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Applied Energy 205 (2017) 260279
Contents lists available at ScienceDirect
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
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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.
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B. Xu et al. / Applied Energy 205 (2017) 260279 263
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
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264 B. Xu et al. / Applied Energy 205 (2017) 260279
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
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B. Xu et al. / Applied Energy 205 (2017) 260279 265
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]:
-
266 B. Xu et al. / Applied Energy 205 (2017) 260279
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
-
B. Xu et al. / Applied Energy 205 (2017) 260279 267
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
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268 B. Xu et al. / Applied Energy 205 (2017) 260279
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.
B. Xu et al. / Applied Energy 205 (2017) 260279 269
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
-
270 B. Xu et al. / Applied Energy 205 (2017) 260279
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
B. Xu et al. / Applied Energy 205 (2017) 260279 271
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
272 B. Xu et al. / Applied Energy 205 (2017) 260279
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.)
B. Xu et al. / Applied Energy 205 (2017) 260279 273
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
274 B. Xu et al. / Applied Energy 205 (2017) 260279
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.
B. Xu et al. / Applied Energy 205 (2017) 260279 275
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).
276 B. Xu et al. / Applied Energy 205 (2017) 260279
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.)
B. Xu et al. / Applied Energy 205 (2017) 260279 277
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
-
278 B. Xu et al. / Applied Energy 205 (2017) 260279
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
-
B. Xu et al. / Applied Energy 205 (2017) 260279 279
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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