Development of Predictive Gasoline Direct Fuel Injector Model for Improved

In-cylinder Combustion Characterization

Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in

the Graduate School of The Ohio State University

Mohit Atul Mandokhot

Graduate Program in Mechanical Engineering

The Ohio State University

2018

Thesis Committee

Prof. Shawn Midlam-Mohler, Advisor

Prof. Giorgio Rizzoni

Copyrighted by

Mohit Atul Mandokhot

2018

Abstract

Gasoline direct fuel injection systems have gained importance due to the increasing level of emissions regulation on SI combustion systems. Direct fuel injection delivery to cylinder provides better atomization and fuel mixing performance, enabling homogenous mixture and better in-cylinder combustion. Increasing focus over the last few decades has been on better characterization of such gasoline direct fuel injection systems. Solenoid powered injectors act as actuators and enable accurate fuel delivery into the cylinder for a combustion event. Characterization of injector’s fuel delivery performance is an important aspect of achieving improved in-cylinder combustion performance. The objective of the current thesis is to develop a numerical physics based fuel injector model that provides a reliable prediction of flow rate and needle lift, in order to be used to improve in-cylinder combustion performance using 3D CFD model methodology. The developed model provides a reliable estimate of flow rate of developed injector, which is experimentally verified against instantaneous flow rate data provided by typical suppliers. In cases where inadequate prediction performance was noted, the errors arise out of lack of high fidelity electromagnetic modeling data, damping characteristics inside model and lack of geometry data to capture performance of highest accuracy.

Dedication

To the pursuit of truth, a journey which I believe is worth undertaking because of the

trials it brings and one’s flaws it exposes, in return making oneself stronger.

I embarked on this endeavor for my parents and could not have done it without my family

and their support.

iii

Acknowledgments

I would like to gratefully acknowledge Prof. Shawn Midlam-Mohler’s confidence in me, his support and guidance throughout this journey. His confidence in me while I navigated through the waters of research, helped me grow immensely. I would also like to acknowledge Prof. Giorgio Rizzoni for lending his expertise as a committee member on my research. I thank him for earnestly delivering his knowledge during my Master’s courses which have helped me explore this new career.

I must acknowledge David Hillstrom for being a provider of valuable feedback, a wise soundboard for forming ideas and always being up for coffee at 4pm. In SIMCenter’s coterie of excellent graduate students, people who strive every day to grow themselves, I have been lucky to find a lab full of encouragement and fun. Thanks to Clayton, Aditya,

Vivek, Kepin and Ullekh for an environment that fostered growth on wide dimensions while having fun.

My final set of thanks are to Dr. Jeeseon Park-Saltzman.

SIMCenter, Center for Automotive Research and The Ohio State University have helped me grow in new dimensions. I am grateful to God and the people that have made it happen.

Vita

May 2012…………………………………….B.E (Hons.) Mechanical Engineering,

BITS, Pilani – K.K Birla Goa Campus, India

2012 to 2016…………………………………FMC Technologies, Hyderabad, India.

2016 to present………………………………Graduate Research Associate,

SIMCenter, The Ohio State University

Fields of Study

Major Field: Mechanical Engineering

Table of Contents

Abstract ...... ii Dedication ...... iii Acknowledgments...... iv Vita ...... v List of Tables ...... viii List of Figures ...... ix 1. Introduction ...... 1 2. Objective and Scope of Thesis ...... 9 3. Literature Review ...... 10 3.1 Review of 1D-3D Engine Research ...... 10 3.2 Review of Injector Modeling ...... 13 References ...... 20 4. Proposed Technique for Injector Characterization ...... 21 5. Model Development ...... 24 5.1 Injector Driver Circuit ...... 27 5.2 Injector Electromagnetic Circuit ...... 35 5.3 Mechanical Circuit of Injector ...... 48 5.4 Fluid Flow Circuit ...... 56 6. Post-Processing of Model Results ...... 76 6.1 Need for Combined Model ...... 76 6.2 Structure of Models for Combination ...... 81 6.3 Post-Processing Algorithm for Combination of Results ...... 82 7. Results ...... 86 7.1 Experimental Results ...... 86 7.2 Simulation Results ...... 91 vi

8. Error Analysis ...... 102 8.1 Metrics ...... 102 9. Conclusion ...... 115 Bibliography ...... 116

vii

List of Tables

Table 1 – Parameters, Injector Driver Controller, Gasoline Direct Injector ...... 34 Table 2 - Parameters, Electromagnetic Circuit, Gasoline Direct Injector ...... 47 Table 3 - Parameters, Mechanical Circuit, Gasoline Direct Injector ...... 54 Table 4 - Parameters, Flow Circuit, Gasoline Direct Injector ...... 66 Table 5 - Parameters, Core Damping, Gasoline Direct Injector ...... 72 Table 6 – List of Elements for multi-domain physics in Injector Model ...... 73 Table 7 – Operating Conditions of Injector Model ...... 91 Table 8 – Relative RMS Error % per Zones for Cases ...... 114

viii

List of Figures

Figure 1. Gasoline Direct Fuel Injector interface with Cylinder, as shown in [8] ...... 3 Figure 2: Direct Fuel Injection system with Rail and Low Pressure Fuel System, as shown in [8] ...... 4 Figure 3 - Gasoline direct injection rail architecture representation...... 5 Figure 4 - Injector, I/O Diagram ...... 6 Figure 5 – Sample Trapezoidal Instantaneous Flow Rate from Injection Event...... 12 Figure 6 – Silicon moulds used for dimensional analysis in nozzle sac area, as seen in [3] ...... 17 Figure 7 – Dimensional analysis and orientation of silicon moulds of nozzle holes of Gasoline Direct Injector, under SEM, as seen in [3] ...... 18 Figure 8 – Proposed rate shaping of fuel injection using fast response actuator, as seen in [4] ...... 19 Figure 9 – Feed Forward simplistic fuel injection control command architecture in ECU ...... 25 Figure 10 – I/O Diagram of Gasoline Direct Fuel Injector Model ...... 26 Figure 11 – Gasoline Direct Fuel Injector, Subsystem Block Diagram ...... 27 Figure 12 – I/O Block Diagram, Injector Controller, Gasoline Direct Injector ...... 28 Figure 13 – Representative Current Profile, Electromagnetic Circuit, Gasoline Direct Injector ...... 29 Figure 14 – Algorithm, Injector Controller, Gasoline Direct Injector ...... 30 Figure 15 – Peak Current vs. Rail Pressure, Parameter Table, Injector Controller, Gasoline Direct Injector ...... 31 Figure 16 – Pickup Time vs. Rail Pressure, Parameter Table, Injector Controller, Gasoline Direct Injector ...... 32 Figure 17 – Hold Current vs. Rail Pressure, Parameter Table, Injector Controller, Gasoline Direct Injector ...... 32 Figure 18 – Sample Voltage Controller Output, Injector Controller, Gasoline Direct Injector ...... 34 Figure 19 I/O Block Diagram, Electromagnetic Circuit, Gasoline Direct Injector ...... 36 Figure 20 – Representative Electromagnetic Circuit, Gasoline Direct Injector ...... 37 Figure 21 – Solenoid performance, w/ and w/o Iron Core, taken from [7] ...... 39 Figure 22 – Impact of varying reluctance on current profiles, Electromagnetic circuit ... 40 Figure 23 – Representative Solenoid circuit inside the Gasoline Direct Injector...... 42 Figure 24 – Representation of Solenoid as a part of RL circuit of Injector...... 43 Figure 25 – Implementation of Electromagnetic Circuit, GT-Power, Gasoline Direct Injector ...... 46 ix

Figure 26 – I/O Diagram, Mechanical Circuit, Gasoline Direct Injector ...... 48 Figure 27 – Representation of Mechanical Elements, Gasoline Direct Injector ...... 49 Figure 28 – Schematic of the Mechanical Circuit, inside Gasoline Direct Injector ...... 50 Figure 29 – Relative stiffness of springs, mechanical circuit, Gasoline Direct Injector .. 52 Figure 30 – Implementation of Mechanical Circuit, GT-Power, Gasoline Direct Injector ...... 55 Figure 31 – I/O Diagram, Flow Circuit, Gasoline Direct Injector ...... 56 Figure 32 – Link between Mechanical and Flow Circuit, Gasoline Direct Injector ...... 57 Figure 33 – Spatial orientation of plumes, flow circuit, Gasoline Direct Injector ...... 59 Figure 34 – Representation, Injector Volume Pre-Needle, Flow Circuit, Gasoline Direct Injector ...... 61 Figure 35 – Representation, Injector Needle Volume, Flow Circuit, Gasoline Direct Injector ...... 62 Figure 36 – Representation, Pipe Annular Injector Needle Volume, Flow Circuit, Gasoline Direct Injector ...... 63 Figure 37 – Representation, Needle Seat Area, Flow Circuit, Gasoline Direct Injector, as taken from [10] ...... 64 Figure 38 – Implementation. Flow Circuit, Gasoline Direct Injector ...... 67 Figure 39 – Representation, Core Damping Volumes, Gasoline Direct Injector ...... 70 Figure 40 – Core damping non-linear filling dynamics, illustration from internal supplier documentation...... 71 Figure 41 – Implementation of Injector Model, GT-Power, Gasoline Direct Injector ..... 74 Figure 42 – Sample Instantaneous Flow Rate out of a Gasoline Direct Injector ...... 77 Figure 43 – Model structure, combined GT-Power Models, Gasoline Direct Injector .... 81 Figure 44 – Nomenclature b/w Core Damped and Core Undamped Model...... 83 Figure 45 – Post-processing algorithm, combination of model results...... 84 Figure 46 – Representation of Instantaneous Flow Results, Experimental value from Gasoline Direct Injector ...... 87 Figure 47 – Normalized Experimental Cumulative Flow Data from Injector ...... 89 Figure 48 – Results, Case A, Prediction of Instantaneous Flow Rate ...... 93 Figure 49 – Results, Case A, Prediction of Needle Lift ...... 94 Figure 50 - Results, Case B, Prediction of Instantaneous Flow Rate ...... 95 Figure 51 – Results, Case B, Prediction of Needle Lift ...... 96 Figure 52 - Results, Case C, Prediction of Instantaneous Flow Rate ...... 97 Figure 53 - Results, Case C, Prediction of Needle Lift ...... 98 Figure 54 - Results, Case D, Prediction of Instantaneous Flow Rate ...... 99 Figure 55 - Results, Case D, Prediction of Needle Lift ...... 100 Figure 56 – Representation of Error, Total Fuel Injected...... 103 Figure 57 – Results, Cumulative Fuel Injected % Error, Experimental vs. Simulation . 104 Figure 58 – Cumulative Experimental vs. Simulation, Injector Flow Performance Data...... 106 Figure 59 - % Error, Cumulative Flow (Case A & B), Experimental vs. Simulation Data ...... 108

Figure 60 - % Error, Cumulative Flow (Case C & D), Experimental vs. Simulation Data...... 109 Figure 61 – Representation of Error, Relative RMS Error, Whole Fuel Injected ...... 110 Figure 62 – Results, Normalized Relative RMS Error %, Experimental vs. Simulation 111 Figure 63 – Representation, Injection Event, Discretized by Zones for Needle Operation...... 113

1. Introduction

Gasoline Spark Ignited Engines in the 1990’s were being fueled primarily by port fuel injected systems. These systems delivered fuel in the intake runners and relied on pre- mixing within the intake runners then the air-fuel mixture (charge) was fed into the cylinders for a spark ignited combustion. There are some challenges with port fueled injection systems. The port fueled injection is a low pressure injection system that operates at 3-5 bar of fuel pressure. The eventual breakdown of fuel into smaller droplets relies on the turbulence assisted mixing in the intake vanes and as it enters the cylinder.

The atomization performance in a port fueled system depends on the fuel vaporization from the puddle in the intake runner and suspended fuel droplets within the intake runner near the intake valve. The evaporation dynamics from the puzzle are dependent on the temperature near the intake runner. As noted in Fiengo et al. [9], Page 18,

“Even if the engine is fully warmed up, depending on the amount of injected fuel,

it is unlikely that the time interval prior inlet valve opening is enough to complete

mixture preparation out of the cylinder.”

Incomplete atomization and mixing due to port fuel injection specially during cold cranking, or at low speeds (low turbulence and air flow) and partial load causes poor combustion performance in the engine. This causes increased level of emissions of unburned hydrocarbons (UHC) and carbon monoxide (CO).

In the late 1990’s in the lieu of increasing emissions regulation on the automotive industry, larger focus was placed on improving combustion performance with regards to reducing emissions of UHC and CO. Development of direct fuel injections in line with high pressure diesel fuel injection systems was carried out as a remedy to the problems of port fueled injection systems.

A gasoline direct fuel injector enables delivery of fuel into the cylinder for combustion.

Air flows through the intake manifold system, whose flow rate is controlled by the throttle valve and a homogeneous mixture is formed inside the cylinder. This homogenous mixture is ignited using a spark and combustion reaction helps convert the chemical energy stored in the fuel into useful work that moves the piston downwards, rotating the crankshaft.

In order to achieve clean complete combustion, the ECU algorithms estimate the amount of air entering into the cylinder under an intake event. The ECU then determines the time for which the fuel injector is to be opened to meet desired AFR ratio. The gasoline direct fuel injector is hence designed to be a precise fuel delivery device into the combustion cylinder.

Figure 1. Gasoline Direct Fuel Injector interface with Cylinder, as shown in [8]

Figure 1 shows interface of fuel injector with an illustrative single cylinder combustion chamber in a gasoline direct fuel injection system. The intake and exhaust paths for flow of fresh and combusted charge are shown, while also highlighted by the legend are main components of the fuel delivery flow path.

Figure 2: Direct Fuel Injection system with Rail and Low Pressure Fuel System, as shown in [8]

In Figure 2, the fuel is stored in a tank and is delivered to the low pressure side of the rail using an electric fuel pump. The high pressure pump typically a 3 lobed cam driven device provides continuous fuel delivery while amplifying the pressure downstream of the pump to the fuel rail. The fuel rail is equipped with a pressure sensor that sends information about current pressure in the line to the ECU. The pressure in the rail is controlled by the speed of rotation and valve opening inside the HP pump.

Figure 3 - Gasoline direct injection rail architecture representation.

The high pressure pump feeds the fuel rail. The rail can be designed in various architectures to support the wide range of engine block designs. One pattern of rail showcased in Figure 3 indicates common architecture used on a 6 cylinder engine

5 architecture. The fuel rail is a high pressure containing device with attachments / outlets for the individual fuel injectors. These injectors feed fuel into individual cylinders of the engine. High pressure rails also incorporate a pressure sensor that allows the ECU to measure the rail pressure and determine injection duration needed to achieve appropriate load.

Figure 4 - Injector, I/O Diagram

The injector at this level of analysis can be treated as an input-output device see Figure 4.

The injector receives input about the rail pressure and injection duration and delivers the fuel into the cylinder. As noted in the injector literature review, there are various levels at which fidelity of injector modeling is developed. The fidelity of injector modeling is

6 closely linked with the objectives of the model, the amount of data available and the level of experimental validation that can be successfully performed in order to characterize the subsystems of the model. As reviewed in the literature the major objectives of development of fuel injection models are [3, 5]:

1. Development of Combustion Chamber to meet emission standards

2. Investigation of abnormal fuel injection

3. Evaluation of design trends – Higher Pressure Injection, Lower Sac Volume

4. Evaluation of Fuel Injection System Performance by variation of characteristics

The goal of this thesis is development of the fuel injection model to support two primary objectives:

1. Characterization of in-cylinder combustion using 3D CFD methods.

2. Capacity to predict instantaneous during an injection event.

3. Provide data to link experimentally obtained injector spray characteristics.

Characterization of combustion is currently performed by 3D CFD methods. Combustion process is currently simulated by modeling an injection event which delivers spray fuel into the chamber. The 3D CFD model predicts evolution of droplets inside the combustion chamber during the entire engine cycle. With an appropriate ignition boundary condition, the 3D CFD model can predict combustion inside the cylinder chamber. The performance of the combustion model can be measured by metrics such as the capability of the model to predict soot during a combustion event. Other performance parameters include capability of the model to document spray impingement during a combustion event. The current project aims to characterize an injection event via

7 numerical and experimental data and improve the prediction capability of the existing 3D

CFD combustion model. This thesis highlights, existing procedures, state of the art and chosen methodology for fuel injection event characterization.

2. Objective and Scope of Thesis

Objective of this thesis and research are

 Development of validated physics based model of Gasoline Direct Fuel Injector

1. To predict instantaneous flow rate during operation.

2. To predict corresponding instantaneous needle lift during operation.

3. To predict cumulative fuel injected during an operating event.

The scope of the current document is stated below:

 Literature review of Fuel Injector characterization.

 Explain and model physical interactions between injector’s subsystems.

 Detail raw data (geometry, interface, control and flow circuit) needed for Model

Development.

 Explain need for calibration and conduct calibration.

 Document model performance.

 Explain errors in model performance.

3. Literature Review

3.1 Review of 1D-3D Engine Research

An injection event occurs at a specified rail pressure and injector energizing duration.

The injector allows for a specified mass of fuel to enter the chamber, determined by an

AFR control algorithm. The characteristics of an injection event can be encapsulated by experimental measure of droplet sizes, spray plume shape. These characteristics are a function of injector operating condition and change through the temporal scale during an injection event.

Literature review points to two distinct categories of methods to characterize an injection event. First class of methods lays specific focus on development of CFD injection models for a specific injection event involving the injector. These models focus on development of flow inside the injection nozzle. These numerically expensive simulations can account for turbulence and cavitation inside the nozzle, accurately predicting the flow regime in the near nozzle flow zone.

These high fidelity turbulent VoF-LES simulations are challenging to setup, are often performed as a precursor to nozzle design, ensuring near nozzle atomization performance is appropriate for operating conditions. These simulations are performed on research models, whose geometries are tightly controlled and hence results of simulations can be experimentally validated by near nozzle field observations. The advantage of these high fidelity simulations is the ability to simulate evolution of droplet characteristics due to 10 nozzle turbulence and cavitation. However these simulations are computationally expensive and challenging to experimentally validate. These 3D CFD VoF-LES simulations for the nozzle may be coupled with the 3D CFD combustion cylinder model and produces the most accurate prediction of the evolution of droplets inside the cylinder, but is an expensive method that needs extensive experimental validation.

The other method involves coupling of injection event data as boundary conditions to the

3D CFD combustion model. These methods with wide range of fidelity have been used as a boundary condition data to the combustion model. Reviewed literature specifies that droplet sizes are specified by the experimental measured statistical parameter of Sauter

Mean Diameter (SMD). Other characterizations such as Dv90, Dv50 may also be used to reconstruct the histogram of droplet sizing.

The number of droplets introduced into the cylinder as time evolves depends on instantaneous flow rate from the injector. Existing techniques of obtaining and using this information are primitive in nature. Reviewed literature relies on measurement of cumulative injected fuel mass and injection duration. This information is then converted to an average instantaneous flow rate based on an approximate trapezoidal instantaneous flow rate profile. This above approach of coupling experimental flow rate data and droplet diameter characteristics as boundary conditions to the 3D CFD combustion model is observed in the literature.

Figure 5 – Sample Trapezoidal Instantaneous Flow Rate from Injection Event. Certain caveats of such approach need to be highlighted. The assumed trapezoidal instantaneous flow rate profile may not be a fair estimate of the instantaneous flow rate out of the injector especially during needle opening and closing event of the injection.

The rise of needle inside the injector is governed by the electromagnetic force, damping and stiffness of the springs. These interactions govern the response of needle to the

12 commanded injection pulse and impact the flow rate profile of the injector. An assumption of trapezoidal instantaneous flow rate profile fails to capture the increased instantaneous flow out of the nozzle during needle rise and bounce events. This causes inaccurate characterization of droplets entering the cylinder during the designed time span and hence may result in inaccuracies in the resulting 3D CFD combustion performance.

The information about droplet diameters is captured experimentally. An injection event causes droplets with a wide spread of sizes to be injected into the cylinder. This size information is captured statistically with a normalized histogram in most analysis.

However, there does not exist a standardized experimental method of capturing this data.

Variations in data collection arise from lack of standardized test procedures, data measurement devices, position of measurement probe downstream of injector. Such variations are not generally accounted in coupled combustion models because the experimental data and expertise is expensive.

3.2 Review of Injector Modeling

Literature highlights the major objectives behind modeling of injectors. These objectives vary across a wide spectrum of research aims, intended to produce better injection system products (injectors, rails, pumps) or to analyze overall system performance. Modeling of fuel injection systems started taking forefront in the diesel fuel injection devices during early 90s as regulations were imposed to control NOx and particulate matter emissions around that time. It is critical to note that at this point of time, gasoline injection was majorly carbureted or in small market share dominated by port fuel injectors. Significant 13 advances were made in diesel fuel injection systems as these engines operate on the principle of compression ignition, wherein the fuel was always injected in “direct” fashion inside the cylinder. The general trend in diesel fuel injection was to inject the fuel at higher fuel pressure in order to aid atomization of the fuel inside cylinder and enable a homogeneous mixture for ignition under compression. While port fueled injection systems in the Gasoline Engine allowed for simpler designs, their performance under ever increasing stringent emissions requirements on NOx and PM was poor. Hence even

Gasoline Engines began the inevitable shift towards direct injection systems. Since direct injection became common so did the demand to model these systems in a reliable and predictable fashion.

Arcoumanis et al. (1996) highlighted that model based design of fuel injection systems was performed for a wide range of purposes, not least development of combustion chamber design to meet emission standards. They can also be used to investigate abnormal fuel injection such as caused by rail pressure fluctuations due to upstream high pressure pump or understand the impact of changing design parameters such as sac volume, higher pressure on fuel injection systems performance. The authors also highlighted the need to experimentally validate these numerical fuel injection models.

While being in the early era of gasoline direct fuel injection modeling the authors also saw the need to address issues arising from lack of control of rate of fuel injection.

Building on the work performed on Diesel Injectors, Postrioti et al. (2016) document the growing trends of the gasoline injection space moving towards implementing injectors in advanced combustion strategies. These advanced combustion strategies use stratified

14 direct injection and bank on the need to engage in control of the fueling rate from the injectors. Both Postrioti et al. (2016) and Gullaksen (2004) along with many others document the need to understand the impact of pressure pulsations inside the fuel injection system. Gullaksen (2004) documents the physics behind propagation of pressure wave through the tubing at the speed of sound due to compressibility of the fuel. These waves also hit other flow stops and reflect backwards, causing fluctuation of pressure through the piping. Both these sets of authors have invested large amounts of time documenting the importance of developing experimentally validated numerical models of fuel injection systems. Such models allow researchers, product designers and systems engineers a wide range of flexibility to design fueling systems, investigate placement of sensors and manipulate fuel layouts in order to improve performance.

In reviewed literature that spans the last 3 decades there are distinct styles of models that have been used in order to meet these wide array of objectives. At the most fundamental level all models use ordinary differential equations for the plunger and mass dynamics and attempt to capture flow using a 1-D PDEs. In older literature, emphasis was on using

ODE solvers coupled with method of characteristics in order to solve this coupled set of dynamic equations [2], [5] and [6]. These models are implemented in a FORTRAN or

MATLAB and have limitations on the number of physical phenomenon they can suitably capture due to run times and model sizes.

In newer literature [1], [3] and [4], most of the modeling is performed via commercial software such as AMESIM or AVL Boost. These commercial softwares allow access to libraries of physical elements with wide range of options that capture physical

15 phenomenon appropriately. It is also easier to couple these physical elements together and build a complex system from fundamental blocks. These software packages also pack access to numerical solvers that allow solving of PDEs and coupled ODEs with better accuracy than some custom solver code. Choice is also made available to provide higher order solution schemes in order to capture flow and pressure dynamics better. Access to

GUI, post-processing of solution data and ease of use has shifted physics based models from being developed from fundamental code blocks in MATLAB into more advanced physics based modeling packages such as AMESIM, AVL-Boost and GT-Suite.

Literature review highlights the wide array of physical phenomenon that occur inside the injector during an injection event. In order to capture these phenomenon using a numerical model a large amount of data is needed about the performance of the subcomponents inside injector, geometry and designed hydraulics. As presented in

Salvador et al. (2014) most high fidelity models of injectors are developed in-house by suppliers or are built by research teams focused on improving physics based models of injectors in order to improve product design. Development of models with such high fidelity needs precise information about the flow paths through the injectors as well as nozzles whose average dimensions are of the order of 100휇푚. As noted by the authors, these are obtained through development of negatives of flow volumes through silicon moulds and their dimensional verification under a scanning electron microscope as seen in Figure 6. The other challenge is characterization of flow through orifices and bends, which is typically performed by development of scaled test flow rigs of the same flow

16 structure. The access to such data is premium and is usually unavailable to researchers outside of the supplier umbrella.

Figure 6 – Silicon moulds used for dimensional analysis in nozzle sac area, as seen in [3]

Figure 7 – Dimensional analysis and orientation of silicon moulds of nozzle holes of Gasoline Direct Injector, under SEM, as seen in [3]

The final observation from literature review is on the increasing importance of the knowledge of rate of fuel injection in gasoline direct fuel injection systems. Suppliers provide data about the total amount of fuel delivered by the injector under an injection event characterized by rail pressure and injection duration. However the data lacks information about the rate of fuel injection during the injection interval. This information provides engine manufacturers access to additional data to tune their engine, control spark timing and characterize in-cylinder combustion performance better using 3D CFD models. However, it is noted that with increasing emissions requirements, gasoline direct fuel injection systems may need access to rate of fuel injection control strategies that employ fast acting piezoelectric actuators, a significant upgrade over the current solenoid actuation technology. These fast acting actuators may be proposed to be used in stratified

DI injection strategies. If actuators are precise and hence estimators over needle lift can be built, some advanced literature proposes the use of rate shaping of injector fuel flow as shown in Figure 8. Le et al. (2014) propose the use of piezoelectric gasoline direct fuel injectors to enable such advanced rate shaping fuel injection strategies.

Figure 8 – Proposed rate shaping of fuel injection using fast response actuator, as seen in [4]

References

1. Postrioti, L., Cavicchi, A., Paolino, D., Guido, C., Parotto, M., & Di Gioia, R.

(2016). An experimental and numerical analysis of pressure pulsation effects of a

Gasoline Direct Injection system. Fuel, 173, 8-28.

2. Gullaksen, J. (2004). Simulation of Diesel Fuel Injection Dynamics Using

MATLAB (No. 2004-01-2966). SAE Technical Paper.

3. Salvador, F. J., Plazas, A. H., Gimeno, J., & Carreres, M. (2014). Complete

modelling of a piezo actuator last-generation injector for diesel injection

systems. International Journal of Engine Research, 15(1), 3-19.

4. Le, D., Shen, J., Ruikar, N., & Shaver, G. M. (2014). Dynamic modeling of a

piezoelectric fuel injector during rate shaping operation. International Journal of

Engine Research, 15(4), 471-487.

5. Arcoumanis, C., Fairbrother, R. J., Gavaises, M., Flora, H., & French, B. (1996).

Development and validation of a computer simulation model for diesel fuel

injection systems. Proceedings of the Institution of Mechanical Engineers, Part D:

Journal of Automobile Engineering, 210(2), 149-160.

6. Arcoumanis, C., & Fairbrother, R. J. (1992). Computer simulation of fuel

injection systems for DI diesel engines. SAE transactions, 1881-1898.

4. Proposed Technique for Injector Characterization

The current research aims to characterize injectors using the coupled simulation approach. The information about an injection event is applied to the 3D CFD combustion model as boundary conditions. Following information is needed from an injection event in order to act as boundary condition for the 3D CFD simulations:

1. Instantaneous flow rate out of the nozzle

2. SMD of droplets being injected in-cylinder at any instant of time

3. Needle lift at instant of time of the injector

Characterization of injector is typically performed by collecting instantaneous flow rate data. The instantaneous flow rate data is to be obtained here is from a physics based gasoline direct injector model. The flow rate from an injector is contingent on the rail pressure and injection duration and strategy. When an engine operates at such a wide spread of operating conditions, the desired fuel injection may vary widely. Such instantaneous data is expensive to obtain experimentally. Typical supplier generated data provided for validation involves information about cumulative injection quantity

(mm^3/shot), which is also dependent on the operating pulse and rail pressure. In order to obtain instantaneous flow rate data at all operating conditions a model based approach is deemed appropriate. A physics based model that can predict the instantaneous flow rate of the injector is developed. This model is calibrated as appropriate and can predict the instantaneous flow rate from injector at wide array of operating conditions.

The size of droplets from an injection event are characterized by measuring them experimentally in a spray chamber. Identified caveats in the literature are being addressed as the testing and evaluation of droplet sizing is kept in-line as much as capable at the testing facility with SAE J2715 proposed standards. The committee identified that wide range of practices exist across laboratories and laid down a framework to propose a standard method of approaching droplet sizing experiments and data acquisition. The droplet sizing and data acquisition tests involve capturing data at large number of operating points. The sizes of droplets injected into the chamber during an injection event depend on the conditions in the sac volume at point of injection. The level of cavitation inside the sac volume is dictated by the pressure of the injected fluid and the vapor pressure at the chosen operating point. These conditions inside the sac are dynamic on a temporal scale and dictate the size of the droplets injected through an injection event.

Such dynamic information is best captured experimentally using statistical measures such as histogram of droplet diameters. Wide array of statistical parameters such as SMD,

Dv90, Dv50 have been developed as an attempt to characterize such injection information.

These droplet sizing tests are performed at steady state conditions of needle lift made possible via a modified injector hardware. The data collected from these steady state tests needs to be assembled together to be applied as the boundary condition to the 3D CFD problem. Literature review indicates that the dynamics inside the sac volume occur at a faster time scale than the dynamics of needle lift and motion. At each instant of motion of needle, the dynamics in the sac-volume would have settled and caused flow of particles

22 in accordance with the instantaneous flow rate and sizes as obtained from experimental results. This allows us to use needle lift data obtained from the model in order to link both these datasets together and create boundary conditions for the injector. The information obtained from the simulation model and droplet sizing experiments is coupled as boundary conditions to the 3D CFD combustion model.

It is hypothesized that the current method of characterization of fuel injection can deliver improved combustion model performance when compared with existing method that has similar technique but lower level of detail. Additionally due to the lack of use of 3D CFD models to characterize sac volume and near nozzle field of flow, owing to the expensive nature of simulation and validation, the current proposed methods are computationally cheaper.

Although these methods are computationally cheaper an understanding of the sacrifice due to using steady state data to characterize an inherently dynamic injection event needs to be evaluated. The impact of in-sac non-linear physics such as cavitation need to be evaluated. Needle bounce may not be captured accurately using the numerical solution and the effect of such needs to be treated in the final 3D CFD simulation data.

5. Model Development

A physics based predictive fuel injector model is developed to satisfy stated objectives in

2. Objective and Scope of Thesis. The developed model and the framework described in sections below are tuned to the purpose of the project. Reviewed literature may highlight to alternative modeling techniques, however these techniques need to be reviewed with the intent of meeting goals of the current project.

The injector is designed as an actuator and aims to deliver a certain pre-calibrated amount of fuel based on the commanded signal.

Figure 9 – Feed Forward simplistic fuel injection control command architecture in ECU

The commanded signal is translated from an upper level electronic control unit (ECU) into a fuel injection control unit as shown in Figure 9. The fuel injection control unit 25 receives information about the amount of fuel desired to be injected and current rail pressure (as measured on rail) and engine speed. This information is translated by the control unit into an injector opening duration (푇푖푛푗). Information about the current rail pressure and the injection duration are fed into the injector and help determine the power input to the injector.

The injector assembly which acts as a fuel actuator can be divided into several distinct elements, each with a specific purpose on a block diagram, see Figure 10. At least level of fidelity, the injector can be represented by an I/O block diagram. This representation of injector treats it as a device which seeks rail pressure 푃푟푎푖푙 and injection duration 푇푖푛푗 as inputs, and delivers a temporal flow of fuel out of the nozzle, represented by 푚푖푛푗̇ .

Additional outputs from the injector appropriate for the current project are temporal needle lift 푥푛푒푒푑푙푒 through an injection event.

Figure 10 – I/O Diagram of Gasoline Direct Fuel Injector Model

Higher fidelity diagram of the injector will indicate subsystems housed inside the device that enable operation of the injector. The injector can be divided into four major subsystems, each designed out of fundamental blocks of physics based design. Figure 11, indicates a detailed subsystem block diagram for the injector.

Figure 11 – Gasoline Direct Fuel Injector, Subsystem Block Diagram

The injector actuator can be described as comprised of four major subsystems, each designed from fundamental physics blocks. Each block of the injector is discussed in following subsections.

5.1 Injector Driver Circuit

The electrical driver controller subsystem is a microcontroller device that is implemented inside the driver controller circuit. The objective of the controller is to translate command from the injection control unit to operate the injector. The controller receives information about the common rail pressure upstream of the injector device and commanded injection

27 duration. The output of the electrical driver controller is a temporal voltage pulse across the electromagnetic system that drives the injector, see Figure 12.

Figure 12 – I/O Block Diagram, Injector Controller, Gasoline Direct Injector

The driver circuit (controller) operates in feedback mode. The voltage applied across the electromagnetic circuit drives a current through the solenoid. This current is monitored and used as feedback inside the injector driver circuit. The rail pressure 푃푟푎푖푙 determines the limits of current in each phase of injection. The switch from one zone of injection to the other is determined based on feedback from about the current through downstream electromagnetic circuit.

The injector driver controller has an embedded logic in the electronic circuit. The logic of the controller, produces a desired current profile through the solenoid by application of voltage across terminals of the circuit. The developed model of the injector relies on implementation of this logic in MATLAB/Simulink’s StateFlow logic chart diagrams.

The desired current profile is documented in Figure 13 below. 28

Figure 13 – Representative Current Profile, Electromagnetic Circuit, Gasoline Direct Injector

The current profile is achieved by supplying a voltage profile from the control circuit. A typical voltage profile output by the driver controller is shown below. The algorithm for the switching is detailed below in Figure 14.

Figure 14 – Algorithm, Injector Controller, Gasoline Direct Injector

The charts below specify normalized values of parameters on the current profile which govern the switching logic of the injector driver circuit.

Figure 15 – Peak Current vs. Rail Pressure, Parameter Table, Injector Controller, Gasoline Direct Injector

Figure 16 – Pickup Time vs. Rail Pressure, Parameter Table, Injector Controller, Gasoline Direct Injector

Figure 17 – Hold Current vs. Rail Pressure, Parameter Table, Injector Controller, Gasoline Direct Injector

The charts indicate dependency of the parameters of the current profile on the rail pressure at which injection is carried out. In an event the pressure crosses a certain threshold pressure, the driver controller operates in high pressure mode where additional power is supplied to the electromagnetic circuit to overcome the larger pressure end load on the mechanical elements, fluid damping and achieve same injection response.

The output of the injector driver circuit is a series of voltage pulses across the terminals of the electromagnetic circuit of the injector. A sample output profile of voltage from the device is indicated below in Figure 18.

Figure 18 – Sample Voltage Controller Output, Injector Controller, Gasoline Direct Injector

Table below notes the parameters needed in order to develop the injector driver circuit.

Table 1 – Parameters, Injector Driver Controller, Gasoline Direct Injector

Parameter Description Source Logic of Circuit Controller Logic Injector Specification 퐼푝푒푎푘 Peak Current Specification 퐼ℎ표푙푑 Hold Current Specification 퐼푐푙푎푚푝 Clamp Current Specification

푉퐷퐶 DC Voltage supplied by Battery System / Specification injector driver 푉푏표표푠푡 Boost voltage supplied by Specification injector driver 푁푓푟푒푞 Frequency of ON/OFF Calibrated to match current voltage supply response

5.2 Injector Electromagnetic Circuit

The electromagnetic circuit accepts input from the driver controller and transforms this electrical power input into mechanical power, see Figure 19. The circuit is designed to act as a transformer between two modes of power.

Figure 19 I/O Block Diagram, Electromagnetic Circuit, Gasoline Direct Injector

The injector’s electromagnetic circuit can be characterized by standard electrical circuit with resistive and inductive elements in series. The supplier datasheet for the injector provides information about the measured values of resistance and inductance of the injector. Figure 20 below details a representative electromagnetic circuit of the injector.

Figure 20 – Representative Electromagnetic Circuit, Gasoline Direct Injector

The resistance of the injector arises from the wiring inside the injector and metallic components in the path of current flow. The inductance of the device comes from the solenoid.

The solenoid of an injector is a coil wrapped around a housing, inside which lies the injector core which is made out of magnetic material. It is a long piece of wire wrapped around an iron core, which produces magnetic field as current is flown through the wire.

The addition of an iron core causes the magnetic field to be amplified.

The flow of an electric current through a wire produces a magnetic field. A long straight coil of wire can be used to generate a nearly uniform magnetic field, which can be amplified when used in conjunction with an iron core as documented in Nave [7]. This amplification of magnetic field allows use of the solenoid as an electromagnetic actuator.

The magnetic field inside of a solenoid coil wrapped around with N turns and stretches out to a length L can be described by the formulation derived from an infinite length solenoid as

퐵 = 휇 ∗ 푛 ∗ 퐼

푁 푛 → 푁푢푚푏푒푟 표푓 푡푢푟푛푠 푝푒푟 푢푛𝑖푡 푙푒푛푔푡ℎ ( ) 퐿

푇 휇 → 푃푒푟푚푒푎푏𝑖푙𝑖푡푦 표푓 푑표푚푎𝑖푛 [ ] 퐴 ∗ 푚

퐼 → 퐶푢푟푟푒푛푡 푓푙표푤𝑖푛푔 푡ℎ푟표푢푔ℎ 푡ℎ푒 푤𝑖푟푒 [퐴]

With an iron core wrapped around the solenoid, at the center of the field, the value of magnetic field amplifies to include relative permeability of the magnetic core.

퐵푐표푟푒 = 푘 × 휇 ∗ 푛 ∗ 퐼

푘 → 푅푒푙푎푡𝑖푣푒 푝푒푟푚푒푎푏𝑖푙𝑖푡푦 표푓 푡ℎ푒 퐼푟표푛 퐶표푟푒

Figure 21 – Solenoid performance, w/ and w/o Iron Core, taken from [7]

Figure 21 illustrates the amplification of magnetic field due to wrapping the solenoid around the iron-core in the designed electromagnetic circuit of the injector.

The circuit for the electromagnetics inside the injector can be simplified as an equivalent

RL circuit, with the inductance obtained due to ‘N’ turned solenoid coil described above.

When the electric parameters of the circuit are measured through an LQR meter, it indicates that the resistance and inductance inside the circuit are constant in nature.

A sample response of the current through an equivalent RL circuit with measured values is compared with the experimentally observed current profile through the injector circuit.

Figure 22 – Impact of varying reluctance on current profiles, Electromagnetic circuit

Figures compare experimental current readings with simulated current profiles for a certain injection event. The simulated current profile is obtained with injector’s driver

40 controller defined in Sec 5.1, however parameters for the equivalent circuit were chosen to be static values obtained from injector specifications and measurements.

The value of resistance as defined in the specifications matches the measurement and produces appropriate value of current response.

The value of inductance as defined in the specification and as measured does not produce a response appropriate with the current profile measured experimentally. If the inductance was thought off as an inertia, the response of current indicates that the inductance needs to be much lighter to allow the current to fall more rapidly as peak value of current is reached. This indicates that the inductance of the circuit varies through the injection event. Further evaluation of the electromagnetic and injector circuit indicate that physics relevant to such a behavior arise from the solenoid and motion of the core of the injector. Following sections explore this idea.

Figure 23 – Representative Solenoid circuit inside the Gasoline Direct Injector.

The solenoid circuit is shown in Figure 23, as referenced with the representative injector.

The figure indicates the location of solenoid coil, iron shell, magnetic core, air gap and the stopper connector on the injector and the representative solenoid circuit diagram. The solenoid circuit diagram is detailed here because the physics that lead to response of the current in the RL circuit arise from the dynamics of the motion of core inside this circuit.

The fundamental essence of the physics is that the inductance of the circuit is not constant as documented on the specification document, however it varies depending on the position of the core and the length of the air gap. 42

Figure 24 – Representation of Solenoid as a part of RL circuit of Injector.

The circuit in Figure 24 shows inductance replaced by the solenoid coil, magnetic core with air gap between the moving core and the stopper connector. The motion of core causes change in equivalent reluctance of the electromagnetic circuit. This equivalent reluctance dependent on position of core affects the inductance of the circuit.

퐿푠표푙(푥) = 푓(푥푐표푟푒)

An analysis of the equivalent circuit is performed so as to indicate dynamics of the current flow inside the circuit

In an equivalent RL circuit Kirchoff’s Laws indicates

푉푅 + 푉퐿 − 푉푑푐 = 0

푑휆 𝑖푅 + = 푉 0 푑푡 푑푐

This dictates the dynamics of current in the circuit.

휆 → 퐹푙푢푥 푙𝑖푛푘푎푔푒 𝑖푛푠𝑖푑푒 푚푎푔푛푒푡𝑖푐 푐𝑖푟푐푢𝑖푡

The flux linkage inside magnetic circuit provides resistance against change of external current, by providing back emf. This behaves as an inertia would inside a mechanical circuit.

The flux linkage depends on the amount of flux, which varies inversely with the reluctance of the circuit.

Hence the current dynamics of the circuit can be stated as:

푑휙 𝑖푅 + 푁 ∗ = 푉 0 푑푡 푑푐

𝑖푅0 + 푒퐿 = 푉푑푐

푑휙 푒 = 푁 ∗ 퐿 푑푡

휙 → 퐹푙푢푥 𝑖푛푠𝑖푑푒 푚푎푔푛푒푡𝑖푐 푐𝑖푟푐푢𝑖푡.

휙 = 휙(푥, 𝑖)

The flux inside magnetic circuit of a solenoid depends on both the position of the core and the current flowing through the circuit.

푑휙(푥, 𝑖) 푑푥 푑휙(푥, 𝑖) 푑𝑖 푒 = 푁 ∗ [ ∗ + ∗ ] 퐿 푑푥 푑푡 푑𝑖 푑푡

The expression for the flux in the circuit can be described as

ℱ(𝑖) 푁𝑖 휙(푥, 𝑖) = = 푅푒푞(푥) 푅푒푞(푥)

ℱ(𝑖) → 푀푎푔푛푒푡표푚표푡𝑖푣푒 퐹표푟푐푒

푅푒푞(푥) → 퐸푞푢𝑖푣푎푙푒푛푡 푅푒푙푢푐푡푎푛푐푒 표푓 퐶𝑖푟푐푢𝑖푡, 푓푢푛푐푡𝑖표푛 표푓 푝표푠𝑖푡𝑖표푛

푁𝑖 푑푅푒푞(푥) 푑푥 푁 푑𝑖 푒퐿 = 푁 ∗ [− 2 ∗ ∗ + ∗ ] 푅푒푞(푥) 푑푥 푑푡 푅푒푞(푥) 푑푡

To determine the structure of the magnetic reluctance circuit involving all components inside the injector’s magnetic path requires knowledge of the internal dimensions of the core, air gaps and magnetic material properties of the designed injector. This level of fidelity of information is not available for the formulation of this model.

Hence the electromagnetic circuit for the current analysis is formulated with a fidelity appropriate with the data available for the analysis. Major objectives of the modeling are maintained and additional data that cannot be measured is calibrated.

Characteristics of electromagnetic modeling and fidelity

 Capture dynamics of current in the injector electromagnetic circuit.

 Use lumped parameter low fidelity magnetic elements

 Calibrate values of parameters of magnetic circuit (air-gaps, relative permeability)

 Produce magnetic force on mechanical core

The electromagnetic circuit is modeled in GT-Power using base electro-magnetic block set. The voltage across terminals is supplied by injector driver controller.

Figure 25 – Implementation of Electromagnetic Circuit, GT-Power, Gasoline Direct Injector

Figure 25 shows implementation of the discussed electromagnetic circuit. The resistance of the circuit is as documented in measurements and in the specification document. The inductance of the circuit is obtained from a ‘Coil’ element in GT-Power. The coil element is an interface element between the electrical and magnetic domains, and accepts number of turns of the solenoid coil as a parametric input.

The magnetic air gap element interfaces between the magnetic and mechanical domains as specified in the diagram. The element accepts inputs on the magnetic air gap between the core and the stopper, when both positions are at zero. It also involves use of the cross sectional area of the magnetic air gap. 46

At this fidelity of the circuit, it can be noted that these dimensions are non-physical.

Calibration is needed here to achieve the right inductance to match current profile and generate motion downstream in the mechanical circuit.

Table 2 - Parameters, Electromagnetic Circuit, Gasoline Direct Injector

Parameter Description Source 푅0 Resistance of Measured / Specification Electromagnetic circuit 퐿(푥) Inductance Measured / Calibrated using Model 퐴푔푎푝 Cross section area of Calibrated magnetic air gap 푥푔푎푝 Magnetic air gap distance Calibrated

5.3 Mechanical Circuit of Injector

The power in the electro-magnetic circuit is transmitted to the mechanical circuit. The electrical power is transmitted into mechanical power, which causes the core to actuate.

A standard input output representation of the mechanical circuit is detailed in Figure 26 below.

Figure 26 – I/O Diagram, Mechanical Circuit, Gasoline Direct Injector

The main elements of the mechanical circuit of the injector actuator are detailed in the

Figure 27 below.

Figure 27 – Representation of Mechanical Elements, Gasoline Direct Injector

Moving entities of the injector device are the core and the needle. Motion of these elements is resisted by the position of stoppers and hard stop contact elements designed in the mechanical circuit. The springs control the rate of motion of these elements under external power supplied to the circuit. These elements are modeled in GT-Power using

49 elements provided in the standard library. Illustrations of the mechanical circuit indicate the interacting interfaces in the design as shown in Figure 28.

Figure 28 – Schematic of the Mechanical Circuit, inside Gasoline Direct Injector

There are two springs in the designed injector. The upper spring is in pre-compressed state and has a higher stiffness constant as compared to the lower spring, see Figure 29.

The charts indicate measured spring stiffness of the springs of the injector. These measurements of the spring stiffness were obtained by disassembling the injector. The disassembly of the injector allowed access to the upper spring of the device. The lower spring data was obtained from disassembly of a similar injector from the same supplier, which was available in mass-market production.

Figure 29 – Relative stiffness of springs, mechanical circuit, Gasoline Direct Injector

The needle rests on top of the core via a mechanical shoulder design. The designed shoulder allows transfer of force from the core into the needle, and causes actuation of the device. During the actuation motion of the needle upwards, the motion is resisted by the force applied by upper spring. The upper spring when installed in position has a certain level of pre-compression. In order for the needle to actuate it needs to overcome the preload set in the upper spring and act against the stiffness of the spring.

The electromagnetic circuit provides energy to overcome the opposing forces and cause motion of the combined core and needle when gap between them is closed. The force causes the core to move and hit the designed upper connector stopper. This travel of the core from the starting position to the point where connector / stopper element is impacted is designed and corresponds to the needle lift specification of the injector.

The kinetic energy transferred into the needle via the shoulder causes continued motion of the needle despite separation between shoulder contact of the core and needle. This continued motion causes needle lift to exceed designed core travel. This motion of the needle is restrained by the stiffness of the upper spring. However this excess energy in the spring is eventually dissipated as the needle, spring and fluid system is a damped system. This motion of needle with the excess energy, restrained by needle upper spring produces bounce in the needle lift. Another restricting mechanism designed in the needle core interface is the existence of lower shoulder, press fitted onto the needle which puts a hard limit on the overshoot of the needle lift.

On exceeding the injection duration 푇푖푛푗, the controller decides to switch into CLAMP mode, see Figure 14. This mode of operation causes a negative force to act on the core, causing it to move downwards. The spring force on the needle causes downward force on the needle which also causes it to force close and follow the core’s downward motion.

Both needle and core move downwards until the core rests on top of the lower spring.

This lower spring is designed as a compression only spring with a fixed length that does not elongate as the core travels through the needle lift. The lower spring is relatively softer as compared to the upper spring. The lower spring catches the core’s motion

53 downward and it’s stiffness along with the presence of the fluid causes the energy of the core to be dissipated and motion of such a device to be held back after some needle bounce. The designed mechanical circuit with its interfaces, shoulders and contacts / gaps allows appropriate transfer of electrical power into mechanical power causing needle lift with controlled bounce. Figure 30 implements the mechanical circuit in GT-Power using fundamental block elements.

Table 3 - Parameters, Mechanical Circuit, Gasoline Direct Injector

Parameter Description Source 푀푐표푟푒 Mass of Core Specification 푀푛푒푒푑푙푒 Mass of Needle Measured 퐾푈푆 Upper Spring Stiffness Measured 퐾퐿푆 Lower Spring Stiffness Measured / Estimated Contact Gaps Clearances b/w Estimated / Calibrated mechanical elements

Figure 30 – Implementation of Mechanical Circuit, GT-Power, Gasoline Direct Injector

5.4 Fluid Flow Circuit

The flow circuit of an injector interfaces with the high pressure rail system upstream of the injector. The objective of the flow circuit is to create a flow path from the fuel rail into the cylinder. Additionally the flow circuit is designed to inject plumes of fuel into the cylinder under pressure to enable high degree of atomization and mixing due to turbulence. This fluid flow circuit of the injector also interacts with the mechanical system which is tasked to control the opening and closing of the needle, hence the flow.

These interactions are highlighted in Figure 32.

Figure 31 – I/O Diagram, Flow Circuit, Gasoline Direct Injector

Figure 32 – Link between Mechanical and Flow Circuit, Gasoline Direct Injector

The main elements of the Fuel system are its interface with the high pressure rail as shown in Figure 3, interactions with mechanical needle element at the seat area and the designed orifice.

The high pressure rail lies upstream of the set of injectors. All injectors are housed inside the rail and the pressure between these interfaces is held by a gasket. The rail ensures that a large volume of fuel upstream of the injector is kept at a desired supply pressure. The higher pressure differential allows pumping of desired quantity of fuel inside the cylinder in a short injection time span, as necessitated by the engine operation speed and under varied engine start of injection (SoI) points that create back pressure on the nozzle.

The needle from the mechanical circuit interfaces with the flow circuit at the needle seat.

The needle in its resting position creates a barrier between the upstream pressure inside the injector and the downstream sac volume and orifice connection that leads into the cylinder. The fluid is sealed at the needle and seat interface. The motion of needle upwards by the core causes the fluid to enter the sac volume and flow out of the orifices.

The sac volume and orifices are designed to enable fluid flow into the cylinder. The designed orifices have a two particular design characteristics, their diameter and the spatial orientation angle of these orifices. The diameter controls the flow rate of the fluid out of the injection device in the same fashion as an orifice may operate. A small diameter of the orifices also causes atomization of the fluid at the expense of flow rate.

These two counteracting objectives are balanced and optimized to ensure appropriate operation of the injector as a fuel delivery device.

Figure 33 – Spatial orientation of plumes, flow circuit, Gasoline Direct Injector

The pressure differential across sac volume and cylinder leads to flow rate out of the orifices. Modern injector devices have multiple orifices oriented spatially. These spatial orientations lead to plumes of fuel injected in the cylinder. The plumes are spatially

59 oriented to enable dispersion of fuel inside the cylinder volume. The injector’s specifications specify plume orientation angles typically shown in Figure 33. In a 1D analysis however the impact of spatial orientation is not captured and is not of importance.

The geometry, orientation and dimensional information for these characteristics of the flow circuit are obtained from injector BoM diagrams and detailed scans. The geometry representation allows categorization of the flow elements and pipes inside the injector circuit. The injector is broken into three distinct flow sections for convenience. All other small volumes inside the circuit are lumped together into a bigger volume. This model is increased in fidelity, by capturing additional volumes, as needed, to capture performance of the dynamics of flow inside the injector circuit.

Figure 34 – Representation, Injector Volume Pre-Needle, Flow Circuit, Gasoline Direct Injector

Figure 35 – Representation, Injector Needle Volume, Flow Circuit, Gasoline Direct Injector

Figure 36 – Representation, Pipe Annular Injector Needle Volume, Flow Circuit, Gasoline Direct Injector

The needle and seat area of the model is captured via a single element that serves as a sealing entity between the injector pipe volumes and the sac volume downstream. This needle and seat area as designed needs intricate information about the dimensions and

63 angles of the interface. Dimensions of the shaft and seat area help determine the orifice areas of the seat interface. These dimensions are determined from the high fidelity scans of the injector.

Figure 37 – Representation, Needle Seat Area, Flow Circuit, Gasoline Direct Injector, as taken from [10] 64

The final piece of the flow circuit is the interface with sac volume and flow orifices. As discussed earlier the spatial orientation of the orifices is not critical to the objectives of a developed 1D model. The shape and dimensions of the sac volume and nozzle orifices are of the order of 100휇푚. The current injector design has 6 orifices, with dimension in the above mentioned order, obtained from technical data specifications provided by the supplier. In order to verify these dimensions, injector scans with a much higher fidelity are obtained.

In order to create the flow circuit the flow volumes inside the injector are lumped into three major pipe elements as indicated in range of figures (Figure 34 - Figure 37). The first element in the piping circuit is a dummy volume representative of the fuel rail. This volume helps stabilize the pressure in the circuit downstream of the rail, before injections are actuated. The dimensions of this dummy volume is non-physical in nature and can be tuned to achieve a stable response.

The dimensions required for the pipe elements are the flow diameter of the pipes, temperature of fluid flow and length of the pipe element chosen in design. The injector downstream of the core, where the flow volume is also occupied by the mechanical needle element is modeled using a hollow pipe element. Such an element needs internal diameter, external diameter of pipe element and the length over which such an element flows. The dimensions for such a volume in this analysis are treated as equivalent dimensions of the entire volume space and hence are non-physical in nature.

The needle seat dimensions are obtained from the high fidelity scans. The dimensions needed for this element are diameter of the needle poppet, diameter of downstream hole, seat half angle and limitation on discharge coefficient in the model if any. These dimensions of the needle seat are represented in an illustration below.

There are two other elements in the fluid circuit that enable correct capturing of the damping that exists between the core and the connector stopper element introduced in the mechanical circuit. These elements are split volumes that serve to connect both circuits and enforce the right amount of non-linear pressure dependent damping that exists in the mechanical circuit. The flow circuit is implemented in GT-Power as shown in Figure 38.

Table 4 - Parameters, Flow Circuit, Gasoline Direct Injector

Parameter Description Source 푂퐷/퐼퐷 and Volumes Volumes and Dimensions Estimated from scans for Flow Elements Orifice Elements Connection devices Standard GT-Power Values Needle Seat Elements Flow Mechanical Estimated from Scans Interface

Figure 38 – Implementation. Flow Circuit, Gasoline Direct Injector

5.5 CORE DAMPING INSIDE INJECTOR

The core of the injector, under travel experiences damping from the fluid’s pressure and squeeze damping by the fluid near the stopper / connector interface. These two modes of damping control the speed of the core, hence the rate of opening of injector’s needle lift.

Characterization of this damping and balance of the electromagnetic forces is critical to capture the correct needle opening rate of the injector.

The damping inside the injector is governed by the presence of fluid in trapped volumes, rail pressure and flow dynamics. These phenomenon are non-linear in nature. The easiest way to conceptualize the overall damping inside the injector is to distinguish it into two modes of operation:

1. Damping due to viscosity of fluid inside the injector

2. Damping on core due to fluid abutment and filling / emptying dynamics of core.

The fluid inside the injector is under pressure from the upstream rail. This pressurized fluid acts as a sink and absorbs energy that seeks to compress fluid or excess motion inside a confined space. When the injector’s electromagnetic circuit transfers power into the core and needle, the electrical power is transferred into mechanical power by this circuit. This fluid inside the injector owing to its incompressibility and viscosity dissipates the mechanical energy of motion. This is one form of damping inside the injector.

The other predominant damping phenomenon occurs between the core and the stopper interface. The illustration of flow circuit highlights the fluid flow path inside the injector.

The main flow path flows downstream into the injector needle’s bore, then exits radially outwards and downstream towards the nozzle of the injector. The auxiliary flow path in the injector’s flow causes fluid under pressure to occupy space between the core and connector, while also providing support to the underside of the core. These flow volumes above and below the injector are connected to each other via. orifices machined within the core.

The motion of the core under mechanical power transferred by the electrical circuit is also damped by the non-linear core damping arising due to designed core. This damping is contingent on filling dynamics of the connected volumes and transfer of fluid between them through the connected orifice as shown in Figure 39 and Figure 40.

Figure 39 – Representation, Core Damping Volumes, Gasoline Direct Injector

Figure 40 – Core damping non-linear filling dynamics, illustration from internal supplier documentation.

The characterization of both modes of damping needs accurate geometry, flow and fluid property data. The first mode of damping needs evaluation of damping force on the needle and core under effects of fluid viscosity. The non-linear core damping that is

71 depended on flow dynamics is also difficult to characterize without dynamic flow- mechanical models. However to build these models needs precise modeling using CFD approaches at detailed fidelity and access to geometry information. Models with such detailed level of fidelity are not appropriate for the current goals of the project given lack of data to the core geometry.

The proposed solution given the availability of geometry, flow data and objectives of the model is to capture damping within the device using a low fidelity model approach. This involves using lumped parameter damping on needle and core as appropriate. The value of the damping parameters in such models is non-physical. The non-linear core damping that arises due to fluid abutment is attempted to be captured using an analytical film model. The analytical film model is incorporated in GT-Power’s Flapper Valve template.

Both these models are non-physical in nature, are calibrated in order to produce a response congruent with measured flow rate rise from the injector’s nozzle at a certain operating point.

Table 5 - Parameters, Core Damping, Gasoline Direct Injector

Parameter Description Source Film Damping standoff Gap b/w Core and Calibrated to match Stopper at which film experimental flow response damping is limited Lumped Damping Model A Lumped parameter Calibrated to match damping at the Core experimental flow response Lumped Damping Model B Lumped parameter Calibrated to match damping at the Core experimental flow response

5.5 INJECTOR INTEGRATED MODEL

The above sections indicate the individual subsystems that compose the injector. These subsystems are integrated in order to create a working gasoline direct injector model. The interface elements between individual circuits act to integrate the model together. The table below notes such interface elements that are used to link subsystems.

Table 6 – List of Elements for multi-domain physics in Injector Model

Physics Domains GT-Power Elements

Flapper Valve Non Linear Damping of Mechanical - Flow w/ Analytical Film Model, Core Fluid Piston

Motion of Needle from Mechanical – Flow Needle Seat Seat

Voltage to EMAG from Controller - Controller,

Controller Electromagnetic MATLAB/Simulink Link

Power from EMAG to Electromagnetic - Magnetic Air Gap Mechanical Mechanical

These circuits were integrated together to present an integrated model as shown in Figure

41 that can be used to predict injection.

Figure 41 – Implementation of Injector Model, GT-Power, Gasoline Direct Injector 74

The model uses these interface elements to piece together a coupled multi-physics dynamic system. The injector model is commanded to operate at a certain predefined operating point. This data about rail pressure and injection duration is passed into the controller. The controller then determines the appropriate voltage pulse to be supplied to the electromagnetic circuit. The controller also seeks feedback about the current flowing through the circuit to determine the right operating mode of voltage, as the current can be co-related to needle position. The electromagnetic circuit turns this controller supplied electrical power into mechanical power. The mechanical power drives the motion of the core and needle of the injector. The injector’s needle motion causes flow out of the device.

6. Post-Processing of Model Results

6.1 Need for Combined Model

The injector model as described in 5. Model Development details the various components involved in modeling of the fuel injectors. As a review, the injector is a dynamic actuator system whose physics can be described as dependent on interactions between controller, electromagnetics, mechanical and flow systems. The fidelity of models for each system have already been described. This section highlights the challenges that arise in predicting flow rate from an integrated model.

An integrated fuel injector model, based on characterization of core damping in the device, two separate models for the fuel injector is developed because of the limitations that arise due to errors in model damping and electromagnetic circuits. During an injection event both of these calibrated damping models have a regions of operation where prediction of the flow rate wrt. experimental flow rate is more appropriately captured by a particular model. Additionally due to different physics involved in the characterization by a lumped parameter damping vs. a core damping with film modeling, these two models need to be built separately and switching of physics within a single model is not an appropriate solution, unless custom codes are developed for the same.

Figure 42 – Sample Instantaneous Flow Rate out of a Gasoline Direct Injector

The flow rate out of the injector can be distinguished into three distinct injection events as below:

1. Needle Rise

2. Needle Steady State

3. Needle Fall and Bounce

Needle Rise Event

The core damping model with fluid abutment appropriately captures flow rate during a needle rise event. The damping and resistance provided is provided to the core, under external electromagnetic force acting on the core that causes motion. Due to the limitations of current modeling techniques, this non-linear damping phenomenon does not subside in the model. The waning out of such damping is dependent on flow between connected volumes above and below the core through the orifices designed in the core. In order to include this waning out of dynamics in the modeled core damping scheme additional data about interface volumes and sizing of the orifice is needed. The lack of such data and inability to model these dynamics implies that waning out of the core damping as the core reaches full lift and hits the connector / stopper part is not captured correctly.

Needle Steady State – Full Lift

When core’s position nears full designed travel of the injector, the calibrated lumped parameter model provides a better estimate of the needle lift and hence the volumetric flow rate out of the device. The lumped parameter model also incorporates appropriate needle bounce once the core hits the stopper and momentum of the spring is to be stopped by the viscosity of the fluid and the spring stiffness. These behaviors exhibited by the lumped parameter model are typical to those observed in literature for such phase of needle lift.

The injector’s response once needle attains full lift is best characterized by the lumped parameter damping model. The core has already attained full-lift and adequate energy is being provided to it by the electromagnetic circuit to keep it in position. The needle after its characteristic bounce has also stabilized in position at full lift. This causes the flow out of the device to be steady in nature.

Needle Fall & Bounce

Once the clock time during injection exceeds the duration requested by the injector ECU

푇푖푛푗 the controller operates in clamp mode. This causes the core to start its travel downwards and cause the needle to close. It is during this event that the dynamics of filling between the lower and upper volumes of the core act in reverse direction to that which exists during the needle rise event. This damping caused by the inability of the fuel to rapidly move into the upper volume owing to constricted flow through the orifice causes the core fall to fall at a slow rate. The rate of core fall is also non-linear, with most damping occurring during the initial stages of the fall event, while falling rapidly as the core reaches low lift positions. It is noted that the calibrated film damping model, that captures needle rise phase also adequately captures the needle fall phase.

As the needle falls through non-linear damping phase with the delay caused by filling dynamics of the core. The core travels downwards under clamp operating condition, it contacts with the lower spring. The injector controller operates in clamp condition until the current in the circuit drops to zero. However since feedback from the core about its position is not available, it occurs that the core gets larger energy than is required to cause zero lift. Hence the core bounces off the lower spring, subsequently transferring

79 energy into the needle during downward travel of the needle. The downward travel of the needle is primarily caused by transfer of the energy from the core into the needle via lower shoulder and is aided by the stiffness and preload of the upper spring. This needle bounce during closure is also caused by the slamming shut of the needle against the seat, both of which have stiffness and hence some degree of elastic impact associated with the same. An elastic impact, caused by the hardening of the seat area and needle tip is desired in order to maintain structure of the needle and seat area under repeated use of the injector.

Because of these characteristics of the model, it is intended that a post-processing algorithm be used in order to combine the data from both models.

6.2 Structure of Models for Combination

Figure 43 explains the structure of the combined model and the software packages used to realize the structure.

Figure 43 – Model structure, combined GT-Power Models, Gasoline Direct Injector

A MATLAB Script precedes the Simulink Model and loads parameters for the GT-Power

Models, Controllers and Simulink solvers in the workspace. This script can be modified to run the model at wide range of operating conditions. It can also be modified to change sampling time of the model.

The GT-Power physics based models for injectors are housed inside a Simulink model.

The Simulink model returns outputs from both GT-Power injector models. These outputs 81 are fed into a post-processing algorithm that produces results from the combined algorithm.

6.3 Post-Processing Algorithm for Combination of Results

This section serves to introduce and explain the post-processing algorithm that is used to combine results from both models. The algorithm uses needle lift and transition lift data that is set to determine switching and appropriate processing of the algorithm.

Figure 45 below provides a brief overview of the post-processing algorithm.

Figure 44 – Nomenclature b/w Core Damped and Core Undamped Model.

Figure 45 – Post-processing algorithm, combination of model results.

There are two major building blocks of the algorithm:

1. Method to determine zone transition points from raw data

2. Method to join data together

The algorithm is fed with raw data from both models. In addition to raw data, two preset levels of needle lift at which the zones transition are provided to the algorithm. The

84 algorithm uses data from individual models and these preset levels of needle lift

(푡푟푎푛푠퐿𝑖푓푡, 푓푎푙푙퐿𝑖푓푡) to determine transition points for the data to be used between the models.

Once transition points are determined from data, the JOIN METHOD pieces together raw data from individual models per appropriate zones to determine the combined result. The join method allows for the appropriate physics to be used during modes of injector’s needle operation. Section 8. Error Analysis introduces zones of operation of the model which are detailed by Figure 63 .

1. Zone I - Needle Rise

2. Zone II - Needle Steady State

3. Zone III - Needle Fall and Bounce

During Zone I of model’s operation the physics of the injector is best captured by the core damped model, which simulates slower needle rise due to the presence of film damping physics. Zone II of the model is best represented by a weighted average results between both core damped and undamped model, with weights 푤1 = 푤2 = 0.5. This is because both physics act on the model during the needle steady state operation. The Zone

III of the model can be split into needle fall, which is captured well by a core damped model with film damping. This prolongs the fall time of the core. The needle bounce

(dribble) is captured well by the undamped model. The algorithm developed with the join method handles such transitions within the model appropriately.

7. Results

7.1 Experimental Results

The performance of the injector is characterized using supplier provided experimental data. When data is transferred by the supplier, the intention is to provide adequate input output data to generate confidence in the performance of the injector and for tuning the injector’s performance while interfacing in the engine. For the current injector the output data provided by the supplier is classified into three types

1. Instantaneous Flow Rate and Current through Injector

2. Cumulative Flow Rate (mm3/str) at Injection Pressure vs. Injection Duration

3. Cumulative Flow Rate (mm3/str) at Injection Pressure and Duration vs. Interval

b/w sequential durations.

The instantaneous flow rate data from an injector provides an estimate of the flow rate through an injection event. This flow rate data is obtained downstream of the injector device. An upstream measurement of flow rate unless compensated contains fluctuations in flow rate due to pressure wave dynamics that is seen due to open/shut response of the injector. Downstream flow rate measurements are obtained using an experimental test setup that is based on widely reported Bosch Tube technique.

The experimental data available for the current injector at the time of writing this document included instantaneous flow rate response for the injector as provided by the supplier. Instantaneous flow rate data is available for 4 pressure data points, under a single duration of injection event.

Normalized figures for data are presented in order to represent experimental curves.

Figure 46 – Representation of Instantaneous Flow Results, Experimental value from Gasoline Direct Injector

The injector’s performance is also documented by the total injected quantity of fuel under a certain operating condition. Such information is critical as it can be stored on-line as a fuel injector operating performance map that is used by the upper level ECUs to determine appropriate fuel injection duration in order to meet the AFR requirements at a certain engine operating condition.

Tables record information about the net injected quantity under a certain injection pressure for a wide range of injector actuation durations. One such representation is made available here for reference in Figure 47.

Figure 47 – Normalized Experimental Cumulative Flow Data from Injector

At engine operating conditions with high RPM and high load it may be required that a large amount of fuel be delivered to the cylinders under the current operating condition.

The injection occurs once every two revolutions of the crankshaft. In the time domain, it

89 may occur that two subsequent injections occur with relatively small amount of time interval between them. As a standalone injector which is energized for a certain injection duration, if the interval between two subsequent injections is short (owing to high RPM or multi-shot injection strategy) the cumulative flow out of the device changes.

If the interval between two injection events is short, the needle in the first event may not have reached full closure before the next injection event has been actuated. This causes variation in cumulative shot volume injected from the device. It is important to characterize the variations in the injection event based on interval duration as such information can be used by the upper level ECU to make decisions about injection event.

The current model does not account for multi-shot injection strategies with short dwell times, hence this available experimental data was not used in the analysis.

7.2 Simulation Results

Experimental data for instantaneous flow rate from injector is available for four cases of injector operation. The predictive injector model is run for the same four cases in order to demonstrate the model’s capabilities.

The normalized case labels for which the model is run is tabulated below.

Table 7 – Operating Conditions of Injector Model

NORMALIZED NORMALIZED INST. FLOW

INJECTION INJECTION RATE DATA

CASE PRESSURE DURATION AVAILABLE?

A 0.175 LOW YES

B 0.3 LOW YES

C 0.4 LOW YES

D 0.75 LOW YES

Results for Instantaneous Volumetric Flow rate from model are compared with experimentally available data for each of the above cases. For Case A of the injector operation, the model’s prediction of flow rate with experimental results is shown in

Figure 48. It can be seen that the portion of injection within the needle steady state realm and needle fall are accurately predicted by the model. However there exist errors while 91 predicting the needle rise and falling bounce sections of the injection event. Errors in these zones of the model are to be noted even in the prediction of needle lift.

Figure 48 – Results, Case A, Prediction of Instantaneous Flow Rate

Figure 49 – Results, Case A, Prediction of Needle Lift

Figure 50 - Results, Case B, Prediction of Instantaneous Flow Rate

Figure 51 – Results, Case B, Prediction of Needle Lift

Figure 52 - Results, Case C, Prediction of Instantaneous Flow Rate

Figure 53 - Results, Case C, Prediction of Needle Lift

Figure 54 - Results, Case D, Prediction of Instantaneous Flow Rate

Figure 55 - Results, Case D, Prediction of Needle Lift

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The needle lift predicted by the model shows distinct zones of rise, bounce, steady, fall and closure dribble. The experimental instantaneous needle lift data is not possible to obtain on a standard production injector. There have been attempts made to include displacement potentiometers on modified experimental injector replica-setups in order to include a measurement of the displacement of needle. In the current work, such level of detail measurement is not available. Hence, an estimation of errors in the needle lift has to be made from a knowledge of errors on the instantaneous volumetric flow rate. Errors in Case A’s instantaneous flow rate prediction in the needle rise and fall-bounce section also carry forward qualitatively into prediction of needle lift.

Model’s prediction for flow rates is most appropriately captured for the Cases B (Figure

50) and C (Figure 52). The prediction of needle lift (Figure 51 and Figure 53) is also qualitatively better.

In Case D of injector operation Figure 54, the injector operates at 0.75푃푚푎푥. Under this high pressure the prediction of flow rate from the model matches experimental data during the needle rise and steady flow zones. However at the end of injection event, the needle slams shut faster than in other cases. Calibration of the model with existing parameters did not help alleviate this behavior during needle fall-bounce zone, hence incurring larger errors. It is the author’s understanding that such error arises due to the lack of core volume filling dynamics in the current model. Needle lift prediction for Case

D is shown in Figure 55.

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8. Error Analysis

8.1 Metrics

The results section of the current work provides qualitative information about the performance of the model’s prediction.

The prediction performance of the model quantitatively evaluated using three distinct metrics:

1. Total volume of fuel injected per Injection Event.

2. RMS Error between Simulation and Experimental Curves.

3. Zone wise RMS Error between Simulation and Experimental Curves.

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Figure 56 – Representation of Error, Total Fuel Injected.

푎푏푠(푣푠푖푚 − 푣푒푥푝) 푒푐푢푚 = × 100 푣푒푥푝

Comparison of total volume of fuel injected between experimental measurements and simulation provides a recognized procedure to establish quality of model. The results 103 from injection event are measured experimentally and from simulation. Post processing macros are run in order to evaluate the total amount of fuel injected from instantaneous volumetric flow profiles obtained from the model. Availability of experimental instantaneous flow rates measurements allows application of other metrics. If only cumulative flow data for an injection event was made available only metric #1 can be applied for the analysis of model performance.

Figure 57 – Results, Cumulative Fuel Injected % Error, Experimental vs. Simulation

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The above figure indicates the error that arises when the injection model was used to predict fuel injected at a constant injection duration 푇푖푛푗 and varying injector operating pressure. Figure 57 indicates that error in model’s prediction of cumulative injection quantity for cases A, B and C is below 2%. The error in Case D for the current injection event is close to 10%. The current injection duration for the model is a short duration.

The total injected quantity during short injection pulses is small. The error in Case D, due to lack of ability to predict needle fall-bounce zone causes relatively larger errors in the model’s cumulative injection data over a short injection duration.

Standard supplier generated data also provides cumulative injected volume per stroke at a fixed operating pressure when the injection duration is varied. This data (Figure 47) is also compared with that predicted from the model. This will provide an understanding of the error performance of the model over a wide range of injector operation time.

Experimental cumulative injection data is available for four injector operating cases with pressure ranging from 푃 = [0.175, 0.3, 0.4, 0.75] ∗ 푃푚푎푥 and a wide range of injection durations all larger than currently presented. The injector operating durations could not be normalized as there exists no maximum injector operating duration limit on the device.

Results for cumulative injection performance of the model are presented in Figure 58.

Four cases of pressure operation are tested as noted with a large range of opening duration. The cumulative injection performance of the injector model is also evaluated using error plots in the current section.

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Figure 58 – Cumulative Experimental vs. Simulation, Injector Flow Performance Data.

Data indicates that performance of the injector model when used to predict cumulative flow rates is good for moderate injection durations. At the larger time duration end of the injection event, the prediction in cumulative flow by the model falls short of the averaged experimental results at the current injection event. This is because the errors in steady state flow (zone II introduced later) due to different pressure pulsations inside injector become dominant. Figure 61 indicates the % error in each case of injection. For all

106 pressure and injection time ranges the % error in cumulative quantity of fuel injected is less than 2%.

107

Figure 59 - % Error, Cumulative Flow (Case A & B), Experimental vs. Simulation Data

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Figure 60 - % Error, Cumulative Flow (Case C & D), Experimental vs. Simulation Data.

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Another error metric defined in literature when instantaneous flow rate is available is the relative RMS error between experimental and simulation curves. This is evaluated as per formulation described in literature [4].

Figure 61 – Representation of Error, Relative RMS Error, Whole Fuel Injected

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푒(푡) = 푣푓푟푠푖푚(푡) − 푣푓푟푒푥푝(푡)

푇 ( )2 ∫0 푒 푡 푑푡 푒푟푚푠(푡) = √ 푇 ( )2 ∫0 푣푓푟푒푥푝 푡 푑푡

The intent of this error metric is to capture the ratio of relative area between the experimental and simulation curves vs. the area under experimental curve. This provides an estimate of the relative error between the simulation and experiments.

Figure 62 – Results, Normalized Relative RMS Error %, Experimental vs. Simulation 111

Figure 62 indicates the range of relative RMS % error for the four cases where instantaneous flow rate experimental data was available. It is to be noted that the injection duration for the current cases was short. The error RMS data for the current cases hence indicates a large RMS Error% of nearly 15%. Additionally the lack of accurate characterization of needle rise and needle fall-bounce events adds to this accumulative error metric.

The objectives of the current thesis warrant introduction of another important error metric. It is intended to evaluate the performance of the model during the three distinct needle operation modes. The three operation modes are distinguished below:

4. Zone I - Needle Rise

5. Zone II - Needle Steady State

6. Zone III - Needle Fall and Bounce

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Figure 63 – Representation, Injection Event, Discretized by Zones for Needle Operation.

The relative RMS error between experimental and simulation results is performed for each of these three highlighted zones. This serves to provide some idea of the error that

113 may arise in the needle lift prediction by comparing them with the error in instantaneous flow rate from the model.

Error from this third metric is captured in Table 8 below:

Table 8 – Relative RMS Error % per Zones for Cases

Case Zone I Zone II Zone III

A 32.5 2.8 34.7 B 29.8 3.7 43.4 C 22.8 4.0 52.1 D 9.9 17.8 101.7

Results tabulated here provide a quantitative understanding of the zonal error between experimental and simulation performance. Error % in Zone II is below 15%. This error arises due to the pressure fluctuations inside piping in experimental and simulation models, which affects the flow rates out of the device. The error % in Zone I is a maximum of 32.5% for the low pressure case. The needle rise during a low pressure case occurs faster than in the experiment, indicating inappropriate electromagnetic force modeling or incorrect damping characterization. The Zone III error of the Case D model is highest as the needle in highest pressure case has a tendency to slam shut and show relatively low core damping dynamics.

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9. Conclusion

Following conclusions can be drawn from the modeling of injectors in order to meet objectives laid out in section 2. Objective and Scope of Thesis

1. Physics based Models have been used successfully to predict Injector’s

performance.

2. Instantaneous Flow Rate performance from injector model wrt. whole curve RMS

error metric for low and intermediate pressure range has ~ %15 error. For high

pressure, low duration case with experimental data, error is larger.

3. Needle rise can be predicted from physics based block models. Error can be

qualitatively evaluated as experimental measurements or model estimation via

other techniques is unavailable.

4. Cumulative flow data from the injector model for wide range of injector operating

condition is documented. Model predictions have a low error of ~2%.

5. Error in the model arise from lack of high fidelity geometrical, material property

data for the electromagnetic and core filling dynamics damping circuits.

6. These error manifest in injection performance during needle-rise or needle fall-

bounce periods as documented for various cases in this thesis.

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Bibliography

1. Postrioti, L., Cavicchi, A., Paolino, D., Guido, C., Parotto, M., & Di Gioia, R.

(2016). An experimental and numerical analysis of pressure pulsation effects of a

Gasoline Direct Injection system. Fuel, 173, 8-28.

2. Gullaksen, J. (2004). Simulation of Diesel Fuel Injection Dynamics Using

MATLAB (No. 2004-01-2966). SAE Technical Paper.

3. Salvador, F. J., Plazas, A. H., Gimeno, J., & Carreres, M. (2014). Complete

modelling of a piezo actuator last-generation injector for diesel injection

systems. International Journal of Engine Research, 15(1), 3-19.

4. Le, D., Shen, J., Ruikar, N., & Shaver, G. M. (2014). Dynamic modeling of a

piezoelectric fuel injector during rate shaping operation. International Journal of

Engine Research, 15(4), 471-487.

5. Arcoumanis, C., Fairbrother, R. J., Gavaises, M., Flora, H., & French, B. (1996).

Development and validation of a computer simulation model for diesel fuel

injection systems. Proceedings of the Institution of Mechanical Engineers, Part

D: Journal of Automobile Engineering, 210(2), 149-160.

6. Arcoumanis, C., & Fairbrother, R. J. (1992). Computer simulation of fuel

injection systems for DI diesel engines. SAE transactions, 1881-1898.

116

7. Nave, R. (n.d.). Solenoid, Electricity and Magnetism. (Georgia State University)

Retrieved from HyperPhysics: http://hyperphysics.phy-

astr.gsu.edu/hbase/magnetic/solenoid.html#c1

8. Reif, K. (Ed.). (2014). Gasoline Engine Management: Systems and Components.

Springer.

9. Fiengo, G., Di Gaeta, A., Palladino, A., & Giglio, V. (2012). Common Rail

System for GDI Engines: Modelling, Identification, and Control. Springer Science

& Business Media.

10. Gamma Technologies. (GT-ISE v2017). Help File, Double Conical Poppet with

Conical Seat, ConicalPoppetConSeat, Hydraulics and Pneumatics Templates.

117