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SAE TECHNICALPAPER SERIES 2002-01-0213

Numerical Analysis of High-Pressure Fast-Response Common Rail Injector Dynamics

G. M. Bianchi, S. Falfari and P. PelloniDIEM - University of Bologna

Song-Charng Kong and R. D. ReitzUniversity of Wisconsin, Madison

Reprinted From: Diesel Fuel Injection and Sprays 2002(SP–1696)

SAE 2002 World CongressDetroit, Michigan

March 4-7, 2002

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2002-01-0213

Numerical Analysis of High-Pressure Fast-Response Common Rail Injector Dynamics

G.M. Bianchi, S. Falfari and P. Pelloni DIEM - University of Bologna

Song-Charng Kong and R.D. Reitz

University of Wisconsin, Madison Copyright © 2002 Society of Automotive Engineers, Inc

ABSTRACT

Managing the injection rate profile is a powerful tool to control engine performance and emission levels. In particular, Common Rail (C.R.) injection systems allow an almost completely flexible fuel injection event in DI-diesel engines by permitting a free mapping of the start of injection, injection pressure, rate of injection and, in the near future, multiple injections. This research deals with the development of a network-based numerical tool for understanding operating condition limits of the Common Rail injector. The models simulate the electro-fluid-mechanical behavior of the injector accounting for cavitation in the nozzle holes. Validation against experiments has been performed. The model has been used to provide insight into the operating conditions of the injector and in order to highlight the application to injection system design.

INTRODUCTION

A commitment to CO2 reduction as well as the EURO 4 (2005) and EURO 5 (2008) standards are pushing the passenger car fleet toward DI Diesel engines. These engines show the greatest potential in fuel consumption, and in emission reduction at lower costs. Simultaneously, increasing efforts are spent in developing HCCI combustion concepts because it provides theoretically very low engine-out emissions levels with about the same DI diesel engine efficiency. Since HCCI combustion is considered in a medium to long term perspective and GDI engines are still somewhat under development, research is putting attention on Diesel engine technology development. DI Diesel engine development for complying with standards is seen possible at relatively lower costs since the starting base is very promising. The intrinsic lower fuel consumption has been coupled in the last few years to powerful and emission-less engines thanks to developments in injection system technology. It is well known that the first generation of DI Diesel engine equipped with a high-pressure injection system has met quite easily EURO 3 mandatory requirements. The same technology has difficulty in meeting EURO 4. In order to

comply with EURO 4, technology development is mainly oriented to improve extensively and fundamentally the C.R. injection system design. Depending on vehicle weight other techniques are also under development to meet EURO 4: swirl-control ducts, cooled and high-rate EGR, DPF, DeNOx Catalysts. Since the exhaust treatment technologies still need to be well consolidated, current efforts are focused on improvements in engine-out emissions. The results achieved by using high-pressure injection systems have revealed that injection control is the most efficient means to achieve the simultaneous reduction of NOx and soot level emissions, because the improved air-fuel mixing allows the use of higher EGR rates. In other words, the high-pressure injection makes the diesel combustion move toward a more homogeneous combustion typical of HCCI combustion concepts. Pressure can be selected to be independent of engine speed, and as a function of engine parameters.

Despite this development, further steps forward are required for injection systems to comply with EURO 4 and EURO 5 mandatory requirements without penalties in engine performance. Among high-pressure injection systems, the Common Rail seems to be more suited for that goal thanks to its flexible injection parameter mapping [1,2,3,4,5]. The two concepts available in the short-term period for DI Diesel engines are the reduction of the nozzle flow rate, without penalty on engine power delivered, and the possibility to control the heat release rate through the use of multiple injections. The reduction of the nozzle flow rate requires an increase of injection pressure up to 160-180 MPa to maintain a short injection duration for guaranteeing the fixed total injected fuel mass. The multiple injection concept, which has been determined to provide a beneficial reduction of the ignition delay, goes further with respect to current Pilot+Main injections. The idea is to split the injection in more than two pulses, with particular attention on a main injection with a reduced dwell time, as shown in previous work by the authors [7]. The challenge now is to enhance the response capability of the system in order to perform multiple injections over the widest possible range of engine operating conditions.

A reduction of the minimum hydraulic dwell time between two consecutive injections below 500 µs is the main goal [6,7]. This must be accomplished in conjunction with the capability of performing stable and repeatable consecutive injections at different timings and achieving stable and repeatable control of the small amount of fuel injected during pilot and post-injections [4,5]. A precise control of the injection quantity and the possibility to choose the best timing can allow reducing emissions and BSFC.

The multiple injection strategy is currently limited by the performance of the conventional electro-injectors adopted in mass-production engines [5,7,8,9]. The relatively long capacitor recharge time typically does not allow actuation of two consecutive needle lifts below 1000 µs. Hydraulic instability of the injector increases further this limit to 1800 µs in order to keep low the standard deviation of the fuel mass injected over consecutive engine cycles. Imarisio et al. [6] have recently developed a second generation of C.R. injection system capable of splitting the main injection in a sequence of three consecutive injections while maintaining the same capability for pilot and post injection. In order to comply with this target, modification to the electronic injector driving circuit had to be performed. The new circuit can actuate two consecutive main injections with a minimum dwell time of about 250 µs. No data are reported on standard deviations over more injection cycles and over pilot, pre-main, main, after-main and post injection. Simultaneously the authors [10,11] presented the performance of a new driving circuit capable of reducing the minimum switching time of the solenoid valve. Thanks to a reduction in the capacitor recharge time, which allowed a sharper voltage profile, a reduction of actuation time was achieved. Other works have revealed that a different approach for reducing the injector response time is to move towards piezo-electric actuators [4]. This solution has been under development but it seems only to be feasible in a medium to long term period. Most current efforts are spent in improving the conventional solenoid valve dynamics, which seems to be much more cost-effective and feasible in a short time period development effort.

CONTRIBUTION OF THE WORK

The aim of this work is to further contribute in the development of fast injectors to conceive a new fast-response injector by improving the electronic-control and the mechanical and fluid dynamical behavior of C.R. injectors. This purpose is accomplished by using numerical simulation in order to get a fundamental insight in the injector behavior. The approach is based on the development of a network-model of the injector through the Matlab-Simulink environment [11]. The model accurately accounts for injector electronics, mechanics and fluid dynamics sections and operating characteristics. A 1st generation mass-production Bosch injector (Figure 1) equipped with a VCO nozzle has been used to develop and experimentally validate the model.

Then simulations have been carried out in order to investigate the limits of the injector under fast actuation operating conditions like those occurring during multiple injections. The driving pulses for operating multiple injections were derived from those allowed by a fast-response electronic driving circuit already designed and experimentally tested by the authors [10,11]. This solution operates at a higher voltage level (i.e., 100 V) than the standard driving circuit (i.e., 75 V) allowing the anchor to be driven faster than the current solution. Numerical results highlighted that improvements to internal injector fluid dynamics and mechanics are required in order to shorten the minimum hydraulic dwell between two consecutive injections down to 200-300 µs under stable and repeatable injection conditions.

INJECTOR MODEL

In order to study the behavior of the 1st generation C.R. mass-production Bosch injector, shown in Figure 1, a network electro-fluid-mechanical model has been developed. Governing equations have been solved in the Matlab/Simulink environment [11]. The model is constituted of three sub-models for the electronics, mechanics and fluid dynamics simulation. Nozzle cavitation is accounted for by using the model by Von Kuensberg et al. [15]. Model inputs are the injector geometry, feed pipe pressure, engine chamber pressure, physical properties of the liquid fuel and the current profile. The monitoring outputs are the elements lift, velocity and acceleration, pressure traces in different volumes inside the injector, instantaneous volumetric and mass flow rates based on the actual discharge coefficient. The fluid bulk modulus variation with pressure was not taken into account, as well as possible effects of pressure waves inside pipes. The dynamic viscosity is assumed to be constant too. Forces due to the pressures on the surfaces, to the spring load and pre-load, to friction and collisions between the elements were considered.

Figure 1: The 1st generation C.R.: mass-production Bosch injector

ELECTRICAL SUB-MODEL

The electrical sub-model was presented, developed and validated by the authors [10]. Based on this work, the electrical behavior of the control circuit can be modeled by the equations [10]:

dv ridtφ

= + (1)

which is the governing equation of the electrical circuit, and where r is the electrical resistance, v the voltage and φ is the total magnetic flux. Since the current i is a non-linear function of the anchor position, x, and magnetic flux (i.e., i=f(x,φ)), as proposed by Filicori et al. [12] for modeling variable-reluctance motors, the current can be expressed as the sum of two terms: one, which depends on the reluctance, and the other that represents a purely non-linear term:

( ) ( )i J x Wφ= ⋅ + φ

φ

φ

(2)

where J(x) represents a position-dependent term associated with the air-gap reluctance and W(φ) describes the non-linear effects in the iron part of the flux path related to magnetic saturation. The non-linear term W(φ) may be expressed by a monotonic function:

1( )

Kn

nn

W φ γ=

= ∑ (3)

where represents the coefficients and n the order of the expansion, respectively. The new expression for i is:

nγ

∑=

+⋅=K

n

nnxGi

2)( φγφ (4)

where the first-order term of the polynomial expansion has been included in the term G(x) [12], i.e.,

1( ) ( )G x J x γ= + (5)

The expressions for G(x) and W(φ) are:

7( ) 19.2 10 5056G x x= − ⋅ + (6)

15 5 13 4 10 3

7 2

( ) 6.43 10 2.95 10 4.71 102.9 10 6137.4W φ φ φ

φ φ

= ⋅ − ⋅ + ⋅

− ⋅ + (7)

Finally, according to Filicori et al. [12], the magnetic force F may be evaluated as:

212dGFdx

φ = −

(8)

MECHANICAL SUB-MODEL

Measurements have been performed in order to evaluate the real injector mechanical characteristics to be used in the model. The sub-model accounts for the

following forces:

• Internal elastic and viscous actions; • Impact actions; • Electro-magnetic actions; • External elastic actions; • Hydraulic actions.

Each injector component is modeled like a

mass-spring-damper assembly (as shown in Figures 2 and 3), i.e., like a simple forced harmonic oscillator. Every single element of the injector is assumed to have one or more masses, depending on its dimensions. As shown in Figure 2 for the injector needle, a spring and a damper links two masses to model internal actions. The basic equation for the single mass-spring-damper assembly is:

( )0mx cx kx F F+ + + = (9)

where m is the mass of the moving components, c the viscous damping coefficient, k the spring elastic constant, F0 is the total spring pre-load and F is the net force applied to the mass along the injector axis direction. This model is more complex than the model shown in the previous work [10] because the forces induced by pressure and the friction between the elements are accounted for in the present model. In detail, as shown in Figure 3, the pin and the anchor were assumed to consist of two masses. The needle was modeled through four masses (Figure 2) and the nozzle was assumed to have two masses (see Figure 4). The mechanical sub-model was able to reproduce any mass compression by means of this modeling strategy.

The internal elastic and viscous forces are the actions generated between the masses in which each element of the injector has been subdivided and the baseline equations are:

int 1 2( )elasticF k x= − x

x

(10)

1 2( )viscous viscousF k x= − (11)

where kint is the stiffness of the element between two masses m1 and m2, and kviscous is the damping element. The internal actions are assumed to occur along the axial direction, and the expression for kint is:

intEAkL

= (12)

where E is the elasticity modulus, A is the transversal cross-section area of each element and L is its length. In order to take into account the internal viscous actions, the most common expression for kviscous is:

int2viscousk kξ= ⋅ M (13)

where ξ is a damping coefficient (0.001 to 0.01) and M has available value in the model. In case of viscous action between two masses, M is the mean mass; in case of viscous action between the element and the stop, M is the mass of the element only (see Figure 3). The impact action baseline equation is:

F kx= (14)

together with the conditions:

x b≤ or (15) x b≥

where k is the block stiffness (about three orders of magnitude larger than the internal stiffness of the blocked element) and b is the stroke of the block (i.e., its value shows when the contact between the stop and the element starts).

The expression for the magnetic force F is like that proposed in Ref. (8) and the model has been described by means of the expressions shown in the previous work by the authors [10].

The external elastic actions have been generated by the springs of the injector, so their expression is:

0F kx F= + (16)

where k is the stiffness of the spring and F0 is its pre-load, expressed by:

0 0F kx= (17)

where x0 is the initial compression of the unloaded spring. In order to evaluate k, the equation is:

4

38 f

G dkI D

⋅=

⋅ ⋅ (18)

where G is the tangential modulus of elasticity, d is the coil diameter of the spring, If is the number of spirals and D is the mean diameter of the spring.

FLUID-DYNAMIC SUB MODEL

The injector has been assumed to be constituted of inter-connected chambers (see Figures 5 and 6). The hydraulic line simulation is quite complex because many processes are involved. In this model wave effects in the connection pipes were not considered because the wave characteristic travel time is much shorter than the injector actuation time and their amplitude is negligible. The basic equation of this sub-model is the mass conservation equation:

Figure 2: Schematic of injector needle with four masses

Figure 3: The model of the injector upper part

Figure 4: The model of the injector lower part

Figure 5: The injector chambers in the model

Figure 6: Schematic of the fluid-dynamical model

ii

V dp dV QB dt dt

+ = ∑ (19)

where V is the initial volume of each chamber, B is the bulk modulus, Qi is the inlet or outlet volumetric flow rate, dV/dt is the pumping effect. The volumetric flow rate depends on the flow regime. Under laminar flow conditions (i.e., leakage):

3

12b hQ p

lµ⋅

= ∆⋅ ⋅

(20)

where b is the leakage perimeter, h is its height, l is its length and µ is the dynamic viscosity. Under turbulent flow conditions:

2d

pQ C A

ρ⋅ ∆

= ⋅ ⋅ (21)

where Cd is a discharge coefficient (0.56 to 0.62) which has been evaluated by taking into account the open literature and by comparing the results with a fluid-dynamic model built on the AMESim Code [32]. A is the flow cross-section area and ρ is the fuel density. Depending on the leakage amplitude, the expression for volumetric flow rate could be (20) or (21): in the sub model during the nozzle opening and closing period there is a change from (20) to (21) and vice versa. Finally, the pumping effect dV/dt is evaluated by the following expression:

Q A v= ⋅ (22)

where A is the moving element cross-section area and v is its velocity. Obviously the pumping effect exists only when there is a moving element in a chamber, like a piston in a cylinder.

The boundary condition for pressure assumes a

constant value set equal to the nominal rail pressure. Investigations of the effect of pressure variation in time in the rail volume have been considered in [33].

Nozzle

CAVITATION SUB-MODEL

In order to evaluate the effective instantaneous nozzle discharge coefficient, and therefore the effective injection velocity and the effective flow exit area, a cavitation sub-model was introduced. Due to the high injection pressure of Common Rail systems, cavitation is very likely to occur inside the nozzle. In this model only cavitation phenomena inside the nozzle were considered: the extensions to other orifices (i.e., between the control chamber and solenoid valve) and to the high-pressure pipes is in progress. The model formulation and approach are the same as those proposed by Von Kuensberg et al. [15]. Cavitation zones are assumed to occur instantaneously, as soon as the local fluid pressure reaches the vapor pressure [16]. The input parameters to the model are the ideal volumetric flow rate, fuel vapor pressure and chamber pressure, physical properties of the liquid fuel and hole geometrical characteristics (i.e., L/D ratio and R/D ratio, where D is the geometrical hole diameter, L is the hole length and R is the inlet radius of the hole nozzle [15]).

Because of the losses, the mean mass flow rate through the nozzle can be expressed as:

2d geo l

l

pm C A ρρ∆

= ⋅ ⋅ ⋅ (23)

In this case the mean velocity Umean is lower than the ideal Bernoulli velocity:

2mean d Bernoulli d

l

pU C U Cρ∆

= ⋅ = ⋅ (24)

It is possible to note in relations (23) and (24) that in order to evaluate the nozzle discharge coefficient the injection mass flow rate was firstly evaluated and then a fictitious mean velocity was estimated based on the geometrical flow exit area. In the present nozzle flow model, the instantaneous discharge coefficient is first estimated from the following expression:

11d

inlet

CK f l D

=+ ⋅ +

(25)

where Kinlet is a tabulated inlet loss coefficient [15], which depends on nozzle inlet geometry, and f is a Reynolds number function, which takes into account laminar and turbulent flow regimes:

0.25max(0.316 Re ,64 Re)f −= ⋅ (26)

The flow velocity at the vena contracta is further evaluated as:

meanvena

C

UUC

= (27)

0.52

0

1 11.4cC C

− = − ⋅

R D (28)

where C0 is a tabulated contraction coefficient [15]. C0 is assumed equal to 0.62 because of the sharp-edge inlet (i.e., for the injector considered R/D is equal to 0.032).

Based on the vena contracta velocity, the static pressure at the vena contracta can then be calculated:

21 2

lvena venap p Uρ

= − ⋅ (29)

If pvena is lower than pvapor, it is assumed that cavitation has occurred and the upstream pressure p1 and the discharge coefficient Cd will be re-evaluated.

In the cavitating case the nozzle exit conditions can be obtained by applying momentum equilibrium between the vena contracta and the nozzle exit:

2 vaporeff vena

l mean

p pU U

Uρ−

= −⋅

(30)

meaneff geo

eff

UA AU

= (31)

4 effeff

AD

π

⋅= (32)

Ueff, Aeff and Deff are effective exit velocity, flow area and flow diameter, respectively. P2 is the combustion chamber pressure, which is assumed equal to 4 MPa in the present study. When the present injector dynamic model is coupled with an engine CFD code, p2 will be supplied from the CFD code, while Ueff, Aeff and Deff will be used to initialize the spray drop conditions for the drop atomization model [16].

Details of the nozzle flow cavitation model can be found in the original literature [15,16]. The model has been tested simulating CASE 16 (referenced later in Table 1).

VALIDATION OF THE MODEL

The model has been validated by comparisons with measurements in terms of fuel mass injected, as

shown in Figure 7. Measurements have been provided by VM–Motori and have been obtained using a Bosch Injector Test bench. A 1st generation mass-production injector installed on 2.5 liter D.I. Diesel engine has been used. Three different injection pressures (i.e., 250, 800, 1300 bar) and different mass injected amounts (different loads) were considered, as summarized in Table 1. An EMI measurement instrument was used to collect data and to measure the fuel amount injected during both the pilot and main injections. The mean value and the standard deviation were evaluated on 1000 samples. The current driving profiles used in simulations are the same as adopted by VM-Motori for ECU CR engine mapping: they are depicted in Figures 9, 10 and 11 and they are referred to as CASE 16, CASE 1 and CASE 6 in Table 1, respectively. CASE 16 will be used for detailed discussion and investigation in the following. The chamber and injector back-pressure were maintained at 1 bar. Experimental standard deviation was measured varying from 34.47 to 2.9 for the pilot and from 3.61 to 0.24 for the main injections, depending on the injection pressure and amount of fuel injected, as shown in Figure 8. The operating point at 250 bar was experimentally found to be particularly unstable with a standard deviation close to 35%. This is because the nominal rail pressure of 250 bar is very close to the minimum value required for opening the needle.

Case Injection Pressure

[bar]

Nominal injected fuel mass for

pilot pulse [mg]

Nominal injected fuel mass for

main pulse [mg] 1 250 0.12 - 2 250 - 7.94 3 250 - 20.21 4 800 1.45 - 5 800 - 39.55 6 800 - 51.47 7 1300 1.79 - 8 1300 - 50.35 9 1300 - 67.73 10 250 0.17 8.31 11 250 0.17 20.62 12 800 1.61 39.37 13 800 1.56 51.70 14 1300 1.95 1.98 15 1300 2.34 49.06 16 1300 2.15 66.81

Table 1: Test conditions: nominal rail pressure and injected fuel mass

Other critical conditions for the control of the fuel injected occur during pilot injections when small amounts of fuel are injected because the solenoid valve and needle behave according ballistic dynamics. As a consequence, the disagreement between the numerical prediction and measurements is therefore bigger at low loads (i.e., 250 bar) and for pilot pulses (Figure 7). The model performs much better at high pressure and during the main pulses when the fuel mass injected is above 12 mg. In these conditions, the model presents an average error of the predicted fuel injected in main pulses that is about 5.0%. Reducing the error further is quite difficult because of the complexity of the injector model, which

makes small errors in the sub-model enlarge when an overall parameter such as the mass injected is considered.

It is to be noticed that the maximum voltage level used with the 1st generation injector is about 75V and the corresponding current level is 22A, as shown in Figure 12 for CASE 16. The predicted current profile at 1300 bar, corresponding to the experimental driving pulse of Figure 9, is shown in Figure 13. The maximum current level is about 28A and the predicted trace is quite similar to the measurements shown in Figure 12. Once the current has excited the solenoid valve, the induced magnetic force (Figure 14) pushes up the anchor and the pin (Figure 15). When the voltage goes to zero, the current goes to zero too. The magnetic force (Figure 14) is zero only when the current reaches its zero value. Then the anchor returns back to its initial position. As a consequence there is a delay between the instant when the voltage drops to zero and the instant when the magnetic force on the anchor ends. When the solenoid valve is excited, the anchor is pushed up by the magnetic force, the ball sphere opens and then the pressure drops in the control chamber, as is seen in Figure 16 where the predicted pressure evolution is plotted versus time. As one can see in Figure 16, the pressure in the control chamber drops down to 800 bar during pilot injection and then it recovers the initial value before main injection starts. During the main pulse, the pressure drops down again to 700 bar.

It is to be noticed that, especially during the main injection, ripples affect the pressure recovery from the minimum pressure to the initial value. This pulsating phenomenon is caused by the pumping effect of the injector needle, previously pointed out by Digesu et al. [13]. As a consequence, the pressure in the accumulation volume is greater than the pressure in the control chamber. Two competing forces are generated in the axial direction causing the injector needle to move up, as shown in Figure 17, where the evolution in time of injector and nozzle needle lifts are plotted. It is possible to see that the injector needle upper part is compressed by the above-mentioned forces when the solenoid valve is closed. This compression causes a little delay between the injector needle lift and the nozzle needle lift. The maximum injector needle stroke is 0.2 mm and it reaches this lift only for the main pulses. The injector needle lift causes a local reduction of the control volume, thus causing the pressure to increase up to 1150 bar. When the injection ends, the magnetic force goes to zero and the ball sphere closes. The pressure increases in the control chamber again up to the initial rail pressure (Figure 16) and the injector needle is pushed down to its closed position.

-50

-40

-30

-20

-10

0

10

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

perc

ent e

rror

%

PilotMain

Figure 7: The percent error between predicted and

measured injected fuel mass

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Test number

Stan

dard

dev

iatio

n %

PilotMain

Figure 8: Standard deviation associated with the experimental measurements

-60

-40

-20

0

20

40

60

80

100

0,000 0,002 0,004 0,006 0,008 0,010

Time [s]

Volta

ge [V

]

Figure 9: Experimental driving pulse – CASE 16

-60

-40

-20

0

20

40

60

80

100

0,000 0,000 0,001 0,001 0,002 0,002 0,003 0,003 0,004

Time [s]

Vol

tage

[V]

Figure 10: Experimental driving pulse – CASE 1

-60

-40

-20

0

20

40

60

80

100

0,000 0,000 0,001 0,001 0,002 0,002 0,003 0,003 0,004

Time [s]

Vol

tage

[V]

Figure 11: Experimental driving pulse – CASE 6

0

5

10

15

20

25

0,000 0,002 0,004 0,006 0,008 0,010Time [s]

Curr

ent

[A]

Figure 12: Experimental current profile – CASE 16

Figure 13: Predicted current profile – CASE 16

Figure 14: Predicted magnetic force – CASE 16

Figure 15: Predicted anchor and pin displacement versus time

Figure 16: Predicted control chamber pressure profile versus time

Figure 17: Injector and nozzle needles displacement predicted by the model

Figure 18: Solenoid valve

Some features of the solenoid valve are shown in Figure 18. Currently the solenoid valve of the 1st CR injector generation consists of a pin, an anchor and a

spring (called pin-spring) between the pin and anchor. This design replaced a former one where the anchor and pin constituted a single component [5]. This update was necessary to reduce the probability of the ball-valve re-opening caused by the valve bouncing back against its stop because of its non-zero impact velocity, as reported by Ficarella et al. [5]. The two-component-configuration allows reducing the impact energy since the kinetic energy of the pin can be absorbed by the spring. It is to be noticed that the pin undergoes an extra-displacement, as previously highlighted by the authors [10], when the anchor is opening. When the anchor is closing, initially there is a compression of the pin-spring, and then the anchor gets to its zero position, after some ripples caused by the above-mentioned spring.

Some discussion of the influence of the cavitation sub-model is now presented. As one can see in Figure 19, the Bernoulli velocity is the maximum velocity, while the effective injection velocity Ueff is bigger than the nozzle mean flow velocity Umean. This trend is physically justified because the cavitation phenomenon induces a contraction of the effective flow exit area and for constant mass flow rate the effective injection velocity must increase. In Figure 20 the Reynolds number shows that the flow is laminar or turbulent depending on the injection velocity, as one can expect. Figures 21 shows the evolution in time of the instantaneous discharge coefficient. Analyzing the predicted Cd trace it is seen that its values are quite similar to the values assumed in mathematical models. The discharge coefficient has a higher value for inlet injection velocity of about 100 m/s, then it decreases when the velocity is above 300 m/s, when cavitation may have occurred. It can be seen that there are some oscillations in the discharge coefficient profiles caused by injection velocity oscillations. The initial value for Cd is 0.95 when the injector needle first opens and it is very close to the result of Von Kuensberg et al. [15]. This result indicates the importance of accurately predicting the discharge coefficient during injection. By means of this cavitation model it is possible to evaluate the effective injection velocity, effective flow exit area and flow diameter when the mass flow rate is known. Thus it seems to be very helpful because these parameters strongly affect the fuel drop atomization and the combustion process, and of consequence the exhaust emissions.

MECHANICAL AND FLUID DYNAMICAL LIMITS OF 1ST GENERATION C.R. INJECTORS WITH ADVANCED CONTROL ACTUATION

After the above validation, the present injector model has been used to investigate injector behavior when operating with multiple injections, i.e., with fast actuation driving pulses. Imarisio et al. [6] and Bianchi et al. [10,11] have clearly showed that a new electronic driving circuit must be designed to control a fast-response injector capable of multi injection strategies. In particular, the main limitations of the 1st generation ECU was the long recharging time required by capacitor. Other limits were due to the relatively low voltage

applied to the solenoid coil (i.e., 75 V) compared to the maximum voltage limits of the component. Bianchi et al. [10,11] designed and experimentally tested a new injector electronic driving circuit capable of operating with a minimum dwell between two electrical pulses of about 15 µs. This characteristic cannot be straightforwardly transferred to a similar minimum hydraulic dwell time between two consecutive injections because of mechanical and fluid dynamical phenomena that cause a delay between the start of the command electric pulse and the actual injection flow rate start or end. For the simulations of multiple injections the driving electrical pulse profiles generated by the advanced circuit designed by Bianchi et al. [11] were used as input.

Figure 23 shows a sketch of the new electronic injector driving circuit. The injector was supplied with a voltage of 100 V, significantly higher than the conventional one of 75 V. This allowed a much sharper current rise and drop. In the previous work the authors [10] have shown that a higher value of voltage doesn’t influence the force since iron saturation occurs. Thanks to advanced electronic characteristics, an optimized voltage profile was conceived in order to achieve a better control of the solenoid valve closure. This optimized profile, shown in Figure 24, was designed with the focus on reducing the time required for the opening and closing phases, thus especially resulting in a better control of very small amounts of fuel injected. At the beginning a positive voltage is applied to excite the solenoid coil and to generate a magnetic force greater than the actual one. Then a negative voltage (both equal to 100 V) is used to reduce as quickly as possible the current in the solenoid and hence to close the solenoid valve. The negative voltage allows one to reduce as quickly as possible the current in the solenoid. As a consequence the valve closes more quickly, so the force goes to zero. The corresponding predicted current profile is presented in Figure 25. By means of dwell time variation between the positive and the negative profiles, it is possible to obtain a split injection in two or more pulses. By means of this new optimized voltage profile, it has been clear that it is possible to reduce the total opening and closing time of the injector, and therefore the interval of time between two consecutive injections, thanks to the greater magnetic force.

For simulations, a three-pulse injection strategy at a nominal rail pressure of 1300 bar has been considered in conjunction with minimum dwell times of 1000, 800, 600 and 300 µs between consecutive electrical pulses. It must be pointed out that the actual minimum dwell time, recommended by Bosch, for 1st generation mass-production injectors is 1800 µs.

Calculations reveal that the 1st generation C.R. injectors seem to be able to operate under stable conditions until 0.8 ms of minimum dwell with a fast-response driving circuit of the solenoid valve, as shown by calculations. It is to be noticed that the minimum dwell is defined as occurring between the start of the electrical driving pulse of two consecutive injections: this is an

electrical time. Figure 26 shows the driving pulse profile with a dwell of 0.8 ms. As one can see in Figure 27, the volumetric flow rate is the same for both the two main injections which have the same electrical pulse, with two equal main pulses. The anchor and pin present the same dynamics during the consecutive main injections, as one can note in Figure 28. The evolution of pressure in the control chamber is almost the same during the two main injections (Figure 29). The little difference in the pressure evolution results in a slightly different needle lift in time during the second main injection. In particular, the higher pressure oscillation in the control chamber during the recovery phase of the main injection interrupts the needle closing for a very short time with a negligible influence on the volumetric mass flow rate. It is to be noticed that the voltage profile, shown in Figure 26, ends at 2800 µs, while the anchor (Figure 28) closes only after 700 µs (i.e., at 3500 µs).

These figures show that it is electronically possible to perform an injection strategy with more injection pulses with a relatively short dwell between two consecutive injections. Actually, despite the fact that the electronic circuit allows operation with much shorter minimum dwells, limits still remain in the mechanical and fluid dynamical behavior. A dwell time of 800 µs is feasible since the injector seems to have enough time to recharge its capacitor fluid volumes. As previously mentioned, the target for a new generation of fast-response injector is a minimum dwell time shorter than 500 µs. Therefore, two further simulations have carried out by considering two shorter dwell times of 600 and 300 µs. The corresponding electrical driving pulses are plotted in Figures 31 and 32, respectively.

When a dwell of 600 µs is considered, the simulations reveal that improvements of the driving circuit are strongly limited by the fluid-dynamic behavior of the injector. In particular, when reducing the dwell between pulses, the second main injection becomes influenced by the first main injection. In particular, the volumetric flow rate is particularly unstable at the beginning of the second main pulse, as shown in Figures 33 and 34. The reason for this behavior can be attributed to the very short time available to the injector for recovering the initial conditions, especially the control chamber pressure, as visible in Figure 35. For completeness in Figure 36, the anchor, injector and nozzle needle lift evolution in time are depicted. Figure 35 reveals clearly that the control chamber pressure does not operate under stable conditions between the first and second main pulse. This results in a different evolution of the needle lift in the two main injections because different differences of pressures act on the injector needle, as one can see in Figure 36. Oscillation in control the chamber volume cannot be attributed to different solenoid valve dynamics. In fact, the anchor lift is unaffected by the dwell time and its lift profile remains similar during the two main pulses.

Figure 19: Comparison between different injection

velocity definitions - CASE 16

Figure 20: Reynolds number in nozzle hole - CASE 16

Figure 21: Nozzle hole discharge coefficient Cd -

CASE 16

Figure 22: Predicted effective flow exit area to geometrical flow exit area ratio- CASE 16

B + -

BoostConverter

vc

C

DR vs

SDR

x1 x2

D1

D2

Injector ControlUnit

T1

T2

i

is

Figure 23: The new electronic driving circuit

Figure 24: Generic optimized pulse drive - 1Pilot+1Main

Figure 25: Predicted current profile - 1Pilot+1Main

Figure 26: Imposed driving pulse - 1Pilot+2Main Pinj= 1300 bar - Dwell=800µs

Figure 27: Volumetric flow rate - 1Pilot+2Main Pinj= 1300 bar - Dwell=800µs

Figure 28: Anchor and pin lifts 1Pilot+2Main Pinj= 1300 bar - Dwell=800µs

Figure 29: Control chamber pressure trace Pinj= 1300 bar - Dwell=800µs

Figure 30: Nozzle needle and injector needle lifts 1Pilot+2Main Pinj= 1300 bar - Dwell=800µs

Figure 31: Imposed driving pulse - 1Pilot+2Main Pinj= 1300 bar - Dwell=600µs

Figure 32: Imposed driving pulse - 1Pilot+2Main Pinj= 1300 bar - Dwell=300µs

Figure 33: Predicted volumetric flow rate - 1Pilot+2Main Pinj= 1300 bar - Dwell=600µs

The remarkable pressure ripple can be reasonably caused by the relatively long time allowed by the feeding orifice that is connected to the pre-chamber, fed at almost the same rail pressure, and the control chamber. The diameter of the hole is a critical parameter because it comes from a compromise. It must guarantee that the pressure drop is concentrated in that region on the one hand, and a relatively short pressure recovery time in the control chamber when the sphere valve closes, on the other hand.

When the minimum dwell is 300 µs, the simulations have revealed that it is not possible to operate at this dwell time since the injector does not close between the two injections and, as a consequence, the injected fuel mass is not controllable. It is seen in Figure 37 that the volumetric flow rate is totally uncontrollable. In fact in Figure 38 it is possible to see that the anchor does not have enough time for closing and then opening again. This affects the pin lift, whose evolution is different for each main pulse. The main consequence is the loss of control of the pressure recovery in the control chamber, as shown in Figure 39. The pressure recovers its initial value of 1300 bar only for a short time between the pilot and first main pulses, then the maximum pressure value is 1200 bar. Since the pressure in the accumulation volume (Figure 40) is greater than the one in the control chamber during the time interval between the two main pulses, the nozzle needle cannot close properly against its seat, as one can see in Figure 41. However between the pilot and first main pulses the control chamber pressure reaches 1300 bar as does the accumulation volume pressure: by means of the different surface areas on which these pressures act, the nozzle needle closes after the pilot pulse.

For the sake of completeness it can be demonstrated through Figure 42 that using a dwell time of 1000 µs or longer, all unstable phenomena are eliminated and the two main injections can provide the same flow rate. It must be pointed out that the influence of the dwell time on the injection quantity is investigated in detail in [33]. Therefore all conclusions drawn in the present analysis come from the focus on injector behavior for a given and constant feed rail pressure.

CONCLUSIONS

In order to perform an in depth study of the 1st generation C.R. injector a mathematical model has been developed that uses the Matlab/Simulink environment. This model accounted for electrical, mechanical and fluid dynamical behaviors. A cavitation sub-model is included.

The simulation results were successfully compared to measurement data: the average error between the experimental injected fuel mass and the simulated injected fuel mass for a main pulse was about 5.0%.

An optimized voltage profile, obtained by a new driving circuit, was proposed in order to drive the injector

faster and to reduce the minimum dwell time between two consecutive pulses.

Based on the capability of the injector driving circuit, a sensitivity analysis has been performed in order to investigate the limits of the injector under fast-response operation, i.e., a 1PILOT+2MAIN injection strategy. The two main injections operate with the same driving pulse (i.e., the same fuel injected). Three different minimum dwells were considered for an injection pressure of 1300 bar.

The model has shown that using the new voltage profile the minimum dwell for stable injector operating conditions is about 800 µs, while the circuit is capable of generating two consecutive pulses with an interval up to 15 µs.

Reducing the dwell down to 600 and 300 µs reveals that at 600 µs the injector needle closes but does not provide repeatable main injections. At 300, the injector needle has a ballistic behavior because of the unstable pressure recovery of the control chamber. The result is that the injector needle does not close and the fuel continues to exit from the nozzle holes between the two main injections.

The simulations indicate that using a fast-response driving circuit, the injector actuation capability can be improved by a drastic optimization of the mechanical and fluid dynamical design of the components.

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Figure 34: Zoom of the volumetric flow rate during the beginning of the second pulse Pinj= 1300 bar - Dwell=600µs

Figure 35: Predicted control chamber pressure versus time. Pinj= 1300 bar - Dwell=600µs

Figure 36: Anchor, Injector needle and nozzle needle lifts. Pinj= 1300 bar - Dwell=600µs

Figure 37: Predicted volumetric flow rate - 1Pilot+2Main Pinj= 1300 bar - Dwell=300µs

Figure 38: Anchor and pin lifts 1Pilot+2Main Pinj= 1300 bar - Dwell=300µs

Figure 39: Control chamber pressure trace Pinj= 1300 bar - Dwell=300µs

Figure 40: Predicted pressure in accumulation chamber Pinj= 1300 bar - Dwell=300µs

Figure 41: Injector needle and nozzle needle lifts Pinj= 1300 bar - Dwell=300µs

Figure 42: Comparison between volumetric mass flow rates at dwell time of 600 and 1000 µs

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