droplet diameter. Finally, the effects of fuel mixture equivalence, Cantor temperature, soot and NOx due to the increase of injection pressure, engine efficiency and emissions have been examined. & 2013 National Laboratory for Aeronautics and Astronautics. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction Diesel direct injection (DI) is widely used in automotive and industrial applications. In the past decades, the main n

Corresponding author: Tel.: +98 441 2972000. E-mail address: [email protected] (Sajjad Emami)..

Peer review under responsibility of National Laboratory for Aeronautics and Astronautics, China.

approach is the design of combustion engines and power generation, but because of today's tougher engine emission regulations and standards, a new viewpoint has opened in the motor engineering. Sugiyama and colleagues had studied numerical highpressure fuel spraying only in two cases, 150 MPa and 50 MPa [1]. The results show that when the spray pressure is increased, the maximum pressure inside the combustion chamber increases too and the time to reach maximum pressure is also shorter. Abu Bakar and his colleagues studied the effects of high pressure diesel fuel spraying in a direct spray diesel engine in 2008 [2]. In their study, the range of spraying pressure changes from 100 MPa to

2212-540X & 2013 National Laboratory for Aeronautics and Astronautics. Production and hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jppr.2013.04.003

Multidimensional modeling of the effect of fuel injection pressure on temperature distribution

200 MPa. Based on their results, the best performance of 220 bar (220 102 kPa) of spray pressure engine was obtained and the minimum conditions on fuel consumption and fixed spraying pressure of 200 bar (200 102 kPa) was obtained. Patterson and colleagues used the code KIVA-II for reforms after studying spraying schedule, spraying pressure and multi-level spraying some stages so that the carbon black was reduced to about 30% and the maximum of carbon black was 75% of one level injection [3]. In terms of emission behavior, NOx is produced to a great extent, due to the high local temperatures found in diesel engines which are highly dependent on the initial rise of heat release. In addition, soot production and oxidation are both dependent on the mixing rate and local flame temperatures [4]. The injection velocity is one of the most influencing parameters on the previous factors, because it controls both the mixing process and the rate of heat release. This is why injection system parameters and nozzle geometry have been extensively studied due to their direct relationship with the fuel injection rate and fuel velocity. To support this, it has been recognized that the characteristics of the injection system are some of the most important factors in influencing emissions and performance of diesel engines [5–7]. In recent years, computer codes for simulating threedimensional (3D) combustion in internal combustion engines have been used. This paper studies the theoretical effects of fuel injection pressure and the temperature contours of the emission function equivalence on fourcylinder direct injection diesel engine equipped with a turbocharger in the form of a numerical simulation by CFD code.

163

Figure 1 Injection of the jet fuel from the nozzle [8].

where G ¼ −ρu′i u′j ui;j

ð4Þ

B ¼ ρ′u′i gi

ð5Þ

μt ¼ C μ ρ

k2 ε

ð6Þ

and the coefficients have the following standard values: Cμ

Cε1

Cε2

Cε3

Cε4

sk

sε

sρ

0.09

1.44

1.92

0.80

0.33

1.00

1.30

0.90

2. Governing equations

2.1. The fuel spray

Governing equations including continuity, momentum and energy are modified based on Reynolds average and according to Reynolds-averaged Navier-Stokes (RANS) equations based on semi-implicit method for pressure-linked equations (SIMPLE) algorithm, and k-ε standard turbulence model for numerical simulation of flow inside the combustion chamber is used.

The discrete droplet method is used to spray the fuel through separate droplets. The schematic view of the injection of the jet fuel from the nozzle is shown in Figure 1.

k¼

1 ′ ′ uu 2 i i

Where turbulent kinetic energy (TKE) μ ′ ′ ε¼ u u ρ ij ij

ð1Þ

ð2Þ

where viscous dissipation rate of turbulent kinetic energy

8 ∂k μt > > ρ k ¼ μ þ k þ ρu þ G þ B−ρε > j ;j ;j < ∂t sk ∂ε μt ε ε ε2 > > > : ρ ∂t þ ρuj ε;j ¼ μ þ s ε;j þ C1 k G þ C1 ð1−C3 Þ k B−C2 ρ k ε

ð3Þ

2.2. Model of heat transfer and evaporation of fuel droplets Heat transfer and mass transfer processes by the model obtained by Dukowicz are modeled [9,10]. Assuming a uniform temperature drop, track changes in energy balance equation to determine the temperature drops that heat energy transferred to the drop caused by the drop heating and evaporation will result in the model are as follows: md cpd

: dTd dmd ¼L þQ dt dt

ð7Þ

Heat flux transferred from the gas surrounding the droplet surface is obtained from the following relationship: :

Q ¼ αAS ðT∞ −TS Þ

ð8Þ

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Sajjad Emami, Samad Jafarmadar

2.3. Atomization fuel spray model wave standard In this model, the results of a linear stability analysis of liquid jet, the stability of a column of fluid removed from a circular orifice of radius inside a very large gaseous environment are considered incompressible stationary, the initial perturbations grow on the surface of the fluid and dynamic wavelength and other physical parameters related to the surrounding gas and the liquid sprayed. The oscillation frequency perturbations (surface waves) from the following equation is obtained. ′ 0 I1 ðkaÞ 2kl I1 ðkaÞ I1 ðlaÞ 2 2 ω þ 2υl k ω − I0 ðkaÞ k2 þ l2 I0 ðkaÞ I0 ðlaÞ 2 2 sk l −k I1 ðkaÞ ¼ ρ1 a2 ð1−k2 a2 Þ l2 þ k2 I0 ðkaÞ 2 2 ρ l −k I1 ðkaÞK0 ðkaÞ þ 2 ðU−iw=kÞ2 k 2 2 ð9Þ ρ1 l þ k 2 I0 ðkaÞK1 ðkaÞ In the above equation, k is the wave number and l2 ¼ k2 þ υωl . Drop packets with a characteristic size which equals the diameter of the outlet nozzles are spraying. Maximum frequency of this quadratic equation is obtained by means of disjoint ω ¼ Ω jet fuel into smaller droplets will be, droplets with a size proportional to wavelength surface waves on the surface of the jet fuel are as follows [11]: r ¼ B0 Λ

ð10Þ

The schematic model of fuel atomization wave is shown in Figure 2. Time decay of jet fuel is calculated from the relationship: τ¼

3:726B1 a ΛΩ

ð11Þ

Resize feature original songs unstable droplets are calculated from the relationship: da ¼ −ða−rÞ=τ; dt

r≤a

ð12Þ

Λ-wavelength and Ω-wave growth rate of the jet stability analysis are obtained. Constant B0, for diesel spray by Ritz

Figure 2 Schematic model of fuel atomization wave.

in 1987 vs. 0.61 is proposed. Time constant of B1 is fixed when the injector nozzle and the surface features of the process fluid are dependent on the initial disturbance. This constant is assumed equals 12. Its range is from 5 to 60. The lower the C2, the higher the time atomization and the jet fuel injection [12,13].

2.4. The walls of the jet fuel At high air velocity, the shear force at the film surface tears droplets back into the air flow. These droplets are generated at or near surface waves. This phenomenon is simulated within the wall film module and described under the terms of the entrainment model. In the wall film module, there are two means of generating film. First, films can be introduced via a film feeder. This is simply done by generating mass sources on specified areas of the geometry. The other method is to impinge droplets from the spray model to the wall. This section describes the splashing model, which is a refined model for droplet wall interaction. Due to imperfect atomization and evaporation, a large portion of the injected gasoline droplets impact on the walls of the inlet manifold or on the valve. In diesel engines, these wall collisions occur in the pre-chamber or the combustion chamber. Depending on local physical conditions and droplet momentum, a number of impingement regimes can be identified. A number of empirical investigations have been conducted with mono-size droplet streams to gain insight into droplet impingement behavior. Images of different impingement phenomena, droplet size measurements of reflected droplets and correlation for reflected versus impinged droplets are presented in [14–16]. Depending on the major factors wall temperature and droplet Weber number, a schematic qualitative map of possible regimes is found in [17]. In principle, higher temperatures prevent the formation of wall film due to rapid boiling or due to rebounding because of the Leiden frost phenomenon. For formation of wall film, the evaporative-wetting regime is the most important. Again, sub-regimes have to be distinguished. Droplets can just stick to the wall, spread to build the film and partially reflect or completely atomize. The rather complex physics and the wide range of local conditions render empirical and phenomenological models more advantageous than analytical models. Most of the published models are suitable for diesel conditions [18–21], but gasoline models are also

Figure 3 The walls of jet fuel.


165

published [22]. The schematic of the wall of jet fuel is shown in Figure 3. Model considered in this article is Walljet1 model which makes the engine working conditions; a vapor layer is

Figure 4 Table 1

Wall interactions of droplets.

MT4.244 engine specification.

Bore Stroke Displacement Combustion chamber Compression ratio Number of valves/cylinder Injection type Fuel injection pump Injection pressure (typical) Fuel injection nozzle Maximum power output Maximum torque output Kind of aspirated

100 127.0 mm 3.99 liters Reentrant 17.5 2/4 Direct injection DPA 450 bar (450 102 kPa) 5 hole 61.5 kW @2000 rpm 340 N m @1400 rpm Turbocharged & intercooled

Figure 7 Comparison of pressure versus crank angle inside combustion chamber, experimental and numerical cases.

Figure 5 Details of the computational grid and how to spray.

Figure 8 Comparisons of formation of NOx and soot according to the diesel engine versus crank angle.

Table 2 Comparison of experimental and simulation results for the base engine.

Figure 6 Grid independence compared to the pressure curves according to crankshaft angle.

NOx/(gr/(kW hr)) Soot/(gr/(kW hr)) Power output per cycle

Experimental value

Numeric value

Percentage of lapse

1.15 0.057 72.87

1.38 0.01 71.6

8% 4.3% 1%

166


formed between the droplet and the wall, and depending on the droplet Weber number drops back or slide on the wall [8,23]. Weber number is criterion 80. Phenomenon back in less than this number drops rapidly, but the tangential component of the wall have the vertical velocity component in the previous photo and can change as a function of

Figure 9 Pressure variations versus crankshaft angle at different spraying pressures.

Figure 12

Effect of increased injection pressure on NOx.

Figure 13

Effect of pressure increase on soot.

Figure 10 Energy release versus crankshaft angle at various spraying pressures.

Figure 11 Diagrams of indicated power and indicated specific fuel consumption (ISFC).

Figure 14 diameter.

Impact of the speed of fuel injection on average fuel drop


Weber number drops. 2 =s We ¼ ρd Dd Un;in

ð13Þ

The following empirical relationship between the droplet Weber number and the Weber number drops before dealing relate to: Wenorm;out ¼ C1 ⋅Wenorm;in ⋅e−C2 Wenorm;in

ð14Þ

where C1 and C2 as empirical constants respectively 0.687 and 0.04415 were obtained. Given the above, the reflection angle β¼ (90-β) in the range 0oβo5 will change [24,25]. The tangential angle Ψ on the surface that gets reflected in the changing range of −180oΨo+180 will be determined. This angle is determined by a probability distribution function: π ψ ¼ − ln 1−pð1−e−k Þ k

ð15Þ

In this regard, a random number between 0 and 1 which can change the parameter k is calculated from the following

Figure 15

relationship: k e þ1 sinα ¼ ek −1

167

1 π 2 1þ k

ð16Þ

After the droplet diameter at different, Weber numbers will change as follows: 8 d1 ¼ d0 > < Weo50 50≤We≤300 d1 ¼ d0 ⋅f ðWenorm;in Þ ð17Þ > : We4300 d ¼ 0:2d 1

0

2.5. Spontaneous combustion model In the present work, the spontaneous combustion model Shell [26] is used for the Eddie turbulence combustion model. This model includes a decreased kinetics mechanism which consists of 5 species and 8 general reactions as below. Initiation: Kq

RH þ O2 !2Rn

Temperature contours at different angles of the crankshaft for different injection pressures.

ð18Þ

168


Figure 15

Propagation:

Linear termination:

Kp

ð19Þ

f4 Kp

ð20Þ

Rn !Rn þ P þ heat Rn !Rn þ Q

Continued.

f3 Kp

Rn !termination Quadratic termination: Kt

f2 K p

n

n

R þ Q!R þ B

ð21Þ

Branching: Kb

B!2Rn

ð22Þ

ð23Þ

2Rn !termination

ð24Þ

In the above equations Rn total radical pool, RH hydrocarbon fuel of the structure CnHm, Q intermediate species, B branching agent and P show the oxidized products.


169

2.6. Species transfer model

2.7. Combustion model (eddy break-up)

Species transfer model is generally expressed as below: ∂ ∂ ∂ ∂yk ðρyk Þ þ ðρUi yk Þ ¼ Γ yk þ Syk k ¼ 1; …; Kgas ∂xi ∂t ∂xi ∂xi ð25Þ

Major part of the mixing of combustion in diesel engines is controlled. The interaction between turbulence and chemical reactions must be considered. This model assumes that during the turbulent pre-mixed flames, reactants (fuel and oxygen) are identical with Eddie and the hot combustion products are separated in the receiver. Eddie's reaction to this set of scattering song lyrics: Cfu yox Cpr ⋅ypr ρ̇r fu ¼ ρmin yfu ; ; ð27Þ τR S 1þS

In the equation above, Γ yk and Syk are: Syk ¼ ṙk :Mk :Vcell

ð26Þ

μt Γ yk ¼ ρDk;m þ Sct The Schmidt number in Eq. (26) is assumed to be 0.7 and by the recommendation is considered [27].

Figure 16

One of The two expressions (oxygen or fuel) in parentheses determined limited quantity. The third possibility is the reaction which makes sure the flame does not spread in the absence of hot products [28].

Equivalent contours in different degrees of crankshaft for different injection pressures.

170


2.8. Model of nitrogen oxide formation

2.9. Model of formation soot

To form nitrogen oxide pollutants from the thermal mechanism, Zlodwich's mechanism is used [28].

The overall soot formation rate is modeled as the difference between soot formation and soot oxidation [29,30]: dmsoot dmform dmoxid ¼ − ð36Þ dt dt dt Soot formation rate is: dmform −Ea ¼ Af mfv P0:5 exp ð37Þ dt RT

N2 þ O↔NO þ N

ð28Þ

N þ OH↔NO þ H

ð29Þ

N þ O2 ↔NO þ O

ð30Þ

Maximum of NO will be formed in equivalence rate as 0.9. Therefore, the reaction Eq. (30) can be abandoned. Writing the balance equations for the first and the second reactions, we will have: K1 ½N2 ½O ¼ K2 ½NO½N

ð31Þ

K3 ½N½O2 ¼ K4 ½NO½N

ð32Þ

N2 þ O2 ↔2NO

ð33Þ

ð34Þ ð35Þ

Figure 17

ð38Þ

2.10. Profile engine The engine under study is a commercial DI, water cooled four cylinders, in-line, turbocharged aspirated with intercooler diesel engine of which the major specifications are shown in Table 1 [31]. Figure 5 shows details of the computational grid and how the spray injection is.

2.11. Boundary conditions and initial conditions

Formation discipline related to NO is: d½NO ¼ 2kf ½N2 ½O2 dt A −Ea kf ¼ pffiffiffiffi exp RT T

dmoxid 6Mc ¼ ms Rtot dt ρs ds

Fuel spraying speed is calculated from the following relationship [9,32]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ΔpðθÞ vinj ðθÞ ¼ cv ; cv ¼ 0:92 ð39Þ ρl

Contours NOx in different degrees of crankshaft for different injection pressures.


Figure 17

For penetration of spray (X), the following relationship and for the angle of spray and average diameter of droplets we have [33–36]: !0:25 Δp X ¼ 2:95 d 0:5 t 0:5 ð40Þ ρg −0:22 0:15 0:26 ρg L d θ ¼ 83:5 ð41Þ d D0 ρl d μ SMR ¼ 0:38 Re0:25 We−0:32 l 2 μg

!0:37

ρl ρg

!−0:47 ð42Þ

The pistons were considered as a moving wall. Cylinder head temperature, cylinder wall and piston surface are based on experimental data. Cylinder head temperature was 550 K, cylinder wall temperature 400 K and pistons surface 590 K.

3. Results and discussion Injection pressure is changed from 275 bar to 1000 bar (275 102 kPa to 1000 102 kPa). Comparison of cylinder pressure changing according to crank angle at 14308,

171

Continued.

18604, and 12862 cells is represented in Figure 6. As can be seen, the differences between three diagrams are small.

3.1. Simulation results of motor function and credit rating results From Figure 7, it is observed that the experimental data and numerical solutions are matching well [31]. The above diagram shows about 3% error between numerical and experimental pressures. Value of indicatory power becomes equal to 72.87 kW which has 1% difference with obtained 71.6 kW experimental, and Figure 8 shows the diagram of producing nitrogen oxide and diagram of producing soot based on the crankshaft angle for diesel engine [31]. In Table 2, the amounts of pollutants are compared to the numerical results in which a good match is observed.

3.2. Effect of injection pressure on performance and engine pollutants output In this paper, the results of injection pressure impact on engine performance parameters and engine pollutants output

172


with constant amount of consumable fuel per cycle is checked. In Figure 9, with increasing injection pressure, maximum value of pressure is increased inside the cylinder. Increasing spraying pressure raises the fuel speed and air mixture formation in delay phase of combustion. This provides more mixture for pre-mixing phase. Figure 10 shows energy release in each crankshaft degree for different spraying pressures. As can be seen, by increasing the injection pressure, ignition delay reduces. This means that by increasing the injection pressure, speed of droplets increases. Due to the constant fuel consumption and increase of spraying pressure, sprayed fuel will sprinkle in shorter time and that will cause shorter length of forced combustion, hence is increased the pre-mixed combustion zone. Figure 11 shows indicated power of engine and indicatory special fuel consumption. With the increase of injection pressure, indicated power of engine is increased about 12% and indicated specific fuel consumption (ISFC) of engine is decreased, this means that in return for the same fuel consumption, engine power output is increased that cause combustion process is better. Figure 12 shows effect of fuel injection pressure on NOx pollution per crankshaft angle. From Figure 12, it can be seen that with the increase of injection pressure, NOx increases too. By increasing injection pressure, fuel particles became smaller and in fact atomization of fuel will get better and area of pre-mixing is caused by faster. Figure 13 shows that by increasing the injection pressure from 275 bar to 1000 bar (275 102 kPa to 1000 102 kPa), soot decreases about 58%.

Figure 18

Figure 14 shows the effect of fuel injection pressure on average diameter droplets. By increasing the injection pressure due to the constant fuel consumption per cycle, length of spraying have also reduced. For each injection pressure, the process for average diameter change is: in primary degrees during the expansion course due to the high pressure of premixed combustion, the diameter of droplets decreases, and with the reducing of pressure in cylinder chamber due to the increased mass, average diameter of droplets increases. Figure 15 shows the temperature contours at different angles of the crankshaft for different injection pressures. Considering the temperature contours, the following results are obtained: (1) Non-homogeneous combustion in a diesel engine due to the temperature at some points reaches 2600 K, while in some areas, temperature is much lower and the temperature difference is about 1000 degrees to 1600 degrees in an angle of the crankshaft between the two points. (2) Considering the fact that the start spraying angle is 31 BTDC, it can be seen in the TDC, the fuel injection pressure is increased, more energy is released that it is led to rising temperatures. (3) At 370 and 380 degrees of crankshaft angle, the maximum temperature inside the cylinder can be seen in more locations due to the fuel and air mixing and uniform combustion. (4) At 400 degrees of crankshaft angle, it is observed in the injection pressure 275 times to 500 times, more

Contours of soot in various degrees of crankshaft for different injection pressures.


Figure 18

points have a high temperature of 2000 K. Considering the fact that the amount of fuel output injector pump is constant, at high pressures (pressures above 500 bar (500 102 kPa)) fuel injection is faster and the duration of injection is shorter in which. This causes the diffusion combustion ending earlier and it verifies the results obtained in this section. One important factor in the formation of pollutants is the equivalence ratio. Figure 16 and Figure 17 show the equivalence contours in different degrees of crankshaft so that the formation of these pollutants to reach the maximum value for different fuel injection pressures is shown. Considerable notes on the contours of the equivalent are: (1) With the increased fuel injection pressure, the chamber has more points than near equivalent are stoichiometric mode. (2) In the lower injection pressure around 20 crankshaft degrees after TDC, the mixture was in a burning rich state, but over time, or on the other hand, for the angles that exist after it, the conditions became vice versa. This can be due to the better atomization and

173

Continued.

evaporation of fuel and better mixing of them with the increase of the injection pressure. The temperature contours obtained from the numerical results show that equivalent in areas with a ratio of equivalent (mixed stoichiometric) and temperatures region above 2000 K, nitrous oxide is the highest value. Due to the high pressure fuel injection, temperature of local areas is increased and the production of pollutants in this case further. It can be seen that for the high injection pressure, the NOx is produced, and over time, the value of NOx in this areas will be developed. In Figure 18, soot contours in different degrees of crankshaft are shown for different injection pressures. Considering in fact that the soot is formed in burning rich areas where the penetration rate of oxygen to the combustion zone is not sufficient to achieve stoichiometric conditions, and also considering the temperature contours and the equivalence ratio obtained from the numerical results, it can be obtained that the soot is formed in areas with equivalence from 1.5 to 2 and the temperature ranges from 1900 K to 2300 K.

174

4. Conclusions In this study, the temperature contour and the relationship between the equivalents fuel particles with the fuel injection pressure on diesel engine performance and emissions was discussed. A. This was characterized that with increasing the fuel injection pressure, diameter droplets became smaller and this made the atomization and the fuel evaporate faster and improved the fuel mixture and finally increased the points near the equivalent stoichiometric. B. Thus the maximum pressure inside the cylinder increases, and since the area under the graph of the pressure-crankshaft angle represents that the work output per cycle is constant and with attention to the constant value of the fuel injection per cycle, efficiency and engine indicate power increase. C. With the increase of the spraying pressure and due to faster formation of the air to fuel mixture, combustion delay time was reduced, so the diagram of the maximum energy release was also increased. By Increasing the spraying pressure from 275 bar to 1000 bar (275 102 kPa to 1000 102 kPa), the amount of NOx pollution had been increased to 180%, the soot pollution increased 58% and the indicated power 12%. D. In the lower injection pressure around 20 crankshaft degrees after TDC, the mixture was in a burning rich state, but over time, or on the other hand, for the angles that exist after it, the conditions became vice versa. This is because of the better atomization and evaporation of fuel and better mixing of them with increasing the injection pressure. E. The temperature contours obtained from the equivalent numerical results showed that in areas with a ratio of equivalent equals unit and temperatures above 2000 K, the amount of nitrogen oxide increased. With increasing the injection pressure, due to this fact that further amount of the mixture is formed in shorter time, the ignition time was delayed, thus, the amount of the NOx decreased considerably.

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