15
REGENERATIVE HYDRAULIC ASSISTED TURBOCHARGER Tao Zeng Michigan State University East Lansing, MI, USA Devesh Upadhyay Ford Motor Company Dearborn, MI, USA Harold Sun Ford Motor Company Dearborn, MI, USA Eric Curtis Ford Motor Company Dearborn, MI, USA Guoming G Zhu Michigan State University East Lansing, MI, USA ABSTRACT Engine downsizing and down-speeding are essential in order to meet future US fuel economy mandates. Turbocharging is one technology to meet these goals. Fuel economy improvements must, however, be achieved without sacrificing performance. One significant factor impacting drivability on turbocharged engines is typically referred to as, “Turbo-Lag”. Since Turbo-lag directly impacts the driver’s torque demands, it is usually perceptible as an undesired slow transient boost response or as a sluggish torque response. High throughput turbochargers are especially susceptible to this dynamic and are often equipped with variable geometry turbines (VGT) to mitigate some of this effect. Assisted boosting techniques that add power directly to the TC shaft from a power source that is independent of the engine have been shown to significantly reduce turbo-lag. Single unit assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted turbocharger (RHAT) system is evaluated. A custom designed RHAT system is coupled to a light duty diesel engine and is analyzed via vehicle and engine simulations for performance and energy requirements over standard test cycles. Supplier provided performance maps for the hydraulic turbine, hydraulic turbo pump were used. A production controller was coupled with the engine model and upgraded to control the engagement and disengagement of RHAT, with energy management strategies. Results show some interesting dynamics and shed light on system capabilities especially with regard to the energy balance between the assist and regenerative functions. Design considerations based on open loop simulations are used for sizing the high pressure accumulator. Simulation results show that the proposed RHAT turbocharger system can significantly improve engine transient response. Vehicle level simulations that include the driveline were also conducted and showed potential for up to 4% fuel economy improvement over the FTP 75 drive cycle. This study also identified some technical challenges related to optimal design and operation of the RHAT. Opportunities for additional fuel economy improvements are also discussed. INTRODUCTION The need for assisted turbocharger Engine downsizing via high throughput turbochargers (TC) is a common approach for achieving improved fuel economy (FE). However, exhaust gas TC, including VGT’s are prone to a transient response dynamic commonly referred to as Turbo- lag. Turbo-lag is directly related to the rotational inertia of a TC and is simply the response time to achieve the desired TC speed, N TC , starting form some initial speed. Turbo lag directly translates to slow boost response and hence slow time to torque. This delay in torque response is perceived by the driver as a sluggish engine from a lack of power. In lean burn engines tip- in, turbo-lag is also the main cause for the transient smoke. The effect of turbo-lag is also perceived during tip-out events through an extended slowdown duration during which the compressor continues to pump excess air into the engine leading to oxygen rich combustion with potentially increased NO x emissions. In order to address the impact of turbo lag on transient performance of turbocharged engines, vehicle manufacturers typically resort to one or more of the following measures: 1 Copyright © 2017 ASME Proceedings of ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition GT2017 June 26-30, 2017, Charlotte, NC, USA GT2017-64927 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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Page 1: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

REGENERATIVE HYDRAULIC ASSISTED TURBOCHARGER Tao Zeng

Michigan State University East Lansing, MI, USA

Devesh Upadhyay Ford Motor Company Dearborn, MI, USA

Harold Sun

Ford Motor Company Dearborn, MI, USA

Eric Curtis Ford Motor Company Dearborn, MI, USA

Guoming G Zhu Michigan State University

East Lansing, MI, USA

ABSTRACT Engine downsizing and down-speeding are essential in

order to meet future US fuel economy mandates. Turbocharging is one technology to meet these goals. Fuel economy improvements must, however, be achieved without sacrificing performance. One significant factor impacting drivability on turbocharged engines is typically referred to as, “Turbo-Lag”. Since Turbo-lag directly impacts the driver’s torque demands, it is usually perceptible as an undesired slow transient boost response or as a sluggish torque response. High throughput turbochargers are especially susceptible to this dynamic and are often equipped with variable geometry turbines (VGT) to mitigate some of this effect. Assisted boosting techniques that add power directly to the TC shaft from a power source that is independent of the engine have been shown to significantly reduce turbo-lag. Single unit assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted turbocharger (RHAT) system is evaluated. A custom designed RHAT system is coupled to a light duty diesel engine and is analyzed via vehicle and engine simulations for performance and energy requirements over standard test cycles. Supplier provided performance maps for the hydraulic turbine, hydraulic turbo pump were used. A production controller was coupled with the engine model and upgraded to control the engagement and disengagement of RHAT, with energy management strategies. Results show some interesting dynamics and shed light on system capabilities especially with regard to the energy balance between the assist and regenerative functions. Design considerations based on open loop simulations are used for sizing the high pressure accumulator. Simulation results show that the proposed RHAT

turbocharger system can significantly improve engine transient response. Vehicle level simulations that include the driveline were also conducted and showed potential for up to 4% fuel economy improvement over the FTP 75 drive cycle. This study also identified some technical challenges related to optimal design and operation of the RHAT. Opportunities for additional fuel economy improvements are also discussed. INTRODUCTION The need for assisted turbocharger

Engine downsizing via high throughput turbochargers (TC) is a common approach for achieving improved fuel economy (FE). However, exhaust gas TC, including VGT’s are prone to a transient response dynamic commonly referred to as Turbo-lag. Turbo-lag is directly related to the rotational inertia of a TC and is simply the response time to achieve the desired TC speed, NTC, starting form some initial speed. Turbo lag directly translates to slow boost response and hence slow time to torque. This delay in torque response is perceived by the driver as a sluggish engine from a lack of power. In lean burn engines tip-in, turbo-lag is also the main cause for the transient smoke. The effect of turbo-lag is also perceived during tip-out events through an extended slowdown duration during which the compressor continues to pump excess air into the engine leading to oxygen rich combustion with potentially increased NOx emissions.

In order to address the impact of turbo lag on transient performance of turbocharged engines, vehicle manufacturers typically resort to one or more of the following measures:

1 Copyright © 2017 ASME

Proceedings of ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition GT2017

June 26-30, 2017, Charlotte, NC, USA

GT2017-64927

Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 2: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

1. Downshifting the transmission. A turbocharged diesel engine may take on the order of a few seconds to achieve peak torque (power). Figure 1 shows the instantaneous power of a light-duty diesel engine, measured during a load step test on an engine dynamometer. As a result of the sluggish transient response of this engine, the transmission is forced to downshift to meet the power demand. This however, pushes the engine into a high speed low efficiency operating regime. Since TC assist will improve the transient response a transmission downshift may be avoided. This also translates to some fuel economy improvement.

Figure 1. INSTANTANEOUS ENGINE POWER LUG CURVE BASED ON A LOAD STEP TEST ON A LIGHT DUTY DIESEL ENGINE.

2. Reduction of exhaust gas recirculation (EGR), during the tip-in process, to introduce more fresh-air mass for better torque response. This results in the well-known transient feedgas (FG) NOx spike as shown in Figure 2.

Figure 2. INSTANTANEOUS ENGINE EGR RATE, SOOT AND NOX

EMISSIONS DURING AN LD DIESEL FTP TRANSIENT TEST

3. The smoke limited air-fuel ratio (AFR) may be further relaxed to meet the transient torque demand. However, this increases the FG soot emissions as indicated in Figure 2. In engine without a diesel particulate filter (DPF), this will be observed as tip-in smoke. Increased soot emissions have a

direct fuel economy implication from the increased DPF regeneration frequency.

4. Some engine controller uses an “air reserve” strategy at the onset of an engine tip-in through an aggressive VGT maneuver (shut-open) in order to partially offset the turbo-lag effect. This action, however, is inefficient and leads to increased pumping loss.

5. Tip-out surge is another concern that forces a high surge margin for the compressor thus comprising the width of compressor map available for a nominal operation which in turn compromises peak efficiency. Regenerative hydraulic assisted turbocharger

The hydraulically-assisted turbocharger has been studied since the early-1980's [6]. There have been publications and patents on the use of a hydraulic turbine, driven by high–pressure oil, on the turbocharger shaft to accelerate the turbocharger [2-5]. The hydraulic turbine, in these systems, is a compact design and is integrated into the turbocharger center housing between the conventional compressor and turbine wheels. These designs, however, relied on a stand-alone hydraulic pump to build up and maintain high pressure in the hydraulic accumulator. This design incurred a high equivalent FE penalty from pressurizing the fluid for reserve energy and may have been an important reason for the design not achieving wide acceptability. In this study, we adopted an alternate design where two energy recuperation devices are used. A hydraulic pump is mounted on the TC shaft, just like the hydraulic turbine, and is used to provide energy recovery through TC braking much like the regenerative function of an electrically assisted TC. An additional driveline pump is used to recover vehicle braking energy similar to an integrated starter generator (ISG) [1]. While much of the recovered energy is from the driveline pump, the TC shaft mounted hydraulic pump provides the important additional ability to actively brake the TC. Hence the hydraulic turbine and pump provide the ability to actively control the speed of the TC. This allows benefits such as better surge control and the ability to operate the compressor optimally. The high-speed turbo-pump, like the hydraulic turbine, is a mature technology developed in the aerospace industry [9]. NASA published a report in 1974 indicating that a hydraulic turbo-pump, for rocket applications, was capable of achieving efficiencies on the order of about 73% [9]. Other studies (including research at Ford Motor Company), also indicated around 72% efficiency on larger sized hydraulic turbines [1, 10, 11]. Two types of energy recovery are typically possible. The first mode involves the TC shaft mounted hydraulic turbo pump. The most natural opportunity is during a tip-out situation, when the TC kinetic energy is converted to hydraulic energy by braking the TC via engaging the hydraulic turbo pump. This is free energy. Alternately energy recovery is also possible during firing mode by actively managing the speed of the TC by braking via the pump and over-speeding via the VGT vane, such that the desired TC speed is maintained. This form of energy recovery is not free and has an FE penalty.

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Firing mode energy recovery without fuel penalty is only limited to very high engine loads as discussed in [8]. The second method uses a vehicle driveline mounted pump. The driveline pump recovers energy from the vehicle driveline during vehicle brake events. This is similar to the regeneration mode of the hydraulic hybrid vehicle [13, 14, 15]. However, unlike the hydraulic hybrid vehicle, which must launch the full vehicle, a much smaller hydraulic tank is needed for the RHAT system. The RHAT system nevertheless must have a dedicated hydraulic circuit that includes high and low pressure accumulators and associated fast acting valves. A schematic of the RHAT system is shown in Figure 3 and design details are included in the patent [1]. A brief description of the sequence of events is described. Whenever the vehicle or engine has ‘free’ energy (e.g. during vehicle or engine deceleration, exhaust braking, or steady state when the intake throttle is used for intake oxygen control, or when a wastegate is used, etc.), the driveline pump will be engaged to recover vehicle kinetic energy, while the hydraulic turbo-pump will recover energy from the TC shaft. The power collected by both the turbo-pump and the driveline pump and will pressurize the fluid, and at the same time slow down the TC to “synchronize" it with the decelerating engine to avoid "tip-out" surge. The pressurized fluid is routed through a check valve to a high-pressure hydraulic accumulator. During engine acceleration, the high-pressure fluid from the accumulator will be discharged to drive the hydraulic turbine, which will then accelerate the turbocharger. When the TC turbine wheel receives the external hydraulic energy, the VGT can be opened wider for improved turbine efficiency. Thus the enthalpy drop across the turbine will be reduced (from reduced exhaust manifold pressure). This decreases engine pumping loss and increases net engine power output although with a potential for reduced high-pressure EGR flow. This also has the effect that the turbine operates with a higher U/C ratio and therefore with increased turbine efficiency as was shown by Sun et.al in [16] through the reproduced (here) Figure 4. Higher enthalpy at the TC turbine outlet implies higher exhaust gas temperatures. Hence, the conversion efficiency of the aftertreatment system could potentially see some improvement. Additionally, with external energy input to the TC shaft, the turbine operates with a lower expansion ratio (i.e. at high turbine speed ratio, U/C), as shown in Figure 4. Hence, the turbine does not count on a small nozzle opening in order to collect sufficient exhaust energy to drive the compressor. Therefore, due to the lower expansion ratio, wider open nozzle, and higher turbine speed, the turbine can operate more efficiently (Figure 4). Both the high U/C and relatively less throttled nozzle openings may potentially make the turbine 30-50% more efficient than the turbine of the conventional VGT. The implication here is that RHAT (and other assisted TC’s) can convert exhaust gas energy into mechanical energy more efficiently, thus further improving the engine transient response and fuel economy; the improvement in transient response is partly from external hydraulic energy, and partly from improved turbine and compressor efficiency. During very aggressive tip-out maneuvers, the hydraulic loading on the

turbo shaft (through the turbo pump) will slow down the TC to avoid tip-out surge while recovering the aerodynamic and kinetic energy from the turbocharger.

Figure 3. SYSTEM LAYOUT OF DIESEL ENGINE WITH HYDRAULIC

ASSISTED AND REGENERATIVE TURBOCHARGER (ABOVE), INTEGRATED SYSTEM IN TURBO CENTER HOUSING

Figure 4. WITH ASSISTED TURBOCHARGER, THE TURBOCHARGER

CAN BE REGULATED TO ITS HIGHER EFFICIENCY OPERATION RANGE.

Managing the hydraulic pump and hydraulic turbine in this manner provides a means to "synchronize" the turbocharger with the engine operating conditions and the boost demand while ensuring that the compressor and turbine are working in a narrow but more efficient. Thus the compressor and the exhaust turbine may be designed for higher efficiency without sacrificing operating range.

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A brief discussion of the electrically assisted system The main advantage of RHAT, compared to the electrically

assisted turbocharger system, is power density. Although the regenerative electric assisted turbocharger (REAT) is very attractive, it has the following concerns for medium and heavy-duty automotive diesel applications:

1. As shown in Table 1, most of the current electric assisted motors have the power output in the range of 1.5-10 kW. The desired power requirement to assist the acceleration of large turbochargers may be more than 10kW, depending on turbocharger size. This high assisted power requirement is a challenge for vehicles with 12 volts electric power supply system.

Table 1. A SURVEY FOR CURRENT ELECTRIC MOTOR/ GENERATOR ON TC SHAFT

Reference Max speed

[kRPM]

Max power

[kW]

Volts

[V]

Ibaraki [18] 120 3 72

Pfister, P. D [19] 200 2 65

Takata [20] 220 2 72

Terdich [21] 120 3.5(motor)

5.4(generator) 650

Noguchi [22] 150 1.5 12

Gerada [23] 75 10 200

Winward [12] 180 5 -

2. The power capacity needed to recover exhaust energy

during deceleration and braking/motoring should be in the range of 15-40 kW, since the turbo would be operating at high speed with high kinetic energy when the excessive exhaust energy is available to be harvested. It is challenging for an electric motor of this power to be packaged and integrated into an automotive turbocharger center housing without a dramatic increase in inertia and mechanical stress when operating at high speed. This means that current production-ready 2kW electric motor supported by 12 volts infrastructure will not effectively recover exhaust energy when it is abundant.

3. For the 2 kW REATs that are available today, they typically have a substantial increase in rotational inertia over conventional turbochargers [7] , i.e. during acceleration, more energy will be used to rotate the TC shaft itself.

4. A permanent magnetic electric motor is more efficient and compact than an induction motor, but the performance may deteriorate over time under high temperature; the material strength of the permanent magnet may limit its application to low operation speed, which is incompatible to smaller turbochargers.

The design target of the RHAT system will be 50% “round trip” efficiency, which may be slightly lower than a state-of-the-art regenerative electric-assisted turbocharger. But the advantages like lower inertia, cost, smaller packaging space, and potential better durability make the RHAT an attractive alternative option, especially for medium and heavy-duty turbocharged diesel applications.

In this study, a 1-D simulation approach is used to investigate the benefits and design trade-offs for regenerative hydraulic assisted turbochargers. The paper is organized into three major parts:

1. Engine steady state operation with assisted and regenerative capability

2. Transient response improvement with hydraulic assisted turbocharger

3. RHAT design trade-off investigation through driving cycle study.

The main contribution of this paper is to examine the feasibility of regenerative hydraulic assisted turbocharger system through a systems level approach.

VEHICLE LEVEL INTEGRATED 1-D SIMULATION Simulation platform and control algorithm Vehicle level simulation is utilized to investigate the fuel benefits and design trade-offs for hydraulically assisted turbochargers. The simulation platform, as shown in Figure 5, includes a vehicle model that includes the driveline and a RHAT equipped. Several controllers are used in the simulation and they include a production version engine control with a RHAT controller to replace the conventional VGT based air path controller, a 6-speed transmission controller, and a torque converter controller. Due to the inclusion of the RHAT controller several additional adjustments had to be made.

1. Lower exhaust manifold pressure during assist mode coupled with fast intake manifold pressure rise placed constraints on high pressure EGR flow. Hence EGR deficit had to be managed through the inclusion of a low pressure EGR loop.

2. RHAT control is designed to track the target boost pressure with a fixed gain Proportional-Integral (PI) controller.

3. The driveline pump is controlled to recover vehicle brake energy within the constraint of maximum hydraulic tank pressure.

Simulation platform based on a 10000 Lbs vehicle is investigated with the newly proposed hydraulic systems. Details can be found in Table 2.

Table 2. VEHICLE INFORMATION

Vehicle Weight 10000 Lbs. Engine V8, 6.7L, Diesel

Turbocharger Variable geometry turbocharger

Transmission 6 speed Turbocharger VGT

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Page 5: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

Figure 5. SIMULATION PLATFORM AND CONTROL STRUCTURE

The base transmission shift strategy, boost pressure set-point, fuel injection set-point and EGR fraction set-point are duplicated for the base engine. As mentioned earlier, RHAT is integrated into the air handling control, which is used to regulate the boost pressure and EGR rate set-points, as shown in Figure 6.

Figure 6. ENGINE AIR PATH CONTROLLER OVERVIEW

The vehicle simulation tracks the target vehicle speed. A driver model is used to influence the gas and brake pedal positions through a feedback on vehicle speed. The target engine brake power is based on a calibrated map with inputs of engine speed and gas pedal position. The fuel demand is based on current engine speed and demanded engine torque. Fuel is controlled by both feedback and feedforward loops to achieve target torque output. VGT is feedback controlled to track the required boost pressure in conjunction with the assist. The transmission control is based on a shift schedule map with inputs of engine speed and gas pedal position. Both HP-EGR and LP-EGR are used to achieve target EGR mass flow rate. Both VGT and EGR valve controllers are map based with gain scheduled Proportional-Integral-Derivative (PID) controllers. Detailed engine and turbocharger model validation results can be found in [24].The performance of the vehicle system simulator is shown through the tracking of the desired vehicle velocity trajectory in Figure 7.

Figure 7. VEHICLE MODEL VALIDATION OVER THE FTP_75 DRIVE

CYCLE

Hydraulic components

Preliminary meanline analyses of the hydraulic turbine and turbo pump were conducted. Regular engine oil at 100 deg C was assumed in the meanline analysis. From a friction loss perspective, engine oil may not be the optimal choice, due to its high viscosity. However, the problems associated with sealing different fluids at different pressures, for isolation purposes, makes engine oil the best choice at this point. The preliminary predicted hydraulic turbine map (Figure 8) shows that for turbine power above 10 kW, a substantial operating area of the hydraulic turbine can have an efficiency above 70%. When managed carefully between flow rate and pressure ratio, hydraulic turbine efficiency can be above 60% (Figure 8). Figure 9 shows the preliminary meanline analysis of the performance of the turbo-pump, indicating that the turbo-pump can achieve peak efficiencies in the range of 70%, as long as the pressure in the hydraulic energy storage is managed to match the oil flow rate at the operating TC speed. The performance map for the driveline pump is shown in Figure 10. These maps of a hydraulic turbine, turbo pump and driveline pump out of meanline analyses (Figure 8, Figure 9, Figure 10) were integrated with GT-Power vehicle model. The oil temperature was maintained at 100 deg C throughout the test (FTP-75) cycle. Some other assumptions relating to the RHAT system as used in the simulations include:

1. Hydraulic power rating is 25 kW for the RHAT hydraulic turbine in assisted mode, 25 kW for the RHAT hydraulic turbo pump in energy recovery mode, and 25 kW for the driveline pump for recovery of vehicle kinetic energy during vehicle brake.

2. Hydraulic fluid pressures are 100-150 bar in the high-pressure accumulator tank, and 10-20 bar in the low-pressure accumulator tank; the pressure range for low-pressure tank is set to avoid cavitation in the hydraulic turbo-pump or turbine.

200 400 600 800 1000 12000

20

40

60

80

100

Time [s]

Veh

icle

spe

ed

[km

/h]

vehicle model validation

Dyno test

GT simulation

200 400 600 800 1000 12001

2

3

4

5

6

Time [s]

Tra

nsm

issi

on

ge

ar

nu

mb

er

Dyno test

GT simulation

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Page 6: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

3. Hydraulic tank volume was varied for design trade-off investigation.

4. Hydraulic valve actuator response time is assumed less than 50 ms.

5. With assisted power on the shaft, the TC turbine will operate at lower expansion ratios and higher speed region, compared to operation without assisted power. Thus assisted and regenerative turbocharger needs further data extrapolation out of current turbine flow bench tested map. A further experimental test should be used for wide range turbine operation investigation. In this study, map extrapolations are based on 1-D simulation map fitting and extrapolation methods [25].

A comparable study between hydraulic components and an in-house electric components for assisted turbocharger is illustrated in Figure 11. Hydraulic components (turbine and turbo pump) have much higher power density than an electric motor or generator. It clearly shows that the hydraulic turbine has higher torque than the electric motor below 70K rpm, where the assist is needed for the TC shaft for engine light load tip-ins. For the low-speed region, the assisted torque from the hydraulic turbine is three times of that from an electric generator. The hydraulic turbo pump has much higher torque above 50K rpm, where high regeneration load is needed for energy recovery from the TC shaft. These results clearly show the power density of regenerative hydraulic assisted turbocharger (RHAT) is greater than that of regenerative electric assisted turbocharger (REAT) for both assist mode and regeneration mode.

Figure 8. HYDRAULIC TURBINE EFFICIENCY

Figure 9. HYDRAULIC TURBO PUMP EFFICIENCY

Figure 10. DRIVELINE PUMP EFFICIENCY

Figure 11. TORQUE COMPARISON BETWEEN ELECTRIC MOTOR AND HYDRAULIC COMPONENTS

2 4 6 8 10 12 14

x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Speed [rpm]

Norm

alize

d t

orq

ue

Hydraulic pump torque

Hydraulic turbine torque

Electric motor/generator torque

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SIMULATION RESULTS AND DISCUSSION Engine alone steady state investigation for feedforward calibration

For a given engine speed and fixed fuel injection quantity, with assisted power, exhaust pressure tends to decrease. Thus pumping mean effective pressure (PMEP) and engine brake specific fuel consumption (BSFC) will decrease. However, this improvement can only be maximized with optimal VGT vane position. This means that the VGT must be controlled in coordination with TC assist functions.

With loading power on the TC shaft on the other hand, e.g. during engine throttling mode, TC speed intends to decrease. Lower TC speed will reduce compressor power. Thus compressor mass flow rate and intake manifold pressure decrease. Turbine mass flow rate decreases with lower TC speed. Hence, exhaust pressure intends to increase. Higher exhaust pressure and lower intake manifold pressure will lead to high pumping loss and lower engine efficiency. For different engine operations, thermal energy available to the TC turbine is dependent on engine operation point as well as VGT position. Thus regenerative power on TC shaft will be defined by engine load as well as VGT vane position.

The need for co-ordination between the RHAT system and the conventional VGT-EGR system was already discussed, but is reproduced here along with energy balance equations for the TC shaft Newtonian dynamics.

Assist mode: hydraulic energy (Prhat) is added to the TC shaft for acceleration. The TC is now able accelerate faster than the nominal system that must rely only on the exhaust turbine power( Pturbine.)

Based on the turbocharger power balance equation [26, 27]:

𝐽�̇�𝜔 = 𝑃𝑡𝑢𝑟𝑏𝑖𝑛𝑒 − 𝑃𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑜𝑟 + 𝑃𝑟ℎ𝑎𝑡 𝐽�̇�𝜔 = (�̇�𝑡)2𝜔𝐷

𝑅𝑇𝑖𝑛

𝑃𝑖𝑛tan(𝑓1(𝑢𝑉𝐺𝑇)) − (�̇�𝑐)3𝑓 (

�̇�𝑐

𝜔) + 𝑃𝑟ℎ𝑎𝑡 (1)

where, 𝑓1(𝑢𝑉𝐺𝑇) is vane angle; 𝑢𝑉𝐺𝑇is vane position control input. For a steady state with assisted power, 𝐽�̇�𝜔 = 0, the power balance equation becomes:

(�̇�𝑡)2𝜔𝐷𝑅𝑇𝑖𝑛

𝑃𝑖𝑛tan(𝑓1(𝑢𝑉𝐺𝑇)) + P𝑟ℎ𝑎𝑡

+ = (�̇�𝑐)3𝑓(𝜔

�̇�𝑐) (2)

The maximum hydraulic assist power P𝑟ℎ𝑎𝑡_𝑚𝑎𝑥+ can be defined

by:

P𝑟ℎ𝑎𝑡+ = (�̇�𝑐)3𝑓 (

𝜔

�̇�𝑐) − (�̇�𝑡)2𝜔𝐷

𝑅𝑇𝑖𝑛

𝑃𝑖𝑛tan(𝑓1(𝑢𝑉𝐺𝑇)) (3)

This maximum hydraulic assist power necessary is defined by the boost demand the VGT position and hence the exhaust turbine capability. The maximum assist is, however, constrained by the compressor surge margin.

Regeneration mode: hydraulic energy (P𝑟ℎ𝑎𝑡− ) is removed from

the TC shaft through deceleration. The TC is now able to decelerate faster than the nominal system that must rely only on the vane position for such deceleration.

TC shaft energy regeneration, the power balance equation is:

(�̇�𝑡)2𝜔𝐷𝑅𝑇𝑖𝑛

𝑃𝑖𝑛tan(𝑓1(𝑉𝐺𝑇)) = (�̇�𝑐)3𝑓(

𝜔

�̇�𝑐) + P𝑟ℎ𝑎𝑡

− (4)

The maximum hydraulic regenerative power P𝑟ℎ𝑎𝑡_𝑚𝑎𝑥− is

defined by:

P𝑟ℎ𝑎𝑡_𝑚𝑎𝑥− = (�̇�𝑡)2𝜔𝐷

𝑅𝑇𝑖𝑛

𝑃𝑖𝑛tan(𝑓1(𝑉𝐺𝑇)) − (�̇�𝑐)3𝑓(

𝜔

�̇�𝑐) (5)

The maximum hydraulic regeneration power available from the TC shaft depends on the TC speed during the regeneration event. The TC speed, in turn, depends on the exhaust energy availability as a function of the engine load and the VGT vane position. For a given desired compressor power, there is an optimal VGT vane position for best system efficiency of the unassisted VGT system. With assisted power on the TC shaft, the power needed from the exhaust turbine is reduced. Hence in order to maintain exhaust flow and manage p3 (thereby manage pumping loss), the VGT vane position should be opened wider. The aim of this study is to study these interactions and show the impact of assist and regen functions on engine performance through steady state simulations. The simulation is carried out at 2000 RPM with 60 mg/stroke fuel injection rate. Both EGR (LP and HP) valves are fully closed for simplicity. The VGT vane position varies from 0.15 to 1 (0.15 is fully close and 1 is fully open), and the TC shaft hydraulic loading power varies from -7kW to 7kW (positive is regenerative and negative is assisted power). Results show that the engine BSFC varies with different VGT vane positions, and different assist and regenerative powers applied the TC shaft, as illustrated in Figure 12. For a typical system without assisted power or regenerative power, the best turbine efficiency is achieved at a VGT position of 0.6. In order to have optimal (minimum) BSFC with assist power on the TC shaft at light engine speed and load, the VGT should be opened wider for maximum turbine efficiency. For example, the best VGT position for 7kW assisted power is 0.8. On the contrary in regenerative mode at high engine speed and load, the VGT vanes should be closed to achieve best turbine efficiency. Thus in order to achieve optimal BSFC, both the VGT vane position and the hydraulic assist or regenerative power applied to the TC shaft should be managed optimally as shown in Figure 12.

The regenerative loading capacity depends on the VGT vane position for a given engine operating condition. For the case shown in Figure 12, wide open VGT vane position decreases energy availability to the turbine, leading to lower TC shaft loading (regenerative) capacity. For example, for a VGT vane position of 0.8, the maximum TC shaft steady state regenerative loading power is 2kW. Higher regenerations will lead to TC stall. This means that the steady state turbine power

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Page 8: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

cannot provide the compressor power demand with regeneration power on TC shaft.

Figure 12.ENGINEBSFC UNDER ASSISTED AND REGENERATIVE

MODE

During the assist and regeneration modes, the exhaust turbine power available and the compressor power desired will both vary as a function of the external power applied to the TC shaft. As a case study, we discuss the case for VGT fixed at 0.6. For baseline case at steady state, the compressor power is balanced with the turbine power, as shown in Figure 13. For the assisted cases both the exhaust turbine and compressor powers increase primarily from increased TC speed and increased mass flow rates.

During the regen mode, both the compressor and TC turbine power drop because of lower TC speed and lower mass flow rate. The loss of engine power is mainly due to increased pumping loss thus lower engine efficiency.

Figure 13. COMPRESSOR AND TURBINE POWER DISTRIBUTION UNDER ASSIST AND REGENERATION

Engine air-fuel ratio (AFR) also increases with higher assist power levels as shown in Figure 14. This allows reduced

smoke emission during transient tip-in’s. This also indicates that more fuel can be injected into the cylinder if the same AFR was to be maintained thus achieving higher engine brake power. This would be beneficial for engine performance for both steady state and transient operations. In Figure 16, we compare the baseline case with the assisted case with a 19kW assist while maintaining the same AFR. It is clear that the peak engine power can be significantly improved at light load with assist. Low-speed engine torque increases almost 4 times for the assisted case, relative to the nominal unassisted case. These results are based on the assumption that energy in the hydraulic tank is always available. That is the energy balance constraint was not enforced.

Figure 14. AIR-FUEL RATIO UNDER ASSIST AND REGENERATION

As mentioned previously, TC shaft loading capacity also changes with engine load point and the VGT vane position. As shown in Figure 15, a case at multiple engine load points was studied with different assisted and regenerative power on the TC shaft, as well as with varying VGT vane positions. It is concluded that, for light engine load, it might not be possible to recover any energy during steady state condition, such as engine speed of 500 RPM. At an engine speed of 1500 RPM, the ability to regenerate increases, due to higher engine exhaust energy. For engine speeds in the range 1500 RPM to 2500 RPM, regeneration will lead to high fuel consumption from increased engine pumping losses and reducing engine efficiency. For high engine speed operation (3500 RPM), the regeneration capacity is much wider than at lower engine speed operations (<3500 RPM). Further, TC shaft energy can be recovered with minimum fuel penalty with high engine load region, which agrees with the finding in the literature [8, 12]. It can also be concluded that engine fuel consumption can be reduced with power regeneration at certain conditions, depending on engine load condition. Steady state optimization for each engine operating points can serve as feedforward calibration for RHAT-VGT control. Note that these investigations did not consider the impact on the ability to achieve desired EGR flow rates.

11.4

2 kW regen 1 kW regen baseline 1 kW assist 2 kW assist 5 kW assist

Kw

Power distribution between turbine and compressor

Turbine power Compressor power

23

2 kW regen 1 kW regen baseline 1 kW assist 2 kW assist 5 kW assistA

FR

Air-Fuel Ratio

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Page 9: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

Figure 15. LOADING POWER ON TC SHAFT AND IMPACT ON ENGINE BSFC (+: REGENERATION,-: ASSIST)

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Page 10: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

Figure 16. MAX ENGINE TORQUE WITH 19 KW ASSIST WITH THE SAME AFR

Hence it can be concluded that the hydraulically assisted and regenerative turbocharger introduces additional control degrees of freedom, which increases the dimension of the optimization space. With assist power the engine BSFC will be improved. The proposed high power hydraulic turbine on the TC shaft can significantly improve engine light load torque response. TC shaft regenerative capacity depends on engine speed and load condition. Hence a coordinated control for VGT and RHAT should be implemented for optimal engine BSFC.

Transient response of the RHAT system It is clear that the main function of the assisted TC system

is to improve its transient response. An investigation into the impact of the assist power level on the transient response was performed. For these test cases the engine speed is fixed while the desired torque is increased. The control target is to track the engine torque demand. Fuel injection is feedback controlled to meet the target torque, with a smoke limit (AFR> 16) constraint enforced. Three single-input-single-output (SISO) controllers are used to regulate boost pressure and EGR flow rate for the nominal, unassisted system. The VGT is used to regulate the target boost pressure and the HP and LP EGR valves are used to track the target EGR mass flow rate. The hydraulic turbine is feedforward controlled with varying assist power levels. A total of 8 different hydraulic assist power levels varying from 0 kW to 14 kW were studied. The 0 kW case is the baseline case, where only the VGT vane position is used to regulate boost pressure.

a) Engine transient performance improvement

As shown in Figure 17, all the simulation cases start with 25 kW engine brake power and the same engine speed. Assist power is introduced at various levels for a duration of 0.7 secs. The transient response, with respect to power, is improved for all assist levels. With 14 kW assist power the engine power increased to 140 kW, an increase of about 50kW over the baseline case. As expected the un-assisted case has a significant torque deficit.

Figure 17.ENGINE BRAKE POWER UNDER DIFFERENT ASSISTED POWER

As illustrated by Figure 17, the total time duration for engine acceleration from 28kW to 90kW is 0.3 second with 14 kW assisted power, compared to 0.55 second without assisted power. The acceleration time is reduced by 45% from the baseline case. Although engine fuel injection rate increased with different level of assisted power, total fuel consumption for 14 kW is reduced significantly to achieving the same target engine power (90 kW), thanks to the assisted power, compared to the baseline case with no assisted power.

The impact of assist on transient AFR is shown in Figure 18. As discussed earlier the increased fresh air flow with assisted turbocharging allows higher AFR’s. It is clear from Figure 18 that for the nominal case the AFR achieved remains below the smoke limit (AFR=17) for over 50% of the test duration. Note that smoke limit is used for rich fuel injection. The engine without assisted power has 50% of time operating below AFR=17 during this transient tip-in event. With increased assisted power, the operating time when AFR below 17 decreases. With 5.5 kW assist, the AFR is higher than AFR ≥ 17 over the entire simulation duration. With less time operating below the smoke limit, less soot emission is

500 1000 1500 2000 2500 3000 35000

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ine b

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wer

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Engine speed [rpm]

Eng

ine b

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to

rque

Without assist

With 19 kW assist on TC shaft

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Page 11: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

expected with assisted power. Note that the fluctuation for AFR is due to different sampling rates for GT Power and Simulink.

Figure 18. AIR-FUEL RATIO WITH VARYING ASSIST POWER LEVELS

b) Turbocharger transient performance improvement

Turbocharger response can be significantly improved with different levels of assisted power, as shown in Figure 19. With higher assisted power, the turbocharger speed increases faster. The acceleration time from 20K rpm to 40K rpm can be reduced by 75% compared to the non-assisted case. With higher TC shaft speed, both the compressor and turbine operating efficiencies are improved, as shown in Figure 19. It also shows the hydraulic turbine power and hydraulic tank energy profile for the different levels of assisted power. Different hydraulic power is based on different hydraulic valve positions, the pressure difference across the turbine, as well as the TC shaft speed. Although hydraulic valve position is fixed for each case, the hydraulic power changes with tank pressure and TC shaft speed, with respect to designed hydraulic turbine operation conditions.

During these transient operations, the hydraulic turbine could be controlled through the hydraulic valve position to achieve the desired target value, such as demand turbo speed or output power. The duration that the power assisted mode can sustain itself, to a great degree, depends on how much energy can be recovered through driveline pump and turbo pump without fuel penalty, and how large the storage tank is. In order to evaluate the fuel benefit level for proposed hydraulic assisted turbocharger, a customer driving cycle simulation is investigated in the next section.

Figure 19. TURBOCHARGER SPEED TRANSIENT PROFILE WITH DIFFERENT HYDRAULIC ASSISTED POWER

Design trade-offs for FE benefit through customer driving cycle simulation

In the previous section, the benefit of hydraulic assist operation is discussed. However, in order to achieve sustainable power assisted operation, sufficient hydraulic energy needs to be recovered from both the vehicle and exhaust gas. The total recovered energy depends on the driveline pump sizing as well as hydraulic tank sizing for a given vehicle and engine, for a fixed driving cycle. The hydraulic tank size would be limited by physical packaging space for design considerations.

In this study, vehicle simulations for FTP 75 driving cycle were investigated to understand the design trade-offs for fuel benefit, hydraulic components sizing, and turbine sizing. In traditional VGT control, in order to achieve higher turbine power to drive the compressor at engine light load, the VGT vane position is set to a small opening to increase pre-turbine

10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.316

17

18

19

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24

Time (s)

AF

R

Air Fuel Ratio

0kW

2kW

4kW

5.5kW

7kW

9kW

12kW

14kW

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4

6

8x 10

4

Time (s)

RP

M

Turbocharger Speed

0kW

2kW

4kW

5.5kW

7kW

9kW

12kW

14kW

10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.40.2

0.3

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0.6

0.7

Time (s)

Eff

icie

ncy

Turbine Efficiency

0kW

2kW

4kW

5.5kW

7kW

9kW

12kW

14kW

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0

5

10

15

Time (s)P

ow

er

[kW

]

Hydraulic turbine power

0kW

2kW

4kW

5.5kW

7kW

9kW

12kW

14kW

10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.40.97

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1

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1.02

Time (s)

Norm

alize

d t

ank p

ressure

High pressure hydraulic tank pressure

0kW

2kW

4kW

5.5kW

7kW

9kW

12kW

14kW

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Page 12: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

pressure. In this case, pumping loss increases due to higher engine exhaust pressure, which leads to a fuel economy penalty. With assisted power on the TC shaft, the VGT position can avoid operating at a small opening, which increases turbocharger efficiency and reduces engine pumping loss. But the capability of assisted power depends on energy availability in the hydraulic tank.

The baseline in this study is still the traditional VGT for boost control with both high-pressure exhaust gas recirculation (HP-EGR) and lower pressure exhaust gas recirculation (LP-EGR). For RHAT-VGT turbocharger, the VGT is fixed at positions of 0.5, 0.65, 0.75 and 1 (position 1 being fully open). RHAT is used to control boost pressure to track target pressure. There are two advantages for simulating with fixed VGT positions: first, fuel saving can be easily evaluated without sophisticated control system dealing with interaction with VGT and RHAT control. Second, the result would be used to examine the feasibility of fixed geometry turbocharger (FGT) with hydraulic assisted and regenerative turbocharger, compared to a VGT turbocharger. Increased inertia by the hydraulic turbocharger is considered in this simulation.

Based on the distribution of VGT positions on the FTP driving cycle for traditional VGT control, vane positions 0.5-0.6 and 0.2-0.3 are the most frequent opening positions during the driving cycle. Vane position 0.2-0.3 is used to build up turbine back pressure to drive compressor at very light engine load. This results in high pumping loss and low turbine efficiency. Vane position 0.5-0.6 is the most efficient turbine operation range from design prospect. When the vane position is fixed at large openings, extra assisted power and regenerative power is needed to meet engine boost target and torque demand. Note that, in this simulation study, the performance map for FGT turbine is inherited from the VGT turbocharger with fixed vane position for comparison. But in a practical case, FGT turbine efficiency would be higher without losses across turbine vane nozzles.

The simulation results are shown in Figure 21 and Figure

22. All the simulation cases meet the driver’s demand by achieving the same target vehicle speed. In order to achieve the same vehicle speed, the engine needs to be provided with sufficient fresh air for combustion process to produce the right amount of torque. Thus, different level of energy is needed for a hydraulic turbine with different fixed geometry turbine. The results show that system fuel benefit mainly depends on tank size for a given VGT size. The tank could be sized for largest energy drop during the driving cycle, which may be dictated

by the highway portion of the FTP cycle if supplemental hydraulic energy input to the TC is required. Thus, small VGT opening position results in small tank size since small VGT open position requires less supplemental hydraulic energy. Note that only VGT positions of 0.5 and 0.65 can achieve tank energy balance with current tank size and driveline pump size. In these two cases, the RHAT application with VGT position fixed at 0.5 results in very small FE saving while the case with VGT fixed at 0.65 has a significant fuel saving, respectively.

Figure 20. VGT POSITION DISTRIBUTION FOR TRADITIONAL VGT

CONTROL OVER FTP 75 CYCLE.

Figure 21. FUEL BENEFIT FOR DRIVING CYCLE WITH DIFFERENT

FGT TURBINE

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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/h]

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fixed VGT=0.5+RHAT+Driveline pump

fixed VGT=0.65+RHAT+Driveline pump

fixed VGT=0.75+RHAT+Driveline pump

fixed VGT=1+RHAT+Driveline pump

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alize

d M

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fixed VGT=0.5+RHAT+Driveline pump

fixed VGT=0.65+RHAT+Driveline pump

fixed VGT=0.75+RHAT+Driveline pump

fixed VGT=1+RHAT+Driveline pump

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fixed VGT=0.5+RHAT+Driveline pump

fixed VGT=0.65+RHAT+Driveline pump

fixed VGT=0.75+RHAT+Driveline pump

fixed VGT=1+RHAT+Driveline pump

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Page 13: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

Table 3. VEHICLE FUEL BENEFITS AND TANK ENERGY USAGE

Turbine size (VGT position) 0.5 0.65

Fuel Saving 0 + Tank energy end of cycle 100% 100%

Max tank energy drop 20% 38% State of charge balanced balanced

Figure 22. PUMPING LOSS REDUCTION WITH HYDRAULIC ASSISTED

POWER

Pumping loss reduction for a portion of FTP cycle is shown in Figure 22. Vane position is closed aggressively for high boost pressure demand during vehicle tip-in without assisted power, leading to high pumping loss. With different fixed vane position and assisted power, pumping losses are reduced while meeting the same boost target. This is one of the main reasons for fuel consumption reduction over the driving cycle when assisted power is used. But the level of fuel savings depends on how much hydraulic energy can be recovered during the whole driving cycle. Energy usage and recovery for the hydraulic turbine, TC shaft pump, and driveline pump are shown in Figure 23. It shows that in order to achieve higher fuel benefit, more hydraulic energy is needed. With wider turbine vane open position, there are less energy recovery opportunities for the hydraulic turbo pump on

the TC shaft. Total recovered energy from the hydraulic turbo pump on the TC shaft alone may not be enough to drive turbocharger to meet the same boost demand. Energy recovery mainly depends on the driveline pump. It is concluded that, energy recovery from hydraulic driveline pump itself would generate most RHAT system fuel benefit. Simulation results show that the fuel savings rate is insignificant without driveline energy recovery on the FTP cycle. Note that only turbine size 0.5 and turbine size 0.65 have balanced tank pressure over the cycle in this study.

Figure 23. ENERGY USAGE AND RECOVERY FOR HYDRAULIC COMPONENTS

Note that dual EGR loop is utilized in this system to meet demanded EGR mass flow rate. Results show that the total EGR mass fraction in the intake manifold is equivalent for all the VGT and FGT with RHAT cases. But, with hydraulic assisted power, more LP-EGR is needed to compensate insufficient HP-EGR, because the pre-turbine pressure is decreased with assisted power.

The engine system with RHAT needs to be optimally designed such that the system performance and fuel economy meet the design targets within constraints of hydraulic tank packaging space and cost. Hence, with given hydraulic turbine and hydraulic pump (turbo-pump and driveline pump), as well as engine and vehicle size, the design matrices for RHAT system would be TC turbine size and hydraulic tank size, as shown in Figure 24. Tank size is identified through largest tank energy drop during the drive cycle for four different cases. It clearly shows that in order to have higher fuel benefit, a larger hydraulic tank is needed to store more hydraulic fluid.

345 350 355 360 365 370 3750

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Pu

mpin

g p

ow

er

[kW

]

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VGT no RHAT

fixed VGT=0.5+RHAT

fixed VGT=0.65+RHAT

fixed VGT=0.75+RHAT

fixed VGT=1+RHAT

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Hydraulic TC pump recovered energy

Driveline pump recovered energy

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Page 14: Regenerative Hydraulic Assisted Turbocharger · assisted turbochargers are either electrically assisted or hydraulically assisted. In this study a regenerative hydraulically assisted

Figure 24. DESIGN SPACE FOR HYDRAULIC COMPONENTS WITH NORMALIZED TANK SIZE

CONCLUSIONS Combining a turbo-pump and driveline pump with the

hydraulic assisted turbocharger to recover the exhaust energy and vehicle brake energy to offset the fuel economy penalty as a result of hydraulic power input to the turbo shaft for turbocharger transient response improvement is investigated. Preliminary one-dimensional GT-Power analyses indicate that it is possible to potentially gain up to 4% fuel economy improvement with the RHAT system, compared with the base turbocharged diesel engine, over the FTP 75 transient cycle. This FE improvement does not include the other FE benefits that may be enabled by adopting the RHAT technology, such as engine downsizing, transmission optimization, etc.

The uncertainties in the numerical study include: dynamic responses and flow losses in the hydraulic actuation system and energy storage tank, especially during the warm-up period. These uncertainties will be addressed as the component level technologies are studied and refined.

Like many other innovative technologies, there are some key technical challenges that have yet to be addressed before this RHAT system can see wide application in turbocharged engines, these are:

Development of fast-response hydraulic valves and actuation systems with high-flow capacity and low-flow losses.

The reduction of parasitic or windage loss when the hydraulic wheels are not engaged.

Management of energy storage tank pressure so the turbo pump can work in high-efficiency areas at different flow rates or turbo speeds.

Optimal designs of the hydraulic turbine and turbo pump that can deliver high efficiencies over wide operation range, regarding pressure and turbo speed, without adding excessive thrust loading and excitation on the turbo rotor system.

NOMENCLATURE RHAT Regenerative Hydraulic Assisted Turbocharger REAT Regenerative Electric Assisted Turbocharger EGR Exhaust Gas Recirculation AFR Air Fuel Ratio DPF Diesel Particulate Filter U/C Turbine Speed Ratio VGT Variable Geometry Turbine FE Fuel Economy FG Feed gas BSFC Brake Specific Fuel Consumption PMEP Pumping Mean Effective Pressure P𝑟ℎ𝑎𝑡

+ Assisted Power P𝑟ℎ𝑎𝑡

− Regenerative Power �̇�𝑐 Compressor Mass Flow Rate �̇�𝑡 Turbine Mass Flow Rate 𝜔 Shaft Speed �̇� Shaft Acceleration 𝐷 Turbine Geometry Parameter 𝑃𝑖𝑛 Turbine Inlet Pressure 𝑇𝑖𝑛 Turbine Inlet Temperature R Gas Constant 𝐽 Inertia REFERENCES 1. Sun, H.H., Hanna, D.R., Levin, M., Curtis, E.W. and

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