Transient dynamic modeling and validation of an organic ...sonori/Publications/Applied Energy...

Applied Energy 205 (2017) 260279

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Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Transient dynamic modeling and validation of an organic Rankine cyclewaste heat recovery system for heavy duty diesel engine applications

http://dx.doi.org/10.1016/j.apenergy.2017.07.0380306-2619/ 2017 Elsevier Ltd. All rights reserved.

Corresponding author.E-mail address: [email protected] (B. Xu).

Bin Xu , Dhruvang Rathod, Shreyas Kulkarni, Adamu Yebi, Zoran Filipi, Simona Onori, Mark HoffmanClemson University, Department of Automotive Engineering, 4 Research Dr., Greenville, SC 29607, USA

h i g h l i g h t s

A parallel evaporator organic Rankinecycle Simulink model is presented.

Component models are calibrated andvalidated with experimental data.

Integration and quasi-transientvalidation of the component modelsare given.

Co-simulation of organic Rankinecycle and heavy-duty diesel enginemodels.

Integrated model capability isdemonstrated over a transient drivingcycle.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 21 April 2017Received in revised form 19 June 2017Accepted 15 July 2017

Keywords:Waste heat recoveryOrganic Rankine cycleDynamic finite volume heat exchangermodelingHeavy duty diesel engineTransient operation

a b s t r a c t

This paper presents a dynamic organic Rankine cycle waste heat recovery (ORC-WHR) Simulink modeland an engine model for heavy-duty diesel applications. The dynamic, physics-based ORC-WHR systemmodel includes parallel evaporators, flow control valves, a turbine expander, a reservoir, and pumps. Theevaporator model contains an enhanced pressure drop model, which calculates pressure drop for eachworking fluid phase via a linear relation to the axial location inside each phase. The ORC-WHR componentmodels parameters are identified over large range of steady state and transient experimental data, whichare collected from an ORC-WHR system on a 13 L heavy-duty diesel engine. The component models areintegrated into an entire system model and the boundary conditions, inputs and outputs for the individ-ual models are described. A GT-POWER engine model and its transient validation is presented. Thespeed and torque profiles of a long-haul, constant speed variable-load heavy-duty cycle are processedthrough the engine model to produce the exhaust and recirculated exhaust gas transient conditions rel-evant for the ORC model. The ORC-WHR system then simulated over these highly transient engine con-ditions. Overall, this paper provides detailed guidelines for ORC-WHR system modeling, modelcalibration, and component models integration.

2017 Elsevier Ltd. All rights reserved.

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Nomenclature

a ath boundary of the discretized evaporatorA area [m2]B;n Blasius factorscp heat capacity [J/kg K]C constant of two-phase multiplier correlationd diameter [m]f friction factorF force [N]G mass flux [kg/s m2]h enthalpy [J/kg]H height [m]_H enthalpy flowrate [J/s]I momentum [kg m/s]k kth time stepl; L length [m]m mass [kg]_m mass flow rate [kg/s]N revolution speed [rpm]O valve opening [%]p pressure [Pa]t time [s]T temperature [K]u velocity [m/s], internal energy [J/kg]U heat transfer coefficient [J/kg K]v dynamic viscosity [m2/s]V volume [m3]x vapor qualityX Martinelli parameterz space coordinate [m]a void fractionRe Reynolds numberr ratioPr Prandtl numberNu Nusselt numberc specific heat ratioq density [kg/m3]@ partial derivative operatorX intersection angle between horizontal surface and flow

direction [radius]n friction factorl dynamic viscosity [kg m/s]u two-phase multiplier

AbbreviationsORC organic Rankine cycleWHR waste heat recoveryHDD heavy duty dieselCSVL constant speed variable loadMBM moving boundary methodFVM finite volume method

BC boundary conditionTP tail pipeEGR exhaust gas recirculationHTC heat transfer coefficientturb turbineFRM fast running model

Subscripts and superscriptsf working fluidw walle exhaust gasv vaporl liquidi ith discretized cellin inlet/upstreamout outletp pressurefr frictiong gravitationexc exchangevap saturated vaporsat saturated liquidtp two phases single phaseh hydraulicU heat transfer coefficientis isentropicd discharge0 referencevlv valveflow flowsim simulationexp experimentalcw cooling watercva compressible volume acvb compressible volume bmix mixed working fluid after junctionHPP high pressure pumpFP feed pumpTP tail pipeEGR exhaust gas recirculationCond condensercross cross or sectional surfacepump pumpturb turbineTurbByp turbine bypass valveTurbIn turbine inlet valveTPEvapVlv TP evaporator distribution valveEGREvapVlv EGR evaporator distribution valve

B. Xu et al. / Applied Energy 205 (2017) 260279 261

1. Introduction

In the past decade, waste heat recovery (WHR) techniques havegained a large amount of attention in the automotive industry,especially in heavy-duty truck applications [13]. It is reportedthat up to 45% of fuel energy is wasted as heat in a heavy duty vehi-cle [2]. Given such a large percentage of waste heat, WHR technol-ogy represents an attractive option for improved fuel economy andreduced CO2 emission.

Popular WHR technologies include the thermoelectric genera-tors, the turbo-compounding, and the organic Rankine cycle(ORC). Thermoelectric generators utilize the temperature

difference between the exhaust gas and the thermoelectric mate-rial coolant to produce electricity [46]. These devices are compactand can be simply structured, but their thermal efficiency is lim-ited by the low figure of merit value of existing thermoelectricmaterials. Turbocompounding combines the turbocharger withan electric generator or a crankshaft coupling, respectively, repre-senting the naming convention of electrical versus mechanical tur-bocompounding [79]. Turbocompounding recovers a portion ofenthalpy energy from the exhaust gas. After expansion in the tur-bocharger, the remaining waste heat exists in the form of lowavailability thermal energy that cannot be efficiently recoveredby additional turbocompounding. Additionally, turbocompounding

262 B. Xu et al. / Applied Energy 205 (2017) 260279

generally does not utilize the waste heat in the exhaust gas recir-culation (EGR) circuit, which accounts for approximately one thirdof the total waste heat from a heavy duty diesel (HDD) engine,depending on the operating conditions [10]. ORC is the cycle uti-lized for traditional stationary power generation, except that theworking fluid is organic rather than water due to the heat sourcethermodynamic availability. Through intelligent placement of mul-tiple evaporators, an ORC system is able to extract thermal energyfrom tail pipe (TP) exhaust gas, EGR, charge air, and engine coolant[11,12]. Thus, ORC systems have the highest ceiling for total wasteheat recovery from a HDD engine.

There are several challenges regarding ORC-WHR system controldue to the high degree of coupling between the ORC-WHR systemand the engine through its heat exchangers. In real driving scenar-ios, the engine undergoes transient operation, producing highlydynamic exhaust gas mass flow rates and exhaust gas tempera-tures. This transient heat source power is delivered to ORC-WHRworking fluid with time delays that are determined by: (i) the vol-ume of working fluid in the heat exchanger, (ii) the heat exchangermaterial properties, (iii) thermal mass between the working fluidand exhaust gas, and (iv) the location of each evaporator.

ORC response time is influenced by working fluid volume andwall mass. The response time increases as working fluid volumeor evaporator wall mass increases. In a vehicle application, evapo-rator size is restricted, limiting working fluid volume and wallmass. Thus boiler response time in a vehicle application is muchshorter than traditional stationary ORC applications (generally, inthe range of 0100 s [13]). Thus, compared with stationary applica-tions, the transient nature of automotive systems introduces a sub-stantial control challenge.

Power generated by the ORC-WHR expander is utilized topower the electrical accessories (e.g. air conditioner, refrigerator,etc.) or to add mechanical crankshaft torque [10]. Either applica-tion method reduces the engine power demanded at any instant,lowering the fuel consumption and reducing the engine load. Asa result, less power is produced by ORC-WHR system at subse-quent time steps due to reduced engine load, and the vehiclepower management system needs to recalculate the engine powerrequest.

Besides the temporal delays and power management challengespresented by coupling an ORC-WHR system with an engine, the

Fig. 1. Schematic of ORC-WHR system. TP evaporato

ORC-WHR system itself is highly dynamic with multiple coupledactuators. Both the working fluid pump and the expander inlet/bypass valves affect the evaporation pressure. If any two of theseactuator positions are maintained and the remaining changes,the evaporation pressure will change. Generally, working fluidpump speed is utilized to control the working fluid vapor temper-ature at the evaporator outlet. As working fluid pump speedchanges, the evaporator pressure changes as well. Then, the tur-bine inlet/bypass valves have to respond appropriately to ade-quately control the evaporation pressure. For systems utilizingparallel evaporators and a single pump, the working fluid pumpis coupled with working fluid mass flow rate distribution actuators(Fig. 1) to control the working fluid vapor temperature. In thisinstance, the mass flow distribution actuators are utilized to con-trol the vapor temperature difference between the parallel evapo-rators, while the working fluid pump simultaneously controls themixed vapor temperature.

In order to capture the complex system dynamics mentionedabove, a high fidelity, physics-based ORC-WHR system model isrequired. The dynamic ORC-WHR system model fulfills three keyroles: (i) enabling derivation of a control-oriented model formodel-based control, which improves ORC-WHR control perfor-mance relative to a PID control baseline (feedforward [14], modelpredictive control [15,16], etc.). (ii) serving as a plant model toevaluate the control strategy in the simulation environment beforeexperimental implementation of the control software. Off-line sim-ulation validation of the control strategy saves both time and bud-get. (iii) being utilized in the off-line optimization to explore thepotential ORC-WHR fuel savings and emission reduction.

1.1. ORC system modeling methods

ORC-WHR system modeling can be classified into two groupsbased on the heat exchanger modeling method. One group utilizesthe moving boundary method (MBM), which lumps the workingfluid based on its phase, while the second group utilizes the finitevolume method (FVM) to spatially discretize the evaporator.

For a typical evaporation process, the working fluid has threephases: pure liquid, mixed liquid/vapor, and pure vapor. TheMBM calculates the position of the two boundaries separatingthe three working fluid phases. The MBM enjoys a low computa-

r locates downstream of aftertreatment system.


tional cost due to its limited state dimension. Thus, most researchteams utilize a MBM for control-oriented modeling rather thanhigh-fidelity, spatially discretized modeling [1619]. However, uti-lizing a MBM requires complex model switching/initializationstrategies as the system progresses through transients where notall three working fluid phases exist simultaneously. In short, theMBM experiences singularities as the total length of any phaseapproaches zero. Additionally, as with any lumped model, accuracycan be compromised.

The FVM discretizes the heat exchanger in the fluid flow direc-tion and solves the governing equations in each discretized cell. Ahighly discretized FVM model enjoys high accuracy. Discretizationwith 5, 10, 20, 30 cells shows 10.3%, 3.4%, 1.6%, 0.9% error respec-tively, compared to 100 cell discretization using a typical exhaustgas mass flow rate and temperature, and commanding 40 C ofsuperheat. However, discretized models suffer from high computa-tion cost [13,15,20] relative to a MBM. In this study, accuracy is pri-oritized, resulting in the utilization of the FVM.

1.2. Prior ORC modeling efforts

Quoilin et al. [15] developed a single evaporator ORC-WHR sys-tem model for low-grade heat applications where the heat sourcetemperature was between 120 and 300 C and the system utilizeda volumetric expander. A ten-cell FVM discretization was utilizedto model the heat exchanger. Additionally, the heat transfer coeffi-cient in the hot fluid side was set to a constant value, while theworking fluid heat transfer coefficient varied by working fluidphase. However, there were several simplifications, which leftroom for improvement on this work: (i) The working fluid evapo-ration pressure was assumed to be constant throughout the heatexchanger, (ii) The model is developed without identification orvalidation description, and (iii) The type of heat exchanger wasnot specified.

Yousefzadeh and Uzgoren [21] developed dynamic ORC modelsfor generalized conditions, such as uncertain thermal energy inputrates in small scale solar power systems. Fully coupled tank andcondenser models calculated liquid level in the tank and sub-cooling at the tank exit, which was further analyzed with pumpcapacity factor and expander rotational speed. However, the modelwas only validated over steady state conditions and evaporatorpressure drop was not considered.

Wei et al. [22] presented a comparison between the FVM andthe MBM for a stationary, industrial-sized 100 kW ORC system.The evaporator was discretized into five cells, and linear pressuredrop was assumed across the entire evaporator. The author con-cluded that both the FVM and MBM correctly simulated the systemduring transients and the MBM was preferred for its lower compu-tation cost. However, the component model calibration processeswere not described. Additionally, in the validation process, thetransient heat source conditions were not given and the transientwas mild.

Benato et al. [23] identified critical dynamic events (hot spots)in ORC-WHR boilers of a gas turbine power plant to avoid fluiddecomposition during transient heat source conditions resultingfrom power plant load changes. The heat exchanger was a horizon-tal circular finned-tube with a counter-cross flow configuration,and it was modeled with the FVM [24]. However, the responsetime of the boiler was nearly one hour in the power plant load stepchange, which is much slower than a vehicle application.

Feru et al. [25] presented a parallel evaporator ORC-WHR sys-tem for a HDD application. The modular plate-fin type heatexchanger was modeled with the FVM. The exhaust gas heat trans-fer coefficient varied with time, while the working fluid heat trans-fer coefficient was calculated in each discretized cell rather than ineach fluid phase. The heat exchanger model was identified with ten

steady state points and the identification parameters were fourcoefficients in the linear expressions of exhaust gas and workingfluid mass flow rate as functions of measured values. A reciprocat-ing, piston-type expansion machine was selected. However, thetime derivative of pressure was neglected in working fluid govern-ing equations and there is no pressure drop considered across theevaporator.

Jensen [20] proposed a FVM with a lumped pressure dropmodel. The model was discretized into eight cells and validatedwith concentric pipe experimental data in both steady state andtransient conditions. In some cases, the model exhibited less ther-mal inertia than the experimental results, which was attributed touncertainty regarding the influence of the measurement equip-ment. However, the lumped pressure drop model was unable tocapture the pressure drop in each working fluid phase, limitingits physics representation. Meanwhile, details of the ORC-WHRcomponents modeling, calibration and component models integra-tion were not provided.

1.3. Uniqueness of the current work

Even though Feru et al. [25] built a parallel evaporator ORC-WHR system model for a heavy duty diesel engine application,the evaporator was plate-fin type, which differs from the shell-and-tube type utilized herein. In addition, their evaporator modelignored pressure drop. Finally, the expander considered was a dis-placement type, which behaves very differently than a turbineexpander.

Jensen [20] assumed that the pressure drop across their entireshell-in-tube heat exchanger is linear versus spatial length. In fact,pressure drop in the mixed phase region is larger than the pressuredrop in the pure liquid or pure vapor regions. These details werenot captured. Moreover, the ORC-WHR component models calibra-tion details and integration was not presented.

In this paper, a tube-and-shell evaporator is modeled, includinga pressure drop model in the working fluid flow. Pressure drop isconsidered for each working fluid phase independently by assign-ing each phase its own linear pressure drop versus spatial length. Aturbine expander model is considered and experimental data isobtained for a new turbine design with an integrated electric gen-erator. Moreover, the ORC-WHR component model integration ispresented, which includes the details of boundary conditions,inputs and outputs for each individual component model. The indi-vidual model calibration process is then presented in detail.Finally, a GT-POWER engine model is built, based on a 13 Lheavy-duty diesel engine, to enable co-simulation with the Simu-link ORC-WHR model. The virtual engine model constructedusing the GT-POWER platform supplies real-time exhaust condi-tions to ORC-WHR model at given engine speed/torque profiles.These models can then be used for offline co-simulation and opti-mization studies.

This paper is organized as follows: Section 2 describes the ORC-WHR system configuration. ORC-WHR system modeling, calibra-tion and validation are then presented in Sections 35. Enginemodeling, calibration and validation are provided in Section 6. InSection 7, the ORC-WHR system is simulated over a constant speedvariable load (CSVL) heavy-duty transient cycle utilizing the enginemodel to predict ORC relevant exhaust conditions. The paper endswith conclusion in Sections 8.

2. System configuration

One of the most important factors in the ORC-WHR system con-figuration is the heat source. In a heavy duty diesel engine, poten-tial heat sources include the: TP exhaust gas, EGR, charge air and


engine coolant [11]. Due to the low temperature of charge air andengine coolant compared with the other two heat sources, they arenot considered in this investigation. Only the TP exhaust gas andEGR are considered.

The ORC-WHR system configuration is shown in Fig. 1. Themain components are a high pressure (HP) pump, two parallel-configured evaporators, a turbine expander, and a condenser. Inaddition, two mass flow distribution valves are integrated beforethe parallel evaporators to split the working fluid flow. Two morevalves are installed to facilitate utilization of the turbine expander.One valve is located upstream of turbine to ensure that only vaporphase flow passes through the turbine during system warmup orhighly transient operating conditions. The other valve actuatesthe bypass path around the turbine and is used to control the evap-oration pressure or to bypass non-vapor phase working fluidaround the turbine. An expansion tank is located after the con-denser, acting as a working fluid buffer during operation. A feedpump is utilized to supply working fluid to the HP pump, avoidingcavitation in the HP pump. An exhaust gas bypass valve is utilizedupstream of the TP evaporator to avoid ORC system over-heatingduring engine loads exceeding the condensation capacity of thesystem. No bypass valve is utilized for the EGR evaporator, aslow EGR outlet temperatures are necessary to ensure the engineintake volumetric efficiency. The condenser is cooled by buildingprocess water, which is currently independent of the engine cool-ant circuit. Ethanol is utilized as the working fluid. Note that work-ing fluid selection is an important factor for the ORC-WHR systemdesign and requires systematic analysis, which is not the focus ofthis paper.

Fig. 2. Finite volume method for evaporator modeling. Exhaust gas and workingfluid flow in reverse direction. Heat released from exhaust gas flows into workingfluid through the thermal mass of the wall.

3. System modeling

ORC-WHR system modeling covers seven types of components:heat exchangers, pumps, valves, junctions, compressible pipe vol-umes, a turbine expander, and a reservoir. The following modelsare constructed in Mathworks Simulink. Details for each modelare given below:

3.1. Heat exchanger modeling

In the ORC-WHR system, there are three heat exchangers twoevaporators and one condenser. Evaporators absorb heat from heatsource and release it to working fluid while the condenser releasesworking fluid heat to the cooling water. In this paper, the heatexchanger modeling is presented for the TP evaporator only toavoid duplication. Two crucial assumptions made in the heatexchanger model are: (i) axial heat conduction in working fluid,wall, and exhaust gas are not considered, and (ii) the wall temper-ature in the radial direction is uniform.

Mass balance, energy balance and momentum balance are con-sidered in the evaporator modeling. The mass balance of workingfluid is presented in Eq. (3.1.1).

@Af ;crossqf@t

@ _mf@z

0 3:1:1

where subscript f is working fluid, Across is the cross-sectional area, qis density, _m is mass flow rate, and z is spatial position in the axialdirection. There is no mass flow in the wall between the workingfluid and exhaust gas, eliminating the need for mass balance inthe wall. The energy balance of working fluid and exhaust gas sharethe same general form in Eq. (3.1.2). where p is fluid pressure, h isenthalpy, d is the effective flow path diameter for either the work-ing fluid and exhaust gas, U is the heat transfer coefficient, and DT isthe temperature difference between the fluid (working fluid orexhaust gas) and the wall. Due to the fast dynamics of exhaust

gas, @ _m@z is close to zero. Therefore, the exhaust gas does not require

a mass balance equation.

@Acrossqh Acrossp@t

@ _mh@z

pdUDT 3:1:2

The energy balance of the wall is shown in Eq. (3.1.3).

Aw;crosscp;wqwLwdTwdt

Af ;wUf ;wDTf ;w mgAe;wUe;wDTe;w 3:1:3

where subscript w is wall, cp is heat capacity, L is the length in axialdirection, Af ;w is the heat transfer area between working fluid andwall, Uf ;w is the heat transfer coefficient between working fluidand wall. mg is the heat exchanger efficiency multiplier, whichaccounts for heat loss to the environment, Ae;w is the heat transferarea between exhaust gas and wall, and Ue;w is the heat transfercoefficient between exhaust gas and wall.

A FVM is utilized to solve governing Eqs. (3.1.1)(3.1.3). Theheat exchanger is uniformly discretized into thirty cells, and thegoverning equations are then solved in each cell. A diagram ofthe FVM is shown in Fig. 2. The exhaust gas and working fluid floware in a counter-flow orientation. In each cell, exhaust heat isabsorbed by wall and then released to the working fluid. Fromthe first cell to last cell, the working fluid experiences phasechange from pure liquid to mixed phase and finally to pure vapor.

Boundary conditions (BC) are set at the inlet, outlet and outersurface area. Necessary BC for the exhaust gas include: mass flowrate and pressure at inlet, heat transfer between the exhaust gasand the working fluid tube wall, and heat transfer with the ambi-ent at outer shell of evaporator. In addition, the exhaust gas inletand outlet are considered adiabatic. Exhaust gas heat is releasedto ambient through the shell of evaporator, which is consideredby adding multiplier mg in Eq. (3.1.3). to adjust the amount of heatleft to transfer from the exhaust gas to the working fluid tube wall.The working fluid tube wall is assumed adiabatic at the inlet andoutlet. The spatial temperature distribution within the thicknessof the working fluid tube wall is neglected. The tube wall massabsorbs heat from the exhaust gas and then releases that heat tothe working fluid inside.

The Partial Differential Equations (PDE) (3.1.1) and (3.1.2) aresimplified to Ordinary Differential Equations (ODE) as follows:

dmfdt

_mf ;in _mf ;out 3:1:4

d _mh vpdt

_minhin _mouthout AUDT 3:1:5

where subscripts in and out denote spatial context in the axialdirection, v is the working fluid side volume of one discretized cell.Eqs. (3.1.3)(3.1.5) can be solved as follows:

Tw;tk1 Tw;tk Af ;wUf ;wDTf ;w Ae;wUe;wDTe;wAw;crosscp;wqwLwDt 3:1:6

mf ;tk1 mf ;tk _mf ;in _mf ;outDt 3:1:7


mh t k1 mh tk dvpdt

_minhin _mouthout AUDTDt3:1:8

where k is the time step indices, Dt is length of time step, dvp=dt issolved by Eqs. (3.1.7), (3.4.1) and (3.4.2).

Overall, there are four equations to be solved for each cell: wallenergy balance Eq. (3.1.6), working fluid mass balance Eq. (3.1.7),working fluid energy balance Eq. (3.1.8), and exhaust gas energybalance Eq. (3.1.8).

3.1.1. Pressure drop in the evaporatorInclusion of a pressure drop model improves the pressure calcu-

lation accuracy inside the evaporator. A complete pressure dropderivation is presented in this paper to calculate the working fluidpressure at each location inside the heat exchanger. Pressure dropsare first calculated for each working fluid phase. Then, the pressurewithin individual finite volume cells are defined through a linearrelation within each working fluid phase. Pressure drop is derivedbased on the fundamentals of momentum balance. For a two-phasesituation, an idealized model of momentum transport is shownbelow:

In Fig. 3, v represents vapor, l is liquid, g is gravitational accel-eration, X is the intersection angle between flow path and horizon-tal surface, u is flow velocity, z is axial location, and F is wallfrictional force. The working fluid momentum balance can beexpressed as follows:

dIdt

Fp Ffr Fg Fexc 3:1:1:1

where I is the fluid momentum, Fp is pressure force, Ffr is wall fric-tion force, Fg is gravitational force, and Fexc is the force exchangedbetween liquid and vapor fluid. In one discretized cell, Eq.(3.1.1.1) can be implemented for the liquid and the vapor, whichare shown in Eqs. (3.1.1.2) and (3.1.1.3), respectively.

_ml d _ml ul dul _mlul pAl p dp Al dAl dFl dFi;l AldzqlgsinX d _mlul

3:1:1:2

_mv d _mv uv duv _mvuv pAv pdp Av dAv dFv dFi;v AvdzqvgsinXd _mlul

3:1:1:3According to Newtons third law, the interfacial force balance Eq.(3.1.1.4a) can be derived. The increase of vapor mass flow equals

Fig. 3. Two-phase flow momentum balance in an inclined tube [26].

the reduction of liquid mass flow, Eq. (3.1.1.4b). The flow pathcan be divided into vapor and liquid sections as prescribed by Eq.(3.1.1.4c).

dFi;v dFi;l a d _mv d _ml b A Av Al c

8>: 3:1:1:4Combining Eqs. (3.1.1.2)(3.1.1.4) produces:

Adp pdA dFl dFv Alql Avqv

gdzsinX d _mvuv _mlul3:1:1:5

Friction force is defined via Eq. (3.1.1.6) [26]:

dpdz

fr

Adz dFl dFv 3:1:1:6

Additionally, vapor fluid speed and liquid fluid speed can beexpressed as [26]:

uv Gxqvapa3:1:1:7

ul G 1 x qsat 1 a 3:1:1:8

x h hsathvap sat 3:1:1:9

a AvA

3:1:1:10

where G is mass flux, x is vapor quality, a is void fraction, subscriptvap is saturated vapor, and subscript sat represents saturated liq-uid. Substitution of Eqs. (3.1.1.6)(3.1.1.10) into Eq. (3.1.1.5), yieldsthe two-phase pressure drop spatial derivative:

dpdz

tp

pA

dAdz

dp

dz

fr

1 a qsat aqvaph i

g sinX

1A

ddz

G2x2Aqvapa

G2 1 x 2Aqsat 1 a

" #3:1:1:11

Eq. (3.1.1.11) can be rewritten as follows:

0 dpdz

tppA

dAdz

" # dp

dz

fr

" # 1a qsat aqvaph i

g sinXh i

1A

ddz

G2x2Aqvapa

G2 1x 2Aqsat 1a

" #3:1:1:12

In the pure liquid and pure vapor regions, Eq. (3.1.1.5) reduces toEqs. (3.1.1.13a) and (3.1.1.13b), respectively.

Adp pdA dFl Alql gdzsinX d _mlul a Adp pdA dFv Avqv

gdzsinX d _mvuv b

(

3:1:1:13

Following the same derivation process as used to develop Eq.(3.1.1.12) results in the general form for pure liquid and pure vaporpressure drop as follows:

dpdz

sp

AdAdz

dp

dz

fr;s

qgsinX 1A

ddz

G2Aq

!3:1:1:14

where subscript s represents single phase. dAdz is equal to zero if thediameter of working fluid pipe is constant, which is the case in thisheat exchanger. The frictional pressure gradient of single phase flowin round tubes can be presented as follows [26]:


dpdz

fr;s

2f sG2s

qsdh3:1:1:15

where f s is friction factor, which is calculated by the Blasius corre-lation [27]:

f s BRen BGsdhls

n3:1:1:16

where Re is Reynolds number [28], and B and n are functions of flowpattern. For laminar flow, B = 16 and n = 1 while for turbulent flowB = 0.079 and n = 0.25. The two-phase frictional pressure can bederived from either liquid phase or vapor phase frictional pressurewith a multiplier. In this paper, vapor phase frictional pressure isselected.

dpdz

fr;tp

uv dpdz

fr;v

" # uv

2f vG2v

qvdh3:1:1:17

uv 1 CX X2 3:1:1:18

X dpdz

l

dpdz

v

264

375

0:5

3:1:1:19

where uv is the two-phase multiplier, X is the Martinelli parameterand C is a constant depending on flow pattern. Applying Eqs.(3.1.1.15) and (3.1.1.16) to liquid and vapor phase yields:

dpdz

l 2f lG

2 1 x 2qldh

3:1:1:20

f l BRenl BG1 xdh

ll

n3:1:1:21

dpdz

v 2f vG

2x2

qvdh3:1:1:22

f v BRenv BGxdhlv

n3:1:1:23

Substituting Eqs (3.1.1.20)(3.1.1.23) into Eq. (3.1.1.19), the follow-ing equation is obtained:

X GnvnldnvnlhBlBv

1 x 2nl x 2nv

l nv vl nl l

qvql

" #0:53:1:1:24

The gravity term qgsinX in Eq. (3.1.1.14) cancels because theupward and downward lengths of the working fluid flow path areequal for this evaporator design. Thus, the pressure drop across liq-uid, two-phase and vapor working fluid phases can be derivedrespectively as follows:

Dpl Z zasatz1

dpdz

dz

Z zasatz1

2f lG2

qldh 1A

ddz

G2Aql

! !dz

Xasati1

2f liG2iqlidh

Dz

! G

2asat1

qlasat1

" # G

21

ql1

" # !3:1:1:25

Dptp Z zavap1zasat1

dpdz

dz

XNiav

U2v2f v G2i x

2

qvdhDz

!

G2avap x2avap

qv adew aadew

" # G

2asat1x

2asat1

qv asat1 aasat1

" #

G2avap 1 xavap

2ql avap 1 aavap

24

35 G2asat1 1 xasat1 2

ql asat1 1 aasat1

" #1A 3:1:1:26

Dpv Z zN1zavap

dpdz

dz

Z zN1zavap

2f vG2

qvdh 1A

ddz

G2Aqv

! !dz

XN1iavap

2f v ;iG2iqv;idh

Dz

! G

2N1

qv ;N1

" #

G2avapqv;avap

" #0@1A 3:1:1:27

where a is the ath boundary of the discretized evaporator. Subse-quently, the pressure value at inlet and two-phase boundaries canbe obtained:

pin Dpl Dptp Dpv poutpsat Dptp Dpv poutpvap Dpv pout

8>>>: 3:1:1:28The evaporation pressure in each discretized cell is calculated asfollows:

pi pin ai1asat1 pin psat ; ifasat P aipsat aiasatavapasat psat pvap

; ifavap > ai P asat

pvap aiavapNavap pvap pout

; ifai P avap

8>>>>>:

3:1:1:29

Only heat exchanger inlet and outlet pressure are measured exper-imentally. Therefore, only the total pressure drop is considered forthe pressure drop model validation.

3.1.2. Heat transfer coefficientsHeat transfer coefficients can be classified into two types based

on the fluid considered (either exhaust gas or working fluid). Dueto the fast dynamics in the exhaust gas, all thirty spatial cells uti-lize one heat transfer coefficient, which is only time dependent. Eq.(3.1.2.1) is the expression of friction factor for concentric tubes[29], which is selected here as the evaporator geometry is simpli-fied to that of a concentric tube structure:

ne;TP 1:8log10 Ree;TP

1:5 2

3:1:2:1

Ree;TP Ree;TP1 r2d

lnrd 1 rd1 r2d

lnrd3:1:2:2

rd dindout 3:1:2:3

where n is friction factor, din and dout are inner and outer diametersof concentric tube, respectively. The thermal conductivity of theexhaust gas is shown in Eq. (3.1.2.4).

k1;e;TP 1:07 900Ree;TP 0:63

1 10Pre;TP 3:1:2:4

Ree;TP _me;TPde;TP

Ae;TP;crossvd3:1:2:5

Pre;TP vd;e;TPcp;e;TPke;TP 3:1:2:6

where d is hydraulic diameter, vd is dynamic viscosity, Pr is Prandtlnumber. Nusselt number expression, Eq. (3.1.2.7), of a concentrictube with insulated outer pipe wall is selected based on the heatexchanger structure [30].

Nue;TP ne;TP8

Ree;TPPre;TP

k1;e;TP 12:7ffiffiffiffiffiffiffine;TP8

qPr0:667e;TP 1 1 de;TPl

0:667" #3:1:2:7


where l is length of the pipe in the heat exchanger. The heat transfercoefficient between exhaust gas and wall can be calculated with Eq.(3.1.2.8) [31]. The experimental evaporator construction differsslightly from concentric tubes, so a heat transfer coefficient multi-plier (mU) is applied.

Ue;w;TP mU Nue;TPke;TPde;TP 3:1:2:8

The heat transfer coefficient on the working fluid side has a differ-ent format for each working fluid phase. Each discretized cell hasits own heat transfer coefficient, which is both temporally andspatially dependent. The calculation of pure liquid and pure vaporheat transfer coefficients between the working fluid and the tubewall are given in Eq. (3.1.2.9). These heat transfer coefficients areselected according to the helical coil heat exchanger structure[30].

Uf ;w;TP;i nf ;TP;i8

Ref ;TP;iPrf ;TP;i

1 12:7ffiffiffiffiffiffiffiffinf ;TP;i8

qPr0:667f ;TP;i 1 kf ;TP;idf ;TP;i 3:1:2:9

nf ;TP;i 0:0075df ;TPDf ;TP

0:5 0:079Re0:25f ;TP;i

3:1:2:10

The two-phase heat transfer coefficient between the working fluidand the tube wall is calculated from a vertical tube two-phase heattransfer coefficient expression [30], which shares a similar struc-ture with the helical coil utilized in the experiments. Uf ;w;TP;sat andUf ;w;TP;vap are calculated using single phase Eq. (3.1.2.9). The two-phase heat transfer coefficient expression is shown in Eq.(3.1.2.11):

Uf ;TP;tp 1 x 0:01 1 x 1:9x0:4qf ;satqf ;vap

!0:352435

2:28>>>>>>>>>>>>>>>>>>>>>>>>>>:

3:3:2:1


where c cpcv is heat capacity ratio. Assuming the working fluidexperiences an isentropic process across the valve (hout hin), theoutlet temperature can be calculated:

Tout f pout;hout 3:3:2:2The necessary BC for these two valves are pressure and enthalpy

at the inlet and pressure at the outlet. The valve is assumed to loseno heat to the environment.

3.4. Compressible vapor volume

The volume after the evaporators and upstream of the turbinevalves, is considered a compressible volume, which is utilized tocalculate the evaporator downstream pressure [25]. Three equa-tions are utilized in this volume: mass balance Eq. (3.1.1), energybalance Eq. (3.4.1), and the ideal gas law Eq. (3.4.2) [35]. Threeparameters can be calculated by solving these three equations:working fluid mass inside the volume, working fluid mean temper-ature inside the volume, and mean pressure inside the volume.

udmdt

mcv dTdt _Hin _Hout 3:4:1

RTV

dmdt

pTdTdt

dpdt

0 3:4:2

where u represents specific internal energy, cv represents specificheat capacity, _Hin and _Hout represent inlet and outlet enthalpy flow-rate, R represents ideal gas constant, V represents vapor volume.

BC of the compressible vapor volume are mass flow rate andenthalpy at the inlet, and mass flow rate at the outlet. Meanwhile,the inlet, outlet and outer surfaces are all adiabatic.

3.5. Turbine expander

The turbine is integrated with an electric generator in this work.However, it can also be mechanically connected to engine crankshaft through a transmission, as in [10]. Turbine expander massflow rate has a linear relationship to turbine inlet pressure, Eq.(3.5.1), due to the choked flow status at high expansion ratios(1030).

_mturb aturbpin;turb bturb 3:5:1The outlet enthalpy is calculated by isentropic efficiency as

follows:

hout;turb hin;turb gis;turb hin;turb hout;is;turb 3:5:2

gis;turb mapNturb;pin;turb=pout;turb; Tin;turb 3:5:3

hout;is;turb map sout;turb;pout;turb 3:5:4

sout;turb sin;turb 3:5:5

sin;turb maphin;turb;pin;turb 3:5:6The turbine efficiency map is proprietary to the project sponsor,

BorgWarner Inc. and is not shown here. Outlet temperature,Tout;turb, is calculated from outlet enthalpy and outlet pressure usinga thermodynamic table of the working fluid.

Tout;turb maphout;turb;pout;turb 3:5:7Turbine BC are pressure and enthalpy at inlet, and pressure at out-let. Additionally, the inlet and outlet are adiabatic. The heat transferbetween turbine outer surface and ambient is considered within theturbine isentropic efficiency map.

3.6. Reservoir

The reservoir acts as a buffer for the working fluid as the ORC-WHR system experiences transients. Before the ORC system starts,the working fluid level is low in the reservoir because the entirecircuit is full of liquid. After the system reaches warm conditions,part of the ORC system is occupied by vaporized working fluidand the working fluid level in the reservoir increases comparedto the cold condition. Both mass balance and energy balance areapplied in the reservoir to calculate the working fluid level as wellas the mean temperature. The mass balance shares the same equa-tion with Eq. (3.1.4) while the energy balance is given in Eq. (3.6.1).Reservoir working fluid level is then given by Eq. (3.6.2).

d mh dt

_minhin _mouthout 3:6:1

Hres VV0 3:6:2

where V0 represents the entire reservoir volume. Reservoir BC aremass flow rate and enthalpy at the inlet and mass flow rate at theoutlet. The reservoir is assumed to lose no heat to the environment.

3.7. Pipe junctions

Pressure loss in the system pipe junctions is not considered.Similar to the reservoir, junctions are modeled by mass balanceand energy balance via Eqs. (3.7.1) and (3.7.2), respectively.

_mmix _m1 _m2 3:7:1

_mmixhmix _m1h1 _m2h2 3:7:2The junction BC are mass flow rate and enthalpy at the inlet, whilethe outlet is considered adiabatic. The junctions are assumed to loseno heat to the environment.

4. Model identification

All physical parameters are directly measured, such as the heatexchanger area, evaporator wall mass, pipe volume, etc. For thepump model, there is no parameter to be identified. The turbine,valve and heat exchanger parameter identification processes areprovided in this section.

4.1. Turbine

Two parameters aturb;bturb in Eq. (3.5.2) need to be identified.The turbine inlet pressure and respective mass flow rate are mea-sured experimentally. Identification is achieved via the Matlab

Genetic Algorithm toolbox. The cost function is defined in Eq.(4.1.1) and the results are shown as Eq. (4.1.2).

eflow;turb Xnmap;turbi1

_msim;turb;i _mmap;turb;i 2 4:1:1

aturb 2:43 108bturb 3:3 103

(4:1:2

where nmap;turb is the number of turbine mass flow points in turbinemap.

4.2. Valves manipulating incompressible liquid

Two parameters aEvapVlv , cEvapVlv in Eq. (3.3.2) are identified viathe Matlab Genetic Algorithm toolbox for the mass flow distribu-tion valves. To identify the valve parameters, evaporator mass flow

Fig. 5. Turbine upstream valve and turbine bypass valve discharge coefficient.


rates, HP pump speed, and valve opening data are collected exper-imentally. Operating conditions include transient engine condi-tions as well as transient ORC conditions. The toolbox optimizesthe two parameters by minimizing the mass flow rate error forboth mass flow distribution valves. The error is defined below:

eflow;v lv Z Tsims0

_mTPEvapvlv;sim _mTPEvapvlv ;sim 2ds

Z Tsims0

_mEGREvapvlv;sim _mEGREvapvlv;exp 2ds 4:2:1

where Tsim is the simulation time. The optimized results are plottedin Fig. 4. Even though the experiments are highly transient, thetrends for both simulated valves match well with experiments.The optimized coefficients value are given in Eq. (4.2.2).

aEvapVlv 0:98cEvapVlv 0:5218

4:2:2

4.3. Valves manipulating compressible vapor

The discharge coefficients of the turbine inlet and turbinebypass valves require identification. These two valves are identical,so only the turbine bypass valve identification process is describedhere. The experimental data utilized in the identification includes:valve opening, working fluid mass flow rate, and inlet/outlet pres-sures. Twenty-four operating points are tested experimentally,which span the range of engine conditions (1000 rpm, 1039 N m),(1200 rpm, 1000 N m) with 8%, 12% and 17% EGR rates. The dis-charge coefficient of the turbine bypass valve is given in Eq.(4.3.1) plotted in Fig. 5. As with the other components, the param-eters are identified via the Matlab Genetic Algorithm toolbox. Theidentification results are given in Eq. (4.3.2).

The fitting curve exhibited in Fig. 5 is able capture the mainexperimental trend. However, the error is as large as 10% for certainconditions. This error is caused by the partial opening of turbineinlet valve during the test to bring down the evaporation pressurewhen the turbine is not installed. There are no mass flow rate sen-sors installed to independently measure respective the mass flowrates through the turbine inlet valve and turbine bypass valve. Moreexperimental data are required for enhanced turbine bypass valvecalibration. This data should be collected during low power engineconditions so that turbine inlet valve can fully close while evapora-tion pressure remains within the acceptable range.

Cd;TurbByp a1O2TurbByp a2OTurbByp a3

pevapa4

4:3:1

Fig. 4. Working fluid mass flow rate through the TP and EGR evaporatordistribution valves (normalized by maximum absolute value).

a1 1:109e5a2 1:397e5a3 3:376e6a4 2:1e6

8>>>>>:

4:3:2

4.4. Heat exchangers

The evaporators are shell-and-tube in structure, and the tubesare shaped as compounded coils. The TP exhaust gas evaporatorcontains four parallel helical coils, while the EGR evaporator hasonly two parallel coils. The selected empirical heat transfer coeffi-cient between the exhaust gas and helical coil was designed forheat transfer between fluid flowing in concentric pipes. The work-ing fluid flows inside the tube coiled with a tight radius of curva-ture, which is subsequently spiraled axially around theevaporator centerline in the direction of the exhaust flow. Thiscomplex shape experiences parallel and cross flow heat transfer.For simplicity, this geometry has been modeled as concentrictube-in-tube experiencing counter flow heat transfer with exhaustgas. Due to discrepancies between the physical evaporator designand the selected empirical heat transfer correlations, heat transfercoefficient multipliers and evaporator efficiency multipliers areutilized for evaporator model identification. The efficiency multi-plier mg is introduced in Eq. (3.1.3) and accounts for heat lossesfrom evaporator to environment. The heat transfer coefficient mul-tiplier mU is introduced in Eq. (3.1.2.8) and accounts for the com-plex structure of the experimental heat exchanger relative to thegeometry for which the correlations are derived.

Heat exchanger identification utilizes mass flow rates into eachevaporator (both working fluid and exhaust/EGR gases) in additionto temperature and pressure measurements upstream and down-stream of the evaporators (again, both for the working fluid andthe exhaust/EGR). The experimental data set utilized for evapora-tor and condenser parameter identification is the same as used inturbine bypass valve discharge coefficient identification.

Each evaporator model is identified separately by providing theexperimental inlet conditions for the working fluid and the respec-tive heat source. Simulated evaporator outlet states for the heatsource flow and the working fluid are then compared with exper-imental results for the same inputs. The efficiency multiplier andheat transfer coefficient multiplier are identified by minimizingthe error between simulated and experimentally measured evapo-rator outlet conditions.

The algorithm for adjusting the two multipliers to match thesimulation and experiment results is explained as follows. First,two errors are defined as:

evap Tvap;sim Tvap;exp 4:4:1


eexh;out Texh;out;sim Texh;out;exp 4:4:2Both errors can be positive or negative. Given the simulation resultsfrom any pair of multipliers (mg;mU), a point can be found in thecoordinate system shown in Fig. 6. The dashed line crosses the firstand third quadrant and has an angle a from x axis. This line isdenoted as the accurate HTC line. A heat transfer coefficient(HTC) multiplier on this line is an accurate value. When the temper-ature error from a certain multiplier pair locates on this line in thefirst quadrant, onlymg needs to be reduced by Lg to reach the origin.This is because both the simulated working fluid outlet temperatureand simulated exhaust gas outlet temperature are greater than theexperimental value, indicating that the heat lost from the simulatedevaporator to the environment must be increased in the model.Therefore, the efficiency multiplier should be reduced and thereduction magnitude is proportional to the distance between cur-rent position and the coordinate origin, which is Lg. On the contrary,if the temperature error lies on the dashed line in the third quad-rant, the efficiency multiplier needs to be increased by Lg.

Another dashed line passing through the origin, splitting thesecond and fourth quadrant where only the HTC multiplier, mU ,needs to be adjusted in order to reach the coordinate origin. Thisline is called the accurate efficiency line. When the temperatureerror from a certain multiplier pair locates in the second quadrant,the simulated working fluid outlet temperature is higher thanexperimental result, while the simulated exhaust gas outlet tem-perature is simultaneously lower than the experiment result. Inthis situation, changing the evaporator efficiency multiplier willnot simultaneously reduce both errors. This situation can beresolved by altering the HTC multiplier. The smaller the HTC mul-tiplier value, the lower the HTC between the exhaust gas and thewall. Thus, reducing mU leads to smaller inlet and outletenthalpy/temperature differences in steady state. Therefore, theexhaust gas outlet temperature increases. Meanwhile, less heatpower is transferred to the wall reducing the wall temperatureand decreasing the working fluid outlet temperature. Therefore,decreasing mU drives the working fluid outlet temperature andthe exhaust gas outlet temperature towards each other. The reduc-tion magnitude of mU is defined by the distance between the cur-rent point and the coordinate origin, which is Lh in Fig. 6.Conversely, if the temperature error locates on the dashed line in

Fig. 6. Heat exchanger calibration parameter tuning explanation.

the fourth quadrant, the HTC multiplier should increase by Lh.When the temperature error locates off the dashed lines, both effi-ciency multiplier and HTC multiplier need to be adjusted and theadjusted magnitude are Lg and Lh respectively. The sign of Lg andLh can be described as:

Lg; Lh if region 1Lg; Lh if region 2Lg; Lh if region 3Lg; Lh if region 4

8>>>>>:

4:4:3

The mechanism utilized to simultaneously tune these two mul-tipliers in steady state is as follows: (i) Initial guesses are set; (ii)The simulation runs until steady state is obtained and then thesimulated working fluid outlet temperature and exhaust gas outlettemperature are compared to experimental values; (iii) The totalerror is compared with the preset error tolerance. If calculatederror is larger than the tolerance, the multipliers are updated andthe iterative process restarts at step (ii). The identification processis formulated as the following error minimization problem:

minc

Jc

J w1 Tvap;sim Tvap;exp 2 w2 Texh;out;sim; Texh;out;exp 2

s:t :_xs f xs;us;ws; c ys hxs;us;ws; c

clb 6 c 6 cub

c mg;mU T

4:4:4

where w1=w2 are the weights of vapor temperature and exhaustoutlet temperature errors, respectively.

This minimization problem is solved with the Particle SwarmOptimization (PSO) algorithm. PSO was introduced by Eberhartand Kennedy [36] and it has gained much attention for its simplestructure and high performance. PSO is inspired by the movementof an animal herd/school/swarm. More specifically, a large group ofanimals independently searches for targets over a large space.However, the individuals of the population communicate duringthe search about what they find, deciding the direction each indi-vidual animal moves in the future and how fast each individualshould move in order to gain greater reward. It is a global opti-mization algorithm, which has been proven to avoid local mini-mums of the cost function. More details of PSO can be found inthe Appendix A.

The PSO algorithm is implemented in Matlab [37]. During theoptimization process, the number of generations (iterations) is tenand total population of individual particles is set to thirty. A PSOresult for one operating condition is shown in Fig. 7. The engineand ORC operating conditions are: 1575 rpm, 1534 Nm, 12% EGRrate, 20 bar evaporation pressure, and 280 C vapor temperature.The mean error of all thirty population members and the globalvisited optimal error (error from the best individual of the popula-tion from generation 1) are shown for each generation (iteration).Convergence is observed around 10th generation.

The PSO identification is conducted at each steady state datapoint. Then, correlations fit the identified multipliers across allsteady state data points relative to measureable parametersaccording to Eqs. (4.4.5)(4.4.8). Four experimentally measureablevariables are considered for the evaporator efficiency and heattransfer coefficient multiplier correlations, namely, the mass flowrates and temperatures of both the working fluid and heat sourcegas. Fig. 8 exhibits the fit of these correlations where the horizontalaxis is the optimal multiplier value from identification by the PSOfor that individual case and the vertical axis is the multiplier valuevia the correlation. In Fig. 8, the TP heat transfer coefficient (HTC)multiplier correlation shows strong alignment with experimental

Fig. 7. PSO results at steady state operating conditions (engine condition:1575 rpm, 1534 N m, 12% EGR rate, 20 bar evaporation pressure, ORC condition:280 C vapor temperature).

Table 1Heat exchanger efficiency and heat transfercoefficient multiplier identification results.

meff ;TP a1 4.598a1 1.808a3 -1.207 e2

a4 9.344a5 9.708 e3

a6 1.103 e5

mU;TP b1 6.07b2 -2.968b3 -1.491 e3

meff ;EGR a1 1.705a1 1.262 e1

a3 1.082 e1

a4 -2.031 e1

a5 2.669 e1

a6 -3.109 e1

mU;EGR b1 4.293b2 -7.866 e1

b3 3.716 e1


data predicting within 5% of experimental results. The EGR effi-ciency multiplier exhibits trend-wise agreement although someof the identified points vary from experiments by as much as10%. The values of identified multipliers are shown in Table 1.

meff ;TP a1 a2 _mTP a3TTP;up a4 _m2TP a5 _mTPTTP;up a6T2TP;up4:4:5

Fig. 8. Comparison between PSO optimization results and the correlation results for TPevaporator HTC multiplier, (c) EGR evaporator efficiency multiplier, and (d) EGR evapora

mU;TP b1 be _mTP b3TTP;up 4:4:6

meff ;EGR c1 c2 _mTP c3TEGR;up c4 _m2TP c5 _mTPTEGR;up c6T2EGR;up4:4:7

mU;EGR d1 d2 _mEGR d3TEGR;up 4:4:8

and EGR evaporator identification: (a) TP evaporator efficiency multiplier, (b) TPtor HTC multiplier (All variables are normalized by their maximum absolute value).

Table 2Initial conditions of component models.

ORC-WHR componentmodels

Parameters Initialcondition

TP evaporators Working fluid enthalpy Appendix BWall temperatureExhaust gas temperature

EGR evaporators Working fluid enthalpy Appendix BWall temperatureExhaust gas temperature

Compressible volume a Working fluid mass 0.08 kgWorking fluidtemperature

573 K


The heat exchanger efficiency and heat transfer coefficient multi-plier correlation calibration results improve by considering onlyexhaust gas inlet conditions (mass flow rate and temperature)and quadratic expressions for efficiency multiplier compared with[38]. In the structure of both evaporators, there is no contactbetween working fluid helical coil tube and ambient air andonly the shell contacts the ambient air. However, the exhaustgas directly contacts the evaporators outer shell. Therefore,exhaust gas conditions are more related to evaporator heat loss.Meanwhile, since the HTC multiplier is added in the exhaust side,it is mainly affected by exhaust conditions rather than working fluidconditions.

Working fluid pressure 12 barCompressible volume b Working fluid mass 0.012 kg

Working fluidtemperature

569 K

Working fluid pressure 11.9 barCondenser Working fluid enthalpy 955e5 J/kg

Wall temperature 422 KCooling watertemperature

307 K

Reservoir Working fluid mass 5.46 kgWorking fluid enthalpy 4.78e5 J/kg

5. Model validation

Model validation is conducted with the component modelsconnected as an entire ORC-WHR system. The independent mod-els are integrated in Simulink. Each component model has inletport and outlet port relative to the working fluid flow directionand ignoring working fluid back flow. Mass flow rate, tempera-ture, and pressure are the three key parameters to determinefluid flow along the connected component models. Fig. 9schematically illustrates the interconnection of the componentsubmodels. Inputs and outputs of each component model are rep-resented with red arrows and black dot arrows, respectively.Additionally, actuator command inputs are represented with bluearrows and external inputs are represented with dash purplearrows. External inputs include exhaust gas mass flow rate/temperature to the evaporators and cooling water mass flowrate/temperature to the condenser.

Table 2 provides the initial conditions of the ORC-WHR system.The pump, valves, turbine and junctions are considered static mod-els, which do not need initial conditions. State variables exist in theheat exchangers, compressible volumes, and reservoir. These initialconditions are obtained from a steady state simulation.

Fig. 9. Schematic representation of the ORC-WHR System component model integrationinputs and actuator interactions with the system.

The ORC-WHR system model is validated over experimentaltransient operating conditions. For the validation results, relativeerror is defined by Eq. (5.1).

e jsim expjexp

5:1

The engine undergoes a transient from 1200 rpm, 1000 N m, to1580 rpm, 1250 N m and finally to 1580 rpm, 1535 N m, as plottedin Fig. 10a together with the EGR rate (Fig. 11b). During this tran-sient, the turbine upstream valve is fully open and the turbinebypass valve is fully closed. The turbine upstream vapor tempera-ture is experimentally maintained at a desired trajectory via PIDcontrol applied to the HP pump speed. The temperature differencebetween two evaporators is simultaneously maintained at zero

. Inputs and outputs for each component model are illustrated as well as external

Fig. 10. Engine condition for ORC-WHR model validation: (a) engine speed andtorque, and (b) engine EGR rate.

Fig. 11. (a) Exhaust gas mass flow rate, (b) exhaust gas temperature, (c) HP pumpspeed, (d) distribution valve openings, and (e) turbine bypass valve opening. (Allvalues are normalized by their respective maximum absolute value.)


via another PID control applied to the mass flow split valves down-stream of the HP pump. Some of the transient condition ORC inputsfrom experimental measurements are plotted in Fig. 11.

Comparisons of simulation and experimental results are shownin Figs. 12 and 13. Mass flow distribution valve performance andpressure drop for both evaporators are shown in Fig. 12. Duringthe 3800 s simulation, both the TP and EGR mass flow distributionvalves predict trend-wise mass flow agreement and follow exper-imental values within 5.4% and 6.6%, respectively. Both evaporatorpressure drop magnitudes are captured by the pressure dropmodel. However, the TP evaporator pressure drop model overesti-mates the pressure drop between 2800 and 3300 s. The mean errorfor the two independently calculated pressure drops are 6.8% and3.1% for the TP and EGR evaporators, respectively.

Evaporation pressure, mixed vapor temperature and turbinegenerated power are plotted in Fig. 13. Working fluid evaporatingpressure presents 2.2% mean error and tracks the transient trendwell. Turbine upstream mixed vapor temperature also tracks theexperimental measurements well with an average error of approx-imately 1.4%. However, even though the temperature error is lessthan 2%, the absolute error is around 8 K.

The model also accurately predicts the turbine generated powermagnitude barring short periods of variation from the experiments(900 s, 1500 s and 2000 s). The average error is 5.5%. Note that theturbine power trend shares the same shape as evaporating pres-sure and pump speed (Fig. 11) rather than just the turbineupstream mixed vapor temperature.

Transient ORC model validation demonstrates good perfor-mance in mass flow rate distribution, evaporator pressure and

Fig. 12. (a) Working fluid mass flow rate, (b) TP evaporator pressure drop, and (c)EGR evaporator pressure drop (All parameters are normalized by their maximumabsolute value).

Fig. 13. (a) Evaporation pressure, (b) mix vapor temperature, and (c) turbinegenerated power (All parameters are normalized by their maximum absolutevalue).

Table 3Engine specifications.

Parameter Value

Engine Navistar Maxxforce 12.4 L Inline 6 Turbocharged DieselRated Torque 2305 N m @ 1000 rpmRated Power 357 kW @ 1800 rpmBore stroke 126 mm 176 mmCompression ratio 17.0:1


mixed vapor temperature prediction, while the pressure drop andturbine power experience slightly larger errors. Multiple factorscontribute to the increased pressure drop and turbine power errors.(i) The pressure drop associated with diameter changes in the con-nections between pipes and the evaporators is not considered. (ii)The turbine isentropic efficiency map is merely representative. Itcorresponds to a different turbine generation than the componentinstalled on the experimental system, which could lead to the tur-bine power prediction error and erroneous pressure drop calcula-tion. (iii) Note that the largest disparity between experiment andsimulation pressure drop occurs between 2800 and 3300 s, whichcorresponds to the actuation of the turbine bypass valve opening.This pressure drop error could be indicative of the imperfection cor-relation fit in discharge coefficient versus bypass valve opening.

Table 4Experimental engine test points.

Speed (rpm) Torque (N m) EGR rate (%)

1200 1000 0, 10, 201500 1000 0, 10, 201000 576 0, 5, 10, 16.5, 20, 251900 440 0, 5, 10, 15, 20, 251000 1730 0, 5

6. Engine modeling and validation

A detailed, physics-based engine model is developed whichenables simulation at steady state, quasi-transient cycles and fulltransient cycles. The objective is to gather relevant exhaust gasand EGR data, which can be used as an input to the ORC. Whilethe development of this engine model critically enabled the expan-sion of ORC simulation into transient drive cycles, it is not the focusof this investigation. For completeness, a brief summary of theengine model development is included in this section. Specifica-tions of the test engine are shown in Table 3:

The detailed engine model consists of manifolds, connectingpipes, engine cylinders, crankcase, Variable Geometry Turbine(VGT), and a compressor. The combustion model used is DIPulseversion v75 and the Woschni model is utilized for heat transfer.

A high pressure EGR loop is implemented in this model and theinertia of the turbocharger system is considered. The inputs tothe model are time variant profiles of speed and load (fraction oftorque). These profiles are selected from steady state and heavilytransient drive cycles to check the robustness of the model. AFR,EGR and fuel injection duration maps are calibrated to match theexperimental data. Each of these maps is populated as a 2-D lookuptable with a functional dependence on load fraction and enginespeed. The most relevant outputs from this model are the TPexhaust temperature, TP exhaust mass flow rate, EGR temperature,and EGR mass flow rate.

Three controllers (direct injection fuel quantity, EGR and VGTrack position) are used in the model. These controllers operate inconcert to match the target torque and speed profiles. For any tor-que command, the fuel controller determines the injection quan-tity. Simultaneously, the EGR PID controller operates the intakethrottle and the EGR valve to control the target EGR fraction. Allthe while, the VGT rack position controller attempts to developthe correct boost pressure such that, after throttling, the targetAFR is achieved.

The detailed engine model is experimentally calibrated andthen validated at separate steady state points. Various EGR levelsare considered during the calibration and validation procedure.The experimental test points are shown in Table 4. A sample steadystate comparison between simulated and experimentally mea-sured exhaust temperature is shown in Fig. 14, where, in mostcases, the error is within 5%.

The fully detailed model requires 16 h to simulate a 1200 s tran-sient drive cycle. This proved too computationally intensive andhence a fast running model (FRM) is built by simplifying the modelconstruction as follows. The two intake and exhaust valves arecombined into a single intake and exhaust valve for each cylinder.The multiple runners are also combined into single runner for eachcylinder. All pipes and flow-splits are transformed to one flow splitwith a larger volume. A cylinder slaving technique is employed uti-lizing cylinder 1 as the master cylinder and the remaining fivecylinders are set as identical slave cylinders. This techniquereduces the computational time by eliminating calculation of indi-vidual combustion events for each cylinder. The performance ofthe FRM is validated with the detailed engine model as well asexperimental engine data from the engine dynamometer for steadystate points and quasi-transient operation. Fig. 15 compares theturbocharger outlet exhaust gas temperature between the FRMand the detailed engine model. It is observed that the transientpeaks and valleys are all well maintained by the FRM. Figs. 16and 17 show the behavior of the model relative to experiments

Fig. 14. Engine model calibration results at steady state points.

Fig. 16. Engine torque tracking performance by FRM (simulation) versus theexperimental trace.

Fig. 15. Detailed engine model and fast running engine model comparison,illustrating the close agreement between the two models.


for a constant speed step change in torque. The engine speed wasset to 1300 rpm and the torque changed from 1400 N m to1260 N m.

As shown in Figs. 17 and 18, the FRM traces the experimentaltorque and EGR values smoothly, implying that the model behaveswell with quasi-transients. The root mean squared error (RMSE)values for torque and EGR fraction are 2.0 N m and 0.001, respec-tively. The FRM validation of tailpipe temperature and EGR tem-perature are shown in Figs. 18 and 19, respectively. The FRM

Fig. 17. EGR rate tracking performance by FRM (simulation) versus the experi-mental trace.

Fig. 18. TP exhaust gas temperature comparison between FRM simulation and theexperimental results.

Fig. 19. EGR temperature comparison between FRM simulation and experiment.

Fig. 22. EGR rate tracking performance by FRM (actual) over CSVL heavy-dutyengine driving cycle (target).


reproduces the experimental trends well, with only a slight gain-like error.

The FRM is subsequently operated over a more aggressive con-stant speed variable load (CSVL) cycle. This CSVL cycle represents acommon HDD engine application, long-distance highway driving.During this operational mode, the driver only subtly fluctuatesengine speed while ground speed is maintained over terrain gradi-ents via torque alterations with a fixed gear ratio. Figs. 20 and 21show the speed and torque profiles for the CSVL drive cycle. Thetorque has a heavy transient response, but the FRM is able to con-trol to the target torque with an RMSE value of 21 Nm. As shown inFig. 22, the EGR values track the target values well, with a RMSEvalue of 0.002.

As shown in Figs. 21 and 22, the FRM is able to match the targetvalues for torque, EGR fraction. The transient EGR and tailpipe tem-peratures along with their respective mass flow rates are subse-quently used as inputs to the ORC-WHR model. Reduction of thefully detailed engine model to a simplified, FRM, retains thedesired model performance characteristics while reducing compu-tational time from 16 h to 1.33 h (a factor of 12) for the 1200 stransient drive cycle duration. The CSVL cycle data will be testedon the transient engine dynamometer to validate the model inthe future.

Fig. 20. Speed profile over CSVL heavy-duty engine driving cycle.

Fig. 21. Torque tracking performance by FRM (actual) over CSVL heavy-duty enginedriving cycle (target).

7. ORC-WHR system simulation over a transient driving cycle

The engine model is connected with the Simulink ORC-WHRmodel utilizing the GT-POWER Simulink interface. A GT-POWER library needs to be added in the Simulink library. Then,the GT-POWER model is imported to the Simulink environmentand connected. The input to the GT-POWER block is ORC net powerand the outputs from GT-POWER block are TP/EGR mass flow ratesand temperatures. The co-simulation is conducted in Simulink

environment. The ORC-WHR system is initialized in warm condi-tion. Three PID controllers are utilized to control the mixed vaportemperature, the vapor temperature difference between two evap-orators, and the turbine upstream pressure. The turbine upstreampressure is controlled by the turbine bypass valve to maintain safeoperation, i.e. the bypass valve opens only when the pressure isabove the safety limit. The turbine inlet valve is simulated withonly on/off binary position control. It opens when mixed vaporquality is above 1.05 and closes when mixed vapor quality is below1.05.

Eacct Z t0Pturbsds 7:1

Predicted exhaust gas mass flow rate and temperatures areshown in Fig. 23. Due to the mean EGR rate being around 18%,the TP exhaust gas mass flow rate is much greater than EGRexhaust gas. The ORC-WHR model results are shown in Fig. 24.All the results are normalized based on the maximum value, exceptvapor quality. Cumulative energy is calculated based on Eq. (7.1).The normalized cumulative energy profile along the cycle is shownin Fig. 24b. It is observed that the slope of cumulative energyincreases around 500600 s, as a consequence of the higher wasteheat power during that time span (see Fig. 23a and b). In Fig. 24c,pump power consumption is negligible compared with ORC netpower generation. Working fluid mass flow rate is directly relatedto the net ORC power generation, see Fig. 24a and c. During theperiod of 050 s, 150200 s, 650700 s, and 11801200 s, theexhaust gas mass flow rate is small and turbine power is corre-spondingly low during these periods. Additionally, turbine inletpressure is directly related to the working fluid mass flow rate,as shown in Fig. 24a and f. This behavior is expected, since the tur-bine experiences high expansion ratios and operates in chokedflow mode. Vapor quality indicates the phase status of the working

Fig. 23. TP and EGR exhaust gas conditions: (a) normalized exhaust gas mass flowrate, and (d) normalized exhaust gas temperature. (All parameters are normalizedby their maximum absolute value.)


fluid at the outlet junction of the parallel evaporators. This is a crit-ical index, since the information about the vapor quality cannot bedirectly inferred from the outlet vapor temperature during real-world operation. Fig. 24e shows that vapor quality maintains val-ues greater than 1.0, i.e. working fluid is entirely vaporized throughthe whole cycle.

Predictions of the ORC-WHR performance over the completeCSVL duty cycle reveal the ability of the dynamic ORC-WHR modelto capture variations of highly transient phenomena. The system

Fig. 24. CSVL driving cycle ORC-WHR simulation results: (a) pump working fluid mass flo(e) mixed vapor quality and (f) working fluid evaporation pressure. (All the parameters awhich is the actual value is plotted.) Fig. A1. PSO Principle (determination of the direcposition, personal visited optimal position, and global visited optimal position).

studied in this paper maintains the mixed vapor temperaturearound the set point (0.9, see Fig. 24d), except for periods of highlydynamic engine torque variations between 400 and 800 s. This pro-vides impetus for future work on a more advanced controller, e.g. amodel-based controller. The mixed vapor quality is maintainedabove 1.0 throughout the whole cycle, thus avoiding saturationand enabling safe and uninterrupted turbine operation.

8. Conclusions

This paper presents a dynamic ORC-WHR system model, whichincludes seven types of components: heat exchangers, pumps,valves, compressible volumes, a turbine expander, junctions, anda reservoir. Mass balance, energy balance and momentum balanceare established in the heat exchanger model. Detailed expressionsof heat transfer coefficients for both the exhaust gas and workingfluid within the evaporator are developed. Pressure drop expres-sions along the heat exchanger are derived for each working fluidphase. The two mass flow distribution valves are calibrated undertransient conditions, while the remaining component models arecalibrated in steady state. Subsequently, the models are integratedto create a complete ORC-WHR system simulation. Details of theinlet and outlet parameters for each component model are given.

The dynamic ORC-WHR system is validated over transientengine operating conditions, namely step-changes of enginespeed/torque. Results show that the mixed vapor temperatureand evaporation pressure can be predicted within 2% and 3% meanerror, respectively.

A physics-based, one-dimensional engine model is constructedusing the GT-POWER software platform. The model creates a vir-tual 13 L heavy-duty diesel engine, and enables co-simulation with

w rate, (b) accumulated energy, (c) net power, (d) working fluid vapor temperature,re normalized by their maximum absolute value except for mixed vapor quality, fortion and speed of a particle movement based on current position, last generation


Simulink ORC-WHR model to simulate a transient CSVL cycle. Theengine model is experimentally calibrated and subsequently vali-dated for different operating conditions.

The dynamic ORC-WHR system Simulink model is co-simulatedwith GT-POWER engine model over the transient CSVL cycle andthe model capability is demonstrated.

The system model developed in this paper will be utilized toassist algorithm development for optimized ORC-WHR transientsystem control. In addition, this model will serve as a virtual plantin off-line simulations to explore the potential of fuel economysavings and emission reduction at different heavy-duty truck driv-ing cycles and provide guidelines for the experimental studies.

Acknowledgment

The work contained herein was conducted under a sponsoredresearch grant between BorgWarner Inc. and Clemson University.

Fig. A1. PSO Principle (determination of the direction and speed of a particlemovement based on current position, last generation position, personal visitedoptimal position, and global visited optimal position).

Appendix A

The key of PSO is the update of particle velocity and position,which can be expressed as follows:

vk1i Ikvki a1c1;i Pi xki a2c2;i S xki A:1

xk1i xki vk1i A:2

where v is the velocity, k is the generation, i is the ith particle/indi-vidual, I is the particle inertia which gives rise to a certain momen-tum of the particles, a1;2 are the acceleration constants, c1;2 2 0;1are uniformly distributed random value, Pi is the history optimalposition visited by ith particle up to the current generation, S isthe global optimal position visited by the whole particle society.Eqs. (A.1) and (A.2) can be explained by Fig. A1, where it is shownhow the next position of certain particle is determined based on

Table B1Initial condition for tp and egr evaporators (each row represents a discretized cell).

Name Working fluid enthalpy Wall temperature Exhaust gas enthalpyUnit J/kg K J/kg

1 335879.2 377.5 502113.82 383800.1 386.0 508072.73 430054.7 394.9 513859.84 474539.3 403.8 519445.85 517232.8 412.5 524817.96 558163.1 421.0 529973.87 597387.6 429.2 534916.88 634981.5 437.0 539653.79 671031.2 444.5 544193.710 705630.2 451.6 548547.311 738877.8 458.3 552725.612 770878.4 464.6 556740.713 804774.7 464.0 560605.314 841552.7 461.5 564698.815 880672.4 460.5 569140.316 922052.2 460.0 573864.517 965712.6 459.6 578861.818 1011715.7 459.3 584134.419 1060145.7 459.1 589690.020 1111101.1 459.0 595538.621 1164632.2 458.9 601692.222 1220683.5 458.9 608156.923 1279316.0 458.9 614925.924 1340336.0 459.7 622006.725 1390832.6 488.5 629375.826 1436955.3 503.0 635474.027 1479057.2 516.4 641044.028 1517473.7 528.5 646128.429 1552518.4 539.7 650767.830 1584481.9 549.9 654999.9

the three terms: (i) Ikvki : particle inertia in the direction of speed;(ii) a1c1;i Pi xki

: personal optimal position visited by

ith particle; (iii) a2c2;iS xki : global optimal position visited bythe whole population. The turning angle from current position tonext step position is H, and the speed is kxk1i xki k.

Appendix B

Initial condition for TP and EGR evaporators are given inTable B1:

Working fluid enthalpy Wall temperature Exhaust gas enthalpyJ/kg K J/kg

319871.6 357.7 410534.8353045.3 365.2 418131.7385681.6 372.7 425631.2417720.6 380.2 433009.2449134.1 387.6 440252.1479916.4 394.8 447353.5510077.3 401.9 454312.0539637.1 408.9 461130.0568623.6 415.7 467812.0597070.5 422.4 474364.4625016.1 428.9 480794.7652502.3 435.2 487111.6679575.4 441.4 493324.6706286.0 447.4 499444.1732689.9 453.3 505481.7758850.2 459.0 511449.9784839.4 464.6 517363.1816975.6 462.1 523237.6854950.1 461.2 530502.9899220.8 460.9 539087.9950602.5 460.9 549096.31010124.5 461.1 560712.21079015.4 461.3 574168.41158707.4 461.6 589742.61250362.2 462.1 607758.51353295.4 464.9 628478.91429364.6 518.7 651747.71498914.9 541.4 668941.21562614.3 562.0 684661.21621019.2 580.8 699058.9


References

[1] Nelson CR. Exhaust Energy Recovery. Presented at the Presentation at USDOEDirections in Engine-Efficiency and Emissions Research Conference; 2010.

[2] Park T, Teng H, Hunter GL, van der Velde B, Klaver J. A Rankine Cycle System forRecovering Waste Heat from HD Diesel Engines Experimental Results. SAEInternational, Warrendale, PA 2011-01-1337, 2011/04// 2011.

[3] Dieter S, Thomas L, Jurgen G, Nadja E, Michael H, Ilona K. Waste heat recoveryfor commercial vehicles with a rankine process. In: 21st Aachen ColloquiumAutomobile and Engine technology; 2012.

[4] Crane D, Jackson G, Holloway D. Towards optimization of automotive wasteheat recovery using thermoelectrics. SAE International, Warrendale, PA, SAETechnical Paper 2001-01-1021, 2001/03/05; 2001.

[5] Hendricks TJ, Lustbader JA. Advanced thermoelectric power systeminvestigations for light-duty and heavy duty applications. I. In: Twenty-FirstInternational Conference on Thermoelectrics, 2002. Proceedings ICT 02; 2002.p. 3816.

[6] Zhou Minfeng HYaCY. Numerical simulation of the thermoelectric model onvehicle turbocharged diesel engine intercooler. Res J Appl Sci Eng Technol, p. 5,2014/08/02/18:27:12 2013.

[7] Edwards KD, Wagner R, Briggs T. Investigating potential light-duty efficiencyimprovements through simulation of turbo-compounding and waste-heatrecovery systems. SAE International, Warrendale, PA, SAE Technical Paper2010-01-2209, 2010/10/25; 2010.

[8] Hountalas DT, Katsanos CO, Lamaris VT. Recovering energy from the dieselengine exhaust using mechanical and electrical turbocompounding. SAEInternational, Warrendale, PA, SAE Technical Paper 2007-01-1563, 2007/04/16; 2007.

[9] Ismail Y, Durrieu D, Menegazzi P, Chesse P, Chalet D. Potential of exhaust heatrecovery by turbocompounding. SAE International, Warrendale, PA, SAETechnical Paper 2012-01-1603, 2012/09/10; 2012.

[10] Xu B, Yebi A, Onori S, Filipi Z, Liu X, Shutty J, et al. Power maximization of aheavy duty diesel organic Rankine cycle waste heat recovery system utilizingmechanically coupled and fully electrified turbine expanders. In: Proceedingsof the ASME 2016 Internal Combustion Fall Technical Conference, Greenville,SC, USA; 2016. p. 11.

[11] Arias DA, Shedd TA, Jester RK. Theoretical analysis of waste heat recovery froman internal combustion engine in a hybrid vehicle. SAE Technical Paper 0148-7191; 2006.

[12] Delgado O, Lutsey N. The U.S supertruck program: expediting the developmentof advanced heavy-duty vehicle efficiency technologies. The InternationalCouncil on Clean Transportation; 2014.

[13] Feru E, de Jager B, Willems F, Steinbuch M. Two-phase plate-fin heat exchangermodeling for waste heat recovery systems in diesel engines. Appl Energy2014;133:18396.

[14] Peralez J, Tona P, Lepreux O, Sciarretta A, Voise L, Dufour P, et al. Improving thecontrol performance of an organic Rankine cycle system for waste heatrecovery from a heavy-duty diesel engine using a model-based approach. 2013Ieee 52nd Annual Conference on Decision and Control (Cdc); 2013. p. 68306836.

[15] Quoilin S, Aumann R, Grill A, Schuster A, Lemort V, Spliethoff H. Dynamicmodeling and optimal control strategy of waste heat recovery organic Rankinecycles. Appl Energy 2011;88:218390. 2011.

[16] Yebi A, Xu B, Liu X, Shutty J, Anschel P, Onori S, et al. Nonlinear modelpredictive control of a parallel evaporator waste heat recovery system forheavy-duty diesel engines applications. In: Proceedings of ASME DynamicSystem and Control Conference, Minneapolis, Minnesota, USA; 2016.

[17] Peralez J, Tona P, Sciarretta A, Dufour P, Nadri M. Towards model-based controlof a steam Rankine process for engine waste heat recovery. 2012 Ieee VehiclePower and Propulsion Conference (Vppc); 2012. p. 28994.

[18] Zhang JH, Gao S, Chen YN, Hou GL. Multivariable robust control for organicRankine cycle based waste heat recovery systems. In: Proceedings of the 2013

IEEE 8th Conference on Industrial Electronics and Applications (Iciea); 2013. p.8589.

[19] Esposito MC, Pompini N, Gambarotta A, Chandrasekaran V, Zhou J, Canova M.Nonlinear model predictive control of an organic Rankine cycle for exhaustwaste heat recovery in automotive engines. IFAC-PapersOnLine2015;48:4118.

[20] Jensen JM. Dynamic modeling of thermo-fluid systems with focus onevaporators for regrigeration PhD. Department of Mechanicla Engineering,Technical University of Denmark; 2003.

[21] Yousefzadeh M, Uzgoren E. Mass-conserving dynamic organic Rankine cyclemodel to investigate the link between mass distribution and system state.Energy 2015;93:112839.

[22] Wei D, Lu X, Lu Z, Gu J. Dynamic modeling and simulation of an OrganicRankine Cycle (ORC) system for waste heat recovery. Appl Therm Eng2008;28:121624.

[23] Benato A, Krn MR, Pierobon L, Stoppato A, Haglind F. Analysis of hot spots inboilers of organic Rankine cycle units during transient operation. Appl Energy2015;151:11931.

[24] Casella F, Leva A. Modelica open library for power plant simulation: design andexperimental validation. In: Proceeding of the 2003 Modelica conference,Linkoping, Sweden; 2003.

[25] Feru E, Willems F, de Jager B, Steinbuch M. Modeling and control of a parallelwaste heat recovery system for Euro-VI heavy-duty diesel engines. EnergiesOct 2014;7:657192.

[26] Carey VP. Liquid vapor phase change phenomena: an introduction to thethermophysics of vaporization and condensation processes in heat transferequipment. 2nd ed. New York: CRC Press; 2007.

[27] Blasius H. Das Aehnlichkeitsgesetz bei Reibungsvorgngen in Flssigkeiten. In:Mitteilungen ber Forschungsarbeiten auf dem Gebiete desIngenieurwesens. Berlin Heidelberg: Springer; 1913. p. 141.

[28] Reynolds O. An experimental investigation of the circumstances whichdetermine whether the motion of water shall be direct or sinuous, and ofthe law of resistance in parallel channels. Philos Trans R Soc Lond1883;174:93582. 1883/01/01.

[29] Gnielinski V. Berechnung des Druckverlustes in glatten konzentrischenRingspalten bei ausgebildeter laminarer und turbulenter isothermerStrmung. Chem Ing Tec 2007;79:915. 2007/02/01.

[30] Bla E, Chemieingenieurwesen GVu. VDI-Gesellschaft Verfahrenstechnik undChemieingenieurwesen GVC: gestern, heute, morgen; eine Jubilumsschriftanllich des Jahrestreffens der Verfahrensingenieure 1984 in Mnchen zum50-jhrigen Bestehen der GVC: Saur; 1984.

[31] Bergman TL, Incropera FP, Lavine AS. Fundamentals of heat and masstransfer. John Wiley & Sons; 2011.

[32] Hemodynamics in sinuous cerebral aneurysms: a numerical study.Biorheology 42;2005:1234.

[33] Vetter G. Rotierende Verdrngerpumpen fr die Prozesstechnik. Vulkan-VerlagGmbH; 2006.

[34] Weiss HH, Boshwirth L. A simple but efficient equipment for experimentaldetermination of valve loss coefficient under compressible and steady flowcondtions. In: International Compressor Engineering Conference; 1982. p. 6976.

[35] Michael JM, Howard NS. Fundamentals of engineering thermodynamics. 5thed. John Wiley & Sons, Inc; 2006.

[36] Eberhart RC, Kennedy J. A new optimizer using particle swarm theory. In:Proceedings of the sixth international symposium on micro machine andhuman science; 1995. p. 3943.

[37] Ebbesen S, Kiwitz P, Guzzella L. A generic particle swarm optimization matlabfunction. 2012 American Control Conference (Acc); 2012. p. 15191524.

[38] Xu B, Liu X, Shutty J, Anschel P, Onori S, Filipi Z, et al. Physics-based modelingand transient validation of an organic Rankine cycle waste heat recoverysystem for a heavy-duty diesel engine. SAE Technical Paper 0148-7191; 2016.

http://refhub.elsevier.com/S0306-2619(17)30911-X/h0065http://refhub.elsevier.com/S0306-2619(17)30911-X/h0065http://refhub.elsevier.com/S0306-2619(17)30911-X/h0065http://refhub.elsevier.com/S0306-2619(17)30911-X/h0075http://refhub.elsevier.com/S0306-2619(17)30911-X/h0075http://refhub.elsevier.com/S0306-2619(17)30911-X/h0075http://refhub.elsevier.com/S0306-2619(17)30911-X/h0095http://refhub.elsevier.com/S0306-2619(17)30911-X/h0095http://refhub.elsevier.com/S0306-2619(17)30911-X/h0095http://refhub.elsevier.com/S0306-2619(17)30911-X/h0095http://refhub.elsevier.com/S0306-2619(17)30911-X/h0100http://refhub.elsevier.com/S0306-2619(17)30911-X/h0100http://refhub.elsevier.com/S0306-2619(17)30911-X/h0100http://refhub.elsevier.com/S0306-2619(17)30911-X/h0105http://refhub.elsevier.com/S0306-2619(17)30911-X/h0105http://refhub.elsevier.com/S0306-2619(17)30911-X/h0105http://refhub.elsevier.com/S0306-2619(17)30911-X/h0110http://refhub.elsevier.com/S0306-2619(17)30911-X/h0110http://refhub.elsevier.com/S0306-2619(17)30911-X/h0110http://refhub.elsevier.com/S0306-2619(17)30911-X/h0115http://refhub.elsevier.com/S0306-2619(17)30911-X/h0115http://refhub.elsevier.com/S0306-2619(17)30911-X/h0115http://refhub.elsevier.com/S0306-2619(17)30911-X/h0115http://refhub.elsevier.com/S0306-2619(17)30911-X/h0125http://refhub.elsevier.com/S0306-2619(17)30911-X/h0125http://refhub.elsevier.com/S0306-2619(17)30911-X/h0125http://refhub.elsevier.com/S0306-2619(17)30911-X/h0130http://refhub.elsevier.com/S0306-2619(17)30911-X/h0130http://refhub.elsevier.com/S0306-2619(17)30911-X/h0130http://refhub.elsevier.com/S0306-2619(17)30911-X/h0135http://refhub.elsevier.com/S0306-2619(17)30911-X/h0135http://refhub.elsevier.com/S0306-2619(17)30911-X/h0135http://refhub.elsevier.com/S0306-2619(17)30911-X/h0140http://refhub.elsevier.com/S0306-2619(17)30911-X/h0140http://refhub.elsevier.com/S0306-2619(17)30911-X/h0140http://refhub.elsevier.com/S0306-2619(17)30911-X/h0140http://refhub.elsevier.com/S0306-2619(17)30911-X/h0145http://refhub.elsevier.com/S0306-2619(17)30911-X/h0145http://refhub.elsevier.com/S0306-2619(17)30911-X/h0145http://refhub.elsevier.com/S0306-2619(17)30911-X/h0155http://refhub.elsevier.com/S0306-2619(17)30911-X/h0155http://refhub.elsevier.com/S0306-2619(17)30911-X/h0165http://refhub.elsevier.com/S0306-2619(17)30911-X/h0165http://refhub.elsevier.com/S0306-2619(17)30911-X/h0175http://refhub.elsevier.com/S0306-2619(17)30911-X/h0175

Transient dynamic modeling and validation of an organic Rankine cycle waste heat recovery system for heavy duty diesel engine applications1 Introduction1.1 ORC system modeling methods1.2 Prior ORC modeling efforts1.3 Uniqueness of the current work

2 System configuration3 System modeling3.1 Heat exchanger modeling3.1.1 Pressure drop in the evaporator3.1.2 Heat transfer coefficients

3.2 Pump3.3 Valves3.3.1 Valves experiencing incompressible flow3.3.2 Valves experiencing compressible flow

3.4 Compressible vapor volume3.5 Turbine expander3.6 Reservoir3.7 Pipe junctions

4 Model identification4.1 Turbine4.2 Valves manipulating incompressible liquid4.3 Valves manipulating compressible vapor4.4 Heat exchangers

5 Model validation6 Engine modeling and validation7 ORC-WHR system simulation over a transient driving cycle8 ConclusionsAcknowledgmentAppendix AAppendix BReferences

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