A new control-oriented transient model of variable geometry turbocharger

Accepted Manuscript A New Control-Oriented Transient Model of Variable Geometry Turbocharger

Irfan Bahiuddin, Saiful Amri Mazlan, Fitrian Imaduddin, Ubaidillah PII:

S0360-5442(17)30306-7

DOI:

10.1016/j.energy.2017.02.123

Reference:

EGY 10416

To appear in:

Energy

Received Date:

23 January 2016

Revised Date:

07 February 2017

Accepted Date:

21 February 2017

Please cite this article as: Irfan Bahiuddin, Saiful Amri Mazlan, Fitrian Imaduddin, Ubaidillah, A New Control-Oriented Transient Model of Variable Geometry Turbocharger, Energy (2017), doi: 10.1016 /j.energy.2017.02.123

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ACCEPTED MANUSCRIPT Highlights  A control-oriented model of a variable geometry turbocharger turbine is proposed  Isentropic and actual power behaviour estimations on turbocharger turbine  A simulation tool for developing active control systems of turbocharger turbines

ACCEPTED MANUSCRIPT

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A New Control-Oriented Transient Model of Variable Geometry Turbocharger

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Irfan Bahiuddin1, Saiful Amri Mazlan1*, Fitrian Imaduddin1, Ubaidillah1,2

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Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Jalan Sultan Yahya Petra, 54100 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur, Malaysia 2 Mechanical Engineering Department, Faculty of Engineering, Universitas Sebelas Maret, Jl. Ir. Sutami 36 A, Kentingan, Surakarta, 57126, Central Java, Indonesia *)Corresponding author: [email protected] 1

ABSTRACT

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The flow input of a variable geometry turbocharger turbine is highly unsteady due to

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rapid and periodic pressure dynamics in engine combustion chambers. Several VGT control

14

methods have been developed to recover more energy from the highly pulsating exhaust gas

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flow. To develop a control system for the highly pulsating flow condition, an accurate and valid

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unsteady model is required. This study focuses on the derivation of governing the unsteady

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control-oriented model (COM) for a turbine of an actively controlled turbocharger (ACT). The

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COM has the capability to predict the turbocharger behaviour regarding the instantaneous

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turbine actual and isentropic powers in different effective throat areas. The COM is a modified

20

version of a conventional mean value model (MVM) with an additional feature to calculate the

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turbine angular velocity and torque for determining the actual power. The simulation results

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were further compared with experimental data in two general scenarios. The first scenario was

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simulations on fixed geometry positions. The second simulation scenario considered the nozzle

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movement after receiving a signal from the controller in different cases. The comparison

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between simulation and experimental results showed similarities in the recovered power

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behaviour.

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Keywords: variable geometry turbocharger, turbine, control-oriented model, engine exhaust gas, pulsated flow, extracted power

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1

Introduction

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Stringent emission regulations have driven the enhancement of an efficient combustion

31

engine. Despite a huge investment in the development of greener technologies, internal

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combustion engine remains as the most preferred technology through engine downsizing [1,2].

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The approach is enabled through the implementation of exhaust recovery system,

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turbocharging, and supercharging technologies [3,4]. Such technologies have successfully

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reduced CO2 emission in diesel engines, improved fuel economy, and decreased NOx

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emissions [5,6].

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Among the evolving turbocharger technologies, a variable geometry turbocharger

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(VGT) has been recognised as the most profitable system. Its easiness in utilising exhaust gas

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in different speeds and loads makes the engine operability applicable in a wide range of

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operating conditions and transient conditions [7,8]. Furthermore, it has reached vast markets in

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the last decade, owing to its capability in improving acceleration performance compared with

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the fixed geometry turbocharger (FGT) [9]. In another development, a two-stage turbocharger

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has been implemented together with a VGT, as flexibility is an essential characteristic when

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switching from a smaller turbocharger to a bigger turbocharger or vice versa [10]. A VGT was

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also proposed to be deployed together with exhaust gas recirculation (EGR) when applying a

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control strategy in an engine exhaust gas recovery system [11,12].

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Recently, the VGT had evolved into a more advanced system when Pesiridis and

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Martinez-Botas [13] introduced a new controlling concept through the active adaptation of the

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exhaust gas pulsating behaviour. The VGT system implemented with such a control method is

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called actively controlled turbocharger (ACT). This control technique can optimise energy

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extraction in the VGT turbine. The testing results presented by Pesiridis and Martinez-Botas

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[14] showed that, in average, the ACT has successfully recovered more energy. Later, a

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naturally oscillated actuator driven by the exhaust pressure known as the passively controlled

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turbocharger (PCT) was developed based on the ACT operation [7,15] to reduce the

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instrumentation complexity. Aghaali and Angstrom [16] suggested that the advantages of the

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active control application could be investigated for turbo-compounding applications in future

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studies.

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Although the ACT application has shown improvement in the performance, the

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involvement of control system introduced a new problem on how to obtain an optimised control

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parameter in the rapidly changing operating condition of an engine. The optimum

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determination of a nozzle movement is important as it highly depends on the amplitude of

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pressure, temperature, mass flow, and pulsating period of the exhaust gas [17]. The current

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approach is unable to get the optimum value as it was conducted through a feed forward control

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by averaging the measuring emission properties tested in a test rig [18]. The development of a

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proper optimum ACT control requires a model that can represent the dynamic and unsteady

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characteristics of the energy recovery in various operating conditions of the system. Most

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importantly, the model should be applicable in the controller design process or, in other terms,

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‘control-oriented’ condition.

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The so-called control-oriented model (COM) replicates the input-output relation of

70

systems with low computational effort and necessary precision in both steady and transient

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conditions [19,20]. The orientation of the model should be clearly defined, as the common

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terms of a model in a VGT system are normally associated with the flow model obtained from

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the computational fluid dynamics (CFD). While the CFD-based model is accurate and provides

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details of the flow profile and distribution across the spatial domain, the computational

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requirement of the CFD and the level of information obtained are not suitable for control

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development purposes [21]. The control design process requires only a simplified model that

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contains relevant properties with reasonable accuracy for determining the control parameters

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[8,22].

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Some studies have shown a good use of COMs for simulating the transient dynamics

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of the turbocharged engine systems for control purposes. For instance, an EGR transient

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modelling proposed by Asad et al. [23] can be used as a tool to make a qualitative estimation

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of the EGR characteristic or behaviour with less financial effort. However, the model still

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shows a considerable error. An accuracy of a COM for the transient condition can also be

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enhanced flexibly by other advanced control methods. For instance, the accuracy of an engine

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transient dynamic model was improved by the application of the artificial neural network [24].

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Despite many works used to analyse transient conditions using COMs, none of the models have

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been applied for the turbocharger energy analysis in a transient or unsteady condition,

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especially in the ACT development.

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The main objective of this paper is to develop a COM for the VGT turbine that can be

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used to optimise the ACT controller by predicting the recovered power of exhaust gas. The

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model is derived, especially in terms of the isentropic power and actual power, under pulsating

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flow condition, as both variables are known to be important indicators of the turbine

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performance [25,26]. The isentropic power is related to the power absorption by the hydraulic

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ACCEPTED MANUSCRIPT 94

and thermal system of the turbine, while the actual power represents the power received by the

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turbine that will be regenerated by the compressor. However, the existing mean value models

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(MVMs) are unable to differentiate between the actual and isentropic power. Therefore, a

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gyrator analogy of the VGT turbine is proposed for the actual power calculation. As the gyrator

98

analogy is taken from a bond graph concept, a bond graph representation of the VGT turbine

99

system is also presented. The other systems are modelled by applying MVMs in the bond graph

100

elements.

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This paper presents an improved COM with the aim of enhancing the understanding of

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turbine performance behaviour under pulsating flow conditions, especially for active control

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development purposes. In this paper, the discussion is divided into three sections: the

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explanation of VGT mechanism and conventional COM of a turbine power, followed by a

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detailed derivation of the proposed governing equation for a turbine performance, and then a

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discussion focuses on the validation of the proposed COM in two kinds of movements. The

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first movement is fixed in each geometry position, and the second is conducted by changing

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the geometry positions or throttle area conditions. The moving inlet geometry operations are

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applied based on the ACT concepts proposed by Pesiridis and Martinez-Botas [14] as the most

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recent potential control method for pulsated flow.

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2

VGT Turbine Model

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The VGT works by altering the turbine inlet geometry as a function of speeds and loads

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[7]. The usual mechanism is by varying the nozzle throat area. In this paper, the model

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development is based on the VGT mechanism consisting of pivoting nozzles connected by a

115

ring as shown in Fig. 1. Symbols α and β of the figure are angular displacements of the vane

116

and the ring, respectively. While the ring slid about α radian, the vanes moved along β radian.

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The closer area of the inlet turbine was achieved on the higher β. The tuneable-shape of the

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inlet turbine was applied for different exhaust gas or engine operating conditions such as a

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closer position for a lower engine speed and vice versa.

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Based on the main purpose, the mechanism was modelled for energy analysis,

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especially for the ACT by using COM or MVM. MVM is a powerful tool to analyse or replicate

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a general system dynamic for a control system. The broad application of the model is for

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ACCEPTED MANUSCRIPT 123

identification and control purposes as applied in the previous works [10,27–29]. The common

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MVM for turbine power analysis is specified as isentropic power (𝑃𝑖𝑠𝑒𝑛) [19]. MVM is a

125

function of three variables, which are the turbine mass flow (𝑚𝑡), engine temperature (𝑇𝑒𝑛𝑔),

126

and the expansion ratio of pressure of turbine outlet (𝑝𝑜,𝑡) and inlet (𝑝𝑖,𝑡) as in Equation (1).

127

The symbol 𝑐𝑝 is the specific heat capacities for constant pressure and γ is the heat capacity

128

ratio.

[ [] ]

𝑃𝑖𝑠𝑒𝑛 = 𝑚𝑡𝑐𝑝𝑇𝑒𝑛𝑔 1 ‒

129 130

𝑝𝑜,𝑡

𝛾‒1 𝛾

𝑝𝑖,𝑡

The actual power (𝑃𝑎𝑐𝑡) model is stated in Equation (2) that is a product of torque (𝒯𝑇) and angular speed (𝜔) [3].

𝑃𝑎𝑐𝑡 = 𝒯𝑇𝜔

131 132

(1)

(2)

The turbine torque stated in Equation (3) is obtained by assuming that the power in Equations (1) and (2) is the same [29].

[ [] ]

𝑝𝑜,𝑡 1 𝒯𝑇 = 𝑚𝑡𝑐𝑝𝑇𝑒𝑛𝑔 1 ‒ 𝜔 𝑝𝑖,𝑡

𝛾‒1 𝛾

(3)

133

Consequently, the difference between actual and isentropic power dynamics is

134

eliminated. In the actual testing data, both power types have different values and patterns. The

135

actual power received by the turbine is not the same as the isentropic power defined in Equation

136

(1) [3]. Therefore, in the practical calculation, an efficiency constant is included in Equation

137

(1). Although some evaluation methods for predicting efficiency have been proposed [30], the

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conventional COMs are still unable to differentiate the dynamics between the actual and

139

isentropic power.

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ACCEPTED MANUSCRIPT 140

3

Proposed Model of VGT

141

Power behaviour modelling has a significant role in the analysis of the capability of the

142

energy recovery in a turbine control system, especially while designing the turbocharger for an

143

unsteady flow condition. However, the limitation of predecessor COMs [19,24,29] might result

144

in the inability to predict the actual power received by the turbine. Therefore, this section

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attempts to synthesise a COM for investigating the actual power behaviour.

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Isentropic and actual powers [7] are the two measurement variables proposed to

147

examine the turbocharger capability to recover power from the exhaust gas. Both power

148

variables have different behaviours due to separate measurement points [31]. The isentropic

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power is calculated by measuring mass flow, temperature, and pressure of the exhaust gas in

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the volute of turbine inlet. Meanwhile, the actual power calculation uses the measurement of

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torque and angular velocity of the turbine shaft as in Fig. 2.

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Pesiridis and Martinez-Botas [14] found that when the turbine torque increases, the

153

mass flow (𝑚) also rises. In other words, torque can be represented as a function of mass flow

154

as expressed in Equation (4).

𝜏 = 𝑓(𝑚)

(4)

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The function is similar to the relation of voltage to the angular velocity of a gyrator in

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a motor DC. The similarity can be discovered by using the bond graph concept proposed by

157

Henry Paynter in 1959 [32]. Some previous works [33–35] also proposed the same application

158

for turbines. The first step is by classifying the units to either of two variables called effort and

159

flow. The product of each pair of variables is power. For instance, in a mechanical system, the

160

product of a force as effort variable and velocity as a flow variable is power. The second step

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is by formulating the relation between variables in the component and comparing to the known

162

phenomena.

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The units in the motor DC and turbine system are classified as follows: voltage, torque,

164

and pressure are considered as effort and electrical current, angular velocity, and flow rate are

165

considered as flow. All pair unit products are power. However, for the calculation of an exhaust 6

ACCEPTED MANUSCRIPT 166

gas system, the flow rate is not a common flow variable. Instead, mass flow is a better flow

167

variable representation for a convenient calculation, considering the common governing

168

equations for power calculation [32]. The classification is summarised as in Table 1.

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The known formulation of the gyrator system is used to identify the turbine system

170

properties. The gyrator representation on a bond graph is shown in Fig. 3. The gyrator

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formulation is as in Equation (5) or, in general variables, as in (6).

𝒯𝑜𝑟𝑞𝑢𝑒𝑜𝑢𝑡𝑝𝑢𝑡 (𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑐𝑢𝑟𝑒𝑛𝑡)𝑖𝑛𝑝𝑢𝑡

=

𝑒𝑓𝑓𝑜𝑟𝑡𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑙𝑜𝑤𝑖𝑛𝑝𝑢𝑡

172 173

𝑉𝑜𝑙𝑡𝑎𝑔𝑒𝑖𝑛𝑝𝑢𝑡 (𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦)𝑜𝑢𝑡𝑝𝑢𝑡

=

𝑒𝑓𝑓𝑜𝑟𝑡𝑖𝑛𝑝𝑢𝑡 𝑓𝑙𝑜𝑤𝑜𝑢𝑡𝑝𝑢𝑡

= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡

(5)

(6)

If the relation between the mass flow and torque is assumed as linear, then Equation (4) may be expressed as Equation (7). The 𝑘𝑔𝑦1 is a constant to convert mass flow to torque.

𝒯𝑇 = 𝑘𝑔𝑦1𝑚𝑡

174

= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡

(7)

Equation (7) has the same form as Equation (8), which is derived from Equation (6).

𝑒𝑓𝑓𝑜𝑟𝑡𝑜𝑢𝑡𝑝𝑢𝑡 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ∗ 𝑓𝑙𝑜𝑤𝑖𝑛𝑝𝑢𝑡

(8)

175

Finally, Equations (7) and (8) show a similarity between the gyrator and turbine system.

176

Then, the equation that represents the relationship between the angular velocity 𝜔 and

177

pressure of the turbine inlet (𝑝𝑒,𝑡) is expressed in Equation (9) where 𝑘𝑔𝑦2 is a constant to

178

convert from the angular velocity to pressure drop at the turbine.

𝑝e,t = 𝑘gy2ω

7

(9)

ACCEPTED MANUSCRIPT 179 180

By substituting Equations (7) and (9) into Equation (2), the actual power can also be expressed as a function of mass flow and pressure as stated in Equation (10).

𝑃act = 𝑝e,t 𝑚t 𝑘gy1/𝑘gy2

181 182

(10)

If the turbine outlet is assumed as atmospheric pressure, the 𝑝𝑒,𝑡 can be considered as the pressure drop in the turbine.

183

As the turbine pressure drops (𝑝𝑒,𝑡), the measured pressure (𝑝𝑒,𝑚) can be used to obtain

184

the turbine mass flow as expressed in Equation (11) [26]. The notation 𝑐𝑑,𝑉𝐺𝑇 is a discharge

185

coefficient, 𝐴𝑉𝐺𝑇 is the effective flow area, 𝑥𝑉𝐺𝑇 is the normalised opening and closing of VGT,

186

and 𝑅 is the specific gas constant.

mt = cd,VGTAVGT(xVGT)

187

pe,m RTeng

( )

Ψ

pe,m

(11)

pe,t

Ψ is defined in Equation (12).

( )

Ψ

𝑝𝑒,𝑚 𝑝𝑒,𝑡

=

{

1 2

( )

2 𝛾 𝛾+1

𝛾+1 2(𝛾 ‒ 1)

𝑓𝑜𝑟

(( ) ( ) )

2𝛾 𝑝𝑒,𝑚 𝛾 + 1 𝑝𝑒,𝑡

2 𝛾

‒

𝑝𝑒,𝑚

𝛾+1 𝛾

𝑝𝑒,𝑡

𝑓𝑜𝑟

𝑝𝑒,𝑚 𝑝𝑒,𝑡 𝑝𝑒,𝑚 𝑝𝑒,𝑡

( )

2 ≤ 𝛾+1

𝛾 (𝛾 ‒ 1)

( )

2 > 𝛾+1

𝛾 𝛾‒1

(12)

188

Fig. 4 shows the complete bond graph representation of the turbine system in the test

189

rig as shown at the Imperial College [3]. The figure only shows the hydraulic system as the

190

temperature is assumed as a constant unit. The system consists of a modulated capacitor (MC),

191

modulated resistor (MRv), and a gyrator (Gy). MC is a piping that connects the exhaust

192

manifold and turbine with the detail equation in the Appendix. Finally, given the focus of this

193

paper, Gy is the VGT turbine that is connected only to the dynamometer. The turbine is

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ACCEPTED MANUSCRIPT 194

considered as an inertia element by calculating as stated in the Appendix. A causality diagram

195

can be derived from the bond graph diagram, which will be explained in the next subsection.

196

The term ‘modulated’ is used when a constant of a certain element is affected by another

197

flow or effort. For instance, the constant of the MRV is a function of engine temperature and

198

normalised opening and closing of VGT (𝑥𝑉𝐺𝑇). Meanwhile, the gyrator element can be a

199

modulated element if the temperature or angular velocity or other units can affect the gyrator

200

constant. However, temperature is assumed as constant in the study and the experiment was

201

conducted with a small change in the turbocharger angular velocity. Therefore, the modulated

202

term is not applied in the gyrator element. In other words, the turbine is treated as a fixed

203

gyrator.

204

Furthermore, the experimental results of the mass flow and torque measurement [14]

205

are used to determine the value of the conversion constant of Equation (10), the 𝑘𝑔𝑦1.

206

Meanwhile, the conversion constant of Equation (9), 𝑘𝑔𝑦2, can be approximated from the

207

experiment result of the angular speed and pressure inlet measurement by assuming that the

208

pressure drop in vane is not significant.

209

4

Model Validation Results and Discussion

210

The simulation was carried out in two general modes. First, vanes were set at a fixed

211

position to obtain the model behaviour of the manifold and turbine system. Second, the exhaust

212

gas was determined when the vanes moved. The model validation process was conducted by

213

comparing the simulation results with the measurement data from previous experiments

214

[14,31].

215

4.1 Simulation Scope

216

The parameters for power calculation in the simulation were referred to the real testing

217

facilities. For instance, the isentropic power analysis was determined based on an average mass

218

flow according to the measurement instrument. The geometrical sizes of the real device were

219

also determined based on the data from the apparatus, which is 3,300 mm2 of the throttle area

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ACCEPTED MANUSCRIPT 220

[36,37]. In addition, the angle of the nozzle has a range from 40o to 80o, which are equivalent

221

to 100% and 6% of the normalised area, respectively. The uncertain parameter values such as

222

the resistance effect of the shaft (𝑅𝑇), conversion constant of mass flow to torque (𝑘𝑔𝑦1),

223

volume of manifold (𝑉𝑚), and range of vanes opening and closing were determined by

224

approximation. Furthermore, the turbine angular velocity was set at 48,000 rpm or 80% of the

225

maximum turbocharger operating range as the normal operation of the turbocharger. The mass

226

flow in the simulation was also determined as an average value similar to that in the experiment.

227

The simulation scope can be represented in a causality diagram of the proposed model

228

along with other submodels as shown in Fig. 5. The subsystems were built from the piping

229

system, vanes of VGT, turbocharger inertia, resistive effects of the shaft, and gyrator element.

230

The gyrator model describes that the mass flow (𝑚𝑡) gives effects to the inertia dynamics

231

directly in the form of torque (𝒯𝑡). The figure also shows the angular velocity (𝜔) as a result of

232

inertia dynamics results in the turbine pressure drop (𝑝𝑒,𝑡). The pressure drop causes an effect

233

on the dissipation energy within the VGT vanes and the pressure fluctuation in the piping

234

system.

235

Referring to Fig. 5, the input to the model is the mass flow in a pulsating form produced

236

by the internal combustion engine cylinder. The instantaneous mass flow form (Fig. 6) is

237

similar to a cycle of pressure produced by the engine cylinder, which refers to [7]. The

238

amplitude and bias of the model input were tuned differently for varied frequencies. The

239

Appendix presents the detail equations of the exhaust manifold model.

240

The mass flow and pressure of the exhaust pipe have pulsating behaviour with a

241

frequency (𝑓) as a function of engine speed (𝑁𝑒𝑛𝑔) as described in Equation (13) [7]. 𝐶 is the

242

cylinder number in a group of an engine manifold. 𝐺 is the manifold group number and 𝑛 is the

243

engine stroke number.

𝑓=

2𝑁𝑒𝑛𝑔𝐶𝐺 60𝑛

10

(13)

ACCEPTED MANUSCRIPT 244

In the simulation, the engine was defined as a one manifold group with six-cylinder and

245

four-stroke diesel engine. Meanwhile, the turbocharger was categorised as a twin entry

246

turbocharger. The specification was based on the test rig used for the experiments [7]. The

247

engine’s operating conditions were simulated at engine speeds of 800 rpm and 1,600 rpm or

248

equivalent to 40 Hz and 60 Hz, respectively [3,7].

249

The uncertainties in the measurements can be included as considerations when

250

analysing the comparisons between simulation and experimental results. The uncertainties in

251

the fluctuating torque measurement are represented as root sum square (RSS), which is ± 0.170

252

Nm. The cycle-averaged RSS uncertainties in the angular speed, as the second variable, which

253

affected the actual power measurement, is 0.009 RPS. Meanwhile, variables affecting

254

isentropic energy measurement have average uncertainty of ± 346 Pa, ± 97 Pa, ± 3 K, and ±

255

4.8 kg/s for instantaneous inlet pressure, outlet pressure, temperature, and fluctuated mass flow,

256

respectively [7,37,38].

257

4.2 Fixed Vane Position

258

The first simulation compared the behaviour of the turbine model and the real system

259

in different angles. The variations of the vane positions are 40o, 50o, 70o, 65o, and 60o. The

260

model was evaluated for the actual, isentropic, and cycle-averaged power. In addition, the term

261

‘peak’ region represents the region around the highest value in each data. The term ‘trough’

262

represents the region around the lowest value in each data. The lines with the script ‘peak’ and

263

‘trough’ describe the region period for peak and trough regions, respectively.

264

The actual power simulation result showed different behaviours compared with the

265

isentropic power as in Fig. 7(a) for 40 Hz and Fig. 8(a) for 60 Hz. Meanwhile, the changes

266

from an entire open throat area (40o) to a closer area (70o) made the peak higher. By contrast,

267

the actual power of the trough region became greater in the narrow normalised throttle area.

268

The power as a function of mass flow might have caused the phenomenon. The reason is that

269

the mass flow has the same dynamics as the actual power as in Fig. 9. In addition, although the

270

angular velocity is also one of the important units to calculate the power, it will not make a

271

significant change in such a short time due to the relatively high turbocharger moment of

272

inertia.

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ACCEPTED MANUSCRIPT 273

Refering to the actual power simulation cases, the experimental data of the power at

274

70o vane setting had a contrast difference compared with 50o and 40o vane setting as shown in

275

Fig. 7(b) and Fig. 8(b). Other similarities of the power at 70o were its lowest position at the

276

peak area and the most top position in the trough area. On the peak region, the generated power

277

on 50o and 40o showed a little difference if observed in detail. While the 40 Hz power of 50o

278

and 40o had a superimposed position, the green line of 50o at 60 Hz had reached the highest

279

peak. However, it still maintained the middle position for the most time of one cycle. In other

280

words, the more open position of vanes led to a higher actual power peak with a lower trough.

281

The isentropic power of 40 Hz is first presented in Fig. 10. The upper picture shows the

282

simulation results of the isentropic power for an entirely open (40o), a nearly open (50o), and

283

nearly closed nozzle setting (70o). The peak region was found at 55 kW for the smallest

284

normalised throat area and still the highest at trough region. The lowest value along the cycle

285

of isentropic power remained at the widest area or 40o nozzle angle. The isentropic power had

286

similar dynamics with the inlet pressure as in simulation results in Fig. 12. Therefore, it shows

287

that the inlet pressure dominantly affected the isentropic power dynamics. Meanwhile, the

288

described isentropic power simulation at 40 Hz almost had the same pattern at 60 Hz frequency

289

as shown in Fig. 11(a).

290

The comparison of the simulation results was referred to the previous experimental

291

studies conducted by Rajoo and Martinez-Botas for 40o and 70o vane positions [31] and

292

Szymko for 50o [50] in the same test rig. The testing results, as shown in Fig. 10(b) for 40 Hz

293

and Fig. 11(b) for 60 Hz, had the highest isentropic power at 70o. In the trough region, the

294

isentropic power of the smallest throttle area setting also remained the highest among the others

295

positions in both the frequencies. The second largest peak was on 50o with a difference of

296

around 5 kW higher compared with 40o vane position. For the overall period, the isentropic

297

power of 50o was slightly greater than the power of 40o. In addition, the findings were similar

298

in terms of the isentropic power for each nozzle position setting order at two frequencies.

299

The model can track the changes in the peak and trough of isentropic and actual power

300

as in the experiment when the setting of the vane varies from a smaller position to a higher

301

position. Therefore, the changing behaviour or pattern can be observed by using the simulation.

302

However, the model is incapable of replicating the actual dynamics of fluctuating and filling

12

ACCEPTED MANUSCRIPT 303

and emptying phenomena. This might be because the hysteresis feature is not available in the

304

model and simplification of the details of pressure losses and spatial components. The

305

negligence of the temperature change is another reason for the inaccuracy. It also sometimes

306

results in its incapability for differentiating between the small change in the normalised throttle

307

area. In sum, the model can be used as an estimation tool despite its inaccuracy.

308

Moreover, the actual and isentropic power along the vane positions were investigated

309

by using the cycle-averaged power concept. Fig. 13 shows the cycle-averaged value of the

310

isentropic (a) and actual power (b) for the experiment and simulations. The model used the

311

same parameters and mass flow input for 60 Hz and 40 Hz frequency flow, whereas the

312

experiment used data from previous studies [31] to determine the efficiency based on the

313

measured power. The graphic shows that the cycle’s averaged actual power of simulation and

314

the experiment had a slight difference in various vane angle settings and frequencies. On the

315

other hand, the cycle-averaged isentropic power of the experimental result of 40 Hz was more

316

fluctuating than the model, especially around the 60o and 65o vane positions. The reason is the

317

choked nozzle that made the power to drop. Generally, for the isentropic power cases, the trends

318

of all testing data tend to increase from 40o to 70o. Therefore, the pattern was quite similar to

319

the simulation results of the cycle-averaged isentropic power with different values. The

320

differences might be caused by the choking phenomena in the narrower normalised area, which

321

cannot be well simulated. In conclusion, the behaviour of the model in terms of the cycle-

322

averaged power has a good similarity with a note that the accuracy is enough for the actual

323

power but lacking for the isentropic power. Therefore, the model has a potential for

324

investigating the exhaust gas behaviour by considering the dynamics in the piping connecting

325

the exhaust manifold and turbine of the VGT under an unsteady flow condition. In addition,

326

the uncertainty measurement might affect the power accuracy. Although the uncertainty can be

327

negligible in terms of cycle-averaged power, this measurement uncertainty can be one of the

328

causes of the fluctuation in every millisecond.

329

4.3 Moving Vane Case

330

The second simulation mode was conducted in three case movements. The first

331

movement was motion as in Fig. 14(a) and the second as in Fig. 14(b). The two cases were

332

similar to the ACT movement proposed by Pesiridis [14,17]. The last case or case 3 was a fixed

13

ACCEPTED MANUSCRIPT 333

position at 60o vane setting as a comparison to the mentioned cases. Moreover, the evaluation

334

scope was a comparison between the model and the experiment in terms of the isentropic power

335

and expansion ratio between the turbine inlet and outlet pressure.

336

The experimental and simulation data of the expansion ratio showed that case 2 had the

337

highest peak as in Fig. 15, whereas in trough region, case 1 was above all other lines and case

338

3 was at the bottom. Although it showed similarities, different phenomena occurred in the peak

339

region. The second highest peak in the experimental data was case 1, which became the lowest

340

in Fig. 15(a). The simulation results were also incapable of showing the hysteresis and little

341

fluctuation dynamics along the cycle. The fluctuation could also be caused by the fluid

342

movement and/or the propagated measurement uncertainties of the power variables, such as

343

torque and speed velocity.

344

The isentropic power dynamics in Fig. 16 described many similarities between the

345

testing data and model response. For instance, in the peak region, the highest isentropic power

346

was in case 2 and the isentropic power of case 1 became slightly larger than that of case 3 at

347

the peak region. The trough area also showed that the green line of case 2 dropped lower until

348

crossing with a red line of case 1 but not overlapping with the blue line. Moreover, the blue

349

line of case 3 maintained its lowest position almost in a period.

350

The cycle-averaged values of the isentropic power have been calculated. The details of

351

the simulations results are as follows: case 2 for 15.6 kPa is the highest, followed by case 1 for

352

15.1 kPa, and case 3 for 11.2 kPa is the lowest. The test data pattern shows a similarity with

353

the simulation, with the sequence from higher to lower as the following: case 2 for 14.1 kPa,

354

case 1 for 12.6 kPa, and case 3 for 12.04 kPa.

355

Pesiridis did not conduct the actual power measurement. Therefore, actual power

356

comparisons were conducted based on the Srithar Rajoo experimental setting [7], which were

357

conducted in the same test rig. Two sets of vane movements called case 4 and 5 were input into

358

the model (as shown in Fig. 17). The simulation results showed the same pattern as in the

359

experimental results when switching from case 4 to case 5 as depicted in Fig. 18. In terms of

360

cycle-averaged actual power, both cases in simulation data almost had the same amount on

361

20.42 kPa, which is about 3 kPa higher than the testing data.

14

ACCEPTED MANUSCRIPT 362

The model nozzle area was varied about 80%, 100% and 120% of the original to

363

observe the sensitivity of the model. The simulation results are shown in Fig. 19 in terms of

364

inlet pressure and actual and isentropic power by applying case 1 on moving vane cases. The

365

wider area can lead to a lower inlet pressure that can affect the produced isentropic power. On

366

the other hand, the actual power produced the same pattern as in the fix vane simulation. While

367

comparing the experimental results range, the isentropic power and inlet pressure range overlap

368

with 100% mostly and between the 80% and 120% nozzle area. This simulation also showed

369

that the uncertainty in the measurement of the nozzle area might affect the computation results.

370

In summary, the model has shown its capability as a tool to estimate the actual power

371

and isentropic pattern qualitatively when vanes were moved or fixed. Therefore, the model has

372

a potential for investigating the exhaust gas behaviour when applying the ACT algorithm or

373

PCT. The hybrid system behaviour using PCT and ACT can also be observed by using the

374

model.

375

However, the model still lacks replication of the detailed phenomena of the real

376

experiment as the spatial component of the turbocharger was neglected in the model derivation

377

process. Apart from the measurement uncertainty that might affect the model characterisation

378

when comparing with the experimental results, further development is required to facilitate the

379

fluctuation and hysteresis phenomenon. Furthermore, the investigation of the temperature

380

effect on the conversion factor of gyrator analogy will be a valuable piece of information. In

381

addition, this study was limited only to a test rig to focus only on the VGT and turbine.

382

Therefore, the possible improvement of model scope includes, but is not limited to,

383

model investigation on a wider operating condition and developing the equation, which can

384

cover other phenomena. After the improvement is finished, the model can be used to observe

385

the VGT stability and performance when ACT is applied to an integrated engine.

386

5

Conclusion

387

A new governing equation, of a new control-oriented VGT turbine model and its

388

simulations, has been presented. The novelty of this study compared with previous MVMs in

389

the literature is that it predicts the instantaneous response of turbine actual power by offering 15

ACCEPTED MANUSCRIPT 390

an alternative calculation of torque and angular velocity. The isentropic can also be calculated

391

and simulated with actual power. The simulations were conducted under unsteady flow

392

conditions for different fixed and moved vane positions at different engine speeds. The power

393

variables were also simulated in terms of averaged power in various nozzle positions. The

394

simulation result comparison with the previous experiment data showed the model’s capability

395

for estimating the exhaust gas behaviour qualitatively. In addition, based on the moved nozzles

396

cases, the model has the capability to predict the turbine performance qualitatively when an

397

active control method is applied to a VGT. Thus, the model has a potential to be a tool to design

398

an integrated control system based on the active control concept under an unsteady flow

399

condition. However, the model lacks accuracy, as it was unable to simulate the hysteresis,

400

choked nozzle effect, and fluctuating event. Another idea can still be proposed further to

401

improve the accuracy of the model by adding more features in the governing equation.

402

Therefore, instead of being a final product, this study is considered as a starting point for

403

developing a control-oriented unsteady model for predicting the VGT performance.

404

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522 523

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Appendix A

525

Model of Exhaust Manifold/Piping Connecting Exhaust Manifold and Turbine

526

The input of the exhaust manifold is a total engine gas mass flow (𝑚𝑒𝑛𝑔) decreased by

527

the EGR gas mass flow (𝑚𝑒𝑔𝑟). An amount of the emission gas was accumulated in the

528

manifold (𝑚𝑒,𝑚) and other flows to the turbine (𝑚𝑡) as stated in the mathematical expression

529

as in mass balance Equation (A.1).

𝑑𝑚𝑒,𝑚 𝑑𝑡

530 531

= (𝑚𝑒𝑛𝑔 ‒ 𝑚𝑒𝑔𝑟) ‒ 𝑚𝑡

(A.1)

The derivation of accumulated flow is from the ideal gas law and, then, it is substituted in Equation (A.1) getting,

𝑑𝑝𝑒,𝑚

𝑅𝑇𝑒𝑛𝑔 = ((𝑚𝑒𝑛𝑔 ‒ 𝑚𝑒𝑔𝑟) ‒ 𝑚𝑡) 𝑑𝑡 𝑉𝑒,𝑚

(A.2)

532 533

Model of Effective Area of VGT

534

Normalised opening and closing of VGT (xVGT) have a minimum value as 0 and

535

maximum value as 1. The assumption of the relationship between the normalised angle and the

536

normalised turbine inlet area (𝐴𝑉𝐺𝑇) is linear as stated in Equation (A.3). The effective area has

537

the minimum value of 𝑏 and a gradient of 𝑎.

𝐴𝑉𝐺𝑇 = 𝑎𝑥𝑉𝐺𝑇(𝑡) + 𝑏

(A.3)

538 539

540 541

Inertial Component A mathematical expression for an inertial component Equation (A.4) is derived from the second law of Newton from the mechanical rotation.

20

ACCEPTED MANUSCRIPT

𝑑𝜔 𝒯𝑡 ‒ 𝒯𝑅 = 𝐽 𝑑𝑡

542

(A.4)

where 𝐽 is the moment of inertia.

543

In a real system, the sum of shaft torques consists of the compressor, friction and turbine

544

torque. For this paper purpose, since the validation process only includes the turbine, the

545

dynamic only considers a shaft resistance torque (𝒯𝑅), which is assumed to have linear

546

relationship with a resistance constant (𝒯𝑅≅𝜔𝑅𝑇).

547

21

ACCEPTED MANUSCRIPT FIGURES

548

α Ring

549 550 551

Vane/Nozzle

Fig. 1 Vanes and ring of VGT  Mass Flow  Temperature  Pressure Turbine

Exhaust Manifold

Cooler

 Angular Velocity  Torque

VGT

EGR Valve

Modelling Scope

Intake Manifold Cooler 552 553

Compressor

Fig. 2. Measurement points for calculating the recovered power

554

System 1

Effortinput flowinput

Gy

Effortoutput flowoutput

555 556

Fig. 3. Bond graph representation of a gyrator

22

System 2

ACCEPTED MANUSCRIPT 𝑝𝑒,𝑡

Gy2

𝑚̇𝑒𝑔𝑟

R

𝑝𝑒,𝑚

𝑚̇𝑒𝑛𝑔

Piping ManifoldTurbine

𝑇𝑒𝑛 𝑔

𝑚̇𝑡 𝑥𝑉𝐺𝑇

𝑝𝑜,𝑡

557 558

𝜔

𝒯𝑅

𝑇𝑒𝑛 𝑔

Vanes of VGT

𝒯𝑐 𝒯𝑡

Gy1

Turbocharger Inertia

Turbine

Fig. 4. Causality diagram of the proposed turbine and exhaust manifold model

559

RS 𝑥𝑉𝐺𝑇

𝑇𝑒𝑛 𝑔

MC 𝑝𝑒,𝑚 𝑚̇𝑡𝑒,𝑚

Sf:𝑚̇

𝑚̇𝑒𝑛𝑔 − 𝑚̇𝑒𝑔𝑟

0

MRv

𝑇𝑒𝑛 𝑔

𝒯𝑅 𝜔

J

𝑚̇𝑝𝑒𝑛𝑔 𝑚𝑒,𝑡 ̇ 𝑒𝑔𝑟 𝑚̇𝑡 𝑒,𝑚− 𝑝

𝑝𝑒,𝑚 𝑚̇𝑡

1

𝒯𝑡 𝜔

1

𝒯𝑡 +𝒯𝑅 𝜔

𝑝𝑒,𝑡 𝑚̇𝑡

Gy

560 561

Fig. 5 The bond graph representation of the hydraulic system of turbine of VGT system

562

Mass Flow (kg/s)

1 0.8 Amplitude

0.6 0.4 0.2 0 -0.2

563 564

Bias

One Pulse Cycle Fig. 6. The model input dynamic

23

ACCEPTED MANUSCRIPT

Actual Power (kW)

80

40Hz 48000rpm

60

70deg Sim 50deg Sim 40deg Sim

Trough

40 20 Peak 0 One Pulse Cycle

565 566

(a)

Actual Power (kW)

80

40Hz 48000rpm

60 40

70deg Exp 50deg Exp 40deg Exp

Trough

20 Peak 0 One Pulse Cycle

567 568

(b)

569

Fig. 7. Actual power dynamic at 40 Hz (a) simulation and (b) experiment [31,38]

570

24

ACCEPTED MANUSCRIPT

Actual Power (kW)

80 60Hz 48000rpm

60

70deg Sim 50deg Sim 40deg Sim

Trough

40 20 Peak 0 One Pulse Cycle

571 572

(a)

Actual Power (kW)

80

60Hz 48000rpm

60

70deg Exp 50deg Exp 40deg Exp

Trough

40 20 Peak 0 One Pulse Cycle

573 574 575

(b) Fig. 8. Actual power dynamic at 60 Hz (a) simulation and (b) experiment [31,38] 0.7

40Hz 48000rpm

Massflow (kg/s)

0.6 0.5 0.4 0.3 0.2 0.1 0 576 577

One Pulse Cycle

Fig. 9. Simulation of mass flow at turbine inlet at 40 Hz

25

70deg 50deg 40deg

ACCEPTED MANUSCRIPT 120

40Hz 48000rpm

Isentropic Power (kW)

100

70deg Sim 50deg Sim 40deg Sim

80 Trough

60 40 20

Peak

0 One Pulse Cycle 578 579

(a) 120

40Hz 48000rpm

Isentropic Power (kW)

100

70deg Exp 50deg Exp 40deg Exp

80 60

Trough

40 20

Peak

0 One Pulse Cycle 580 581 582

(b) Fig. 10. Isentropic power dynamic at 40 Hz (a) simulation and (b) experiment [31,38]

26

ACCEPTED MANUSCRIPT 120 60Hz 48000rpm

Isentropic Power (kW)

100

70deg Sim 50deg Sim 40deg Sim

80 Trough

60 40 20

Peak

0 One Pulse Cycle 583 584

(a) 120

60Hz 48000rpm

Isentropic Power (kW)

100 80

70deg Exp 50deg Exp 40deg Exp

Trough

60 40 20

Peak

0 One Pulse Cycle 585 586 587

(b) Fig. 11. Isentropic power dynamic at 60 Hz (a) simulation and (b) experiment [31,38] 500

40Hz 48000rpm

Pressure (kPa)

400 300 200 100 0 588 589

One Pulse Cycle

Fig. 12. Pressure at turbine inlet at 40 Hz

27

70deg Sim 50deg Sim 40deg Sim

ACCEPTED MANUSCRIPT

Cycle Averaged Power (kW)

50

40

60Hz Sim 40Hz Sim 60Hz Exp 40Hz Exp

30

20

10 40

45

590 591

50 55 60 Vanes Position (degree)

65

70

65

70

(a)

Cycle Averaged Power (kW)

40 35 30 25 20 15 10 40 592 593 594 595

60Hz Sim 40Hz Sim 60Hz Exp 40Hz Exp

45

50 55 60 Vanes Position (degree)

(b) Fig. 13. Cycled-averaged of (a) the isentropic power and (b) actual power from the simulation and experiment [31]

596

28

Normalized Throat Area

Normalized Thr

ACCEPTED MANUSCRIPT

10% 20% 10% xVGT

Normalized Throat Area

xACT,min

OneOne Pulse Cycle Pulse Cycle

597 598

Normalized Throat Throat Area Normalized Area

(a)

InletPressure Pressure Inlet

599 600 601

Normalized Throat Area

InletPressure Pressure Inlet

φ=240

o

Normalized Throat Area

10% 20% 20%

Vanes Position

10% 20% 20%

Vanes Position

10% 20% 10% xVGT xACT,min

φ=90o

OneOne Pulse Cycle Pulse Cycle

(b) Fig. 14. Phase settings different flow restrictor movement: (a) case 1, and (b) case 2 [14]

602

29

10%

ACCEPTED MANUSCRIPT

2.4

40Hz 48000rpm

Expansion Ratio

2.2

Case 1 ACT Sim Case 2 ACT Sim Case 3 ACT Sim

2 1.8

Trough

1.6 1.4 1.2

Peak One Pulse Cycle

603 604

(a) 2.5

Expansion Ratio

40Hz 48000rpm

Case 1 ACT Exp Case 2 ACT Exp Case 3 ACT Exp

2 Trough 1.5 Peak 1

605 606 607

One Pulse Cycle

(b) Fig. 15. Expansion ratio dynamic at 40 Hz (a) simulation and (b) experiment [13]

30

ACCEPTED MANUSCRIPT

Isentropic Power (kW)

50 40Hz 48000rpm

40

Case 1 ACT B Sim Case 2 ACT B Sim Case 3 ACT B Sim Trough

30 20 10

Peak

0

One Pulse Cycle

608

(a)

609

Isentropic Power (kW)

50 40Hz 48000rpm

40

Case 1 ACT Exp Case 2 ACT Exp Case 3 ACT Exp

30 Trough 20 10 Peak 0

610

One Pulse Cycle

611

(b)

612

Fig. 16. Isentropic power dynamic at 40 Hz (a) simulation and (b) experiment [13]

31

ACCEPTED MANUSCRIPT

Vane Movement (degree)

80 75 70 65 60 55 50

Case 4 ACT Case 5 ACT

45 613 614

One Pulse Cycle

Fig. 17. Vane Movement Measurement as Inputs to The Nozzle [7] 60 50

Actual Power (kW)

Case 4 ACT Sim Case 5 ACT Sim

40Hz 48000rpm

40 30

Trough

20 10

Peak

0 -10

One Pulse Cycle

615 616

(a) 60 50

Actual Power (kW)

Case 4 ACT Exp Case 5 ACT Exp

40Hz 48000rpm

40 30 Trough

20 10

Peak

0 -10 617 618 619

One Pulse Cycle

(b) Fig. 18. Actual power dynamic at 40 Hz (a) simulation and (b) experiment [7] 32

ACCEPTED MANUSCRIPT 3 40Hz 4800rpm

Expansion Ratio

2.5

80% nozzle area 100% nozzle area 120% nozzle area Experiment

2 1.5 1 0.5

620 621

One Pulse Cycle

(a) 60 40Hz 4800rpm

Actual Power (kW)

50

80% nozzle area 100% nozzle area 120% nozzle area

40 30 20 10

622 623

One Pulse Cycle

(b) 60

40Hz 48000rpm

Isentropic Power (kW)

50 40

80% nozzle area 100% nozzle area 120% nozzle area Experiment

30 20 10 0 -10

624 625 626 627

One Pulse Cycle

(c) Fig. 19. Simulation Results in Term of (a) Inlet Pressure, (b) Actual Power, and (c) Isentropic Power on Various Nozzle Area 33

ACCEPTED MANUSCRIPT 628

TABLES

629

Table 1 Summary of the effort and flow analogy System Exhaust gas Mechanical rotation Electrical system

Effort Pressure Torque Voltage

630

34

Flow Mass flow Angular velocity Current