energies
Article
Numerical Analysis of an Organic Rankine Cycle
with Adjustable Working Fluid Composition,
a Volumetric Expander and a Recuperator
Peter Collings and Zhibin Yu *
School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK; [email protected]
* Correspondence: [email protected]; Tel.: +44-141-330-2530
Academic Editor: Andrew J. Haslam
Received: 31 January 2017; Accepted: 22 March 2017; Published: 27 March 2017
Abstract: Conventional Organic Rankine Cycles (ORCs) using ambient air as their coolant cannot
fully utilize the greater temperature differential available to them during the colder months. However,
changing the working fluid composition so its boiling temperature matches the ambient temperature
as it changes has been shown to have potential to increase year-round electricity generation. Previous
research has assumed that the cycle pressure ratio is able to vary without a major loss in the isentropic
efficiency of the turbine. This paper investigates if small scale ORC systems that normally use
positive-displacement expanders with fixed expansion ratios could also benefit from this new
concept. A numerical model was firstly established, based on which a comprehensive analysis
was then conducted. The results showed that it can be applied to systems with positive-displacement
expanders and improve their year-round electricity generation. However, such an improvement is
less than that of the systems using turbine expanders with variable expansion ratios. Furthermore,
such an improvement relies on heat recovery via the recuperator. This is because expanders with
a fixed expansion ratio have a relatively constant pressure ratio between their inlet and outlet.
The increase of pressure ratio between the evaporator and condenser by tuning the condensing
temperature to match colder ambient condition in winter cannot be utilised by such expanders.
However, with the recuperator in place, the higher discharging temperature of the expander could
increase the heat recovery and consequently reduce the heat input at the evaporator, increasing the
thermal efficiency and the specific power. The higher the amount of heat energy transferred in the
recuperator, the higher the efficiency improvement.
Keywords: dynamic; Organic Rankine Cycle; positive displacement expander; zeotropic fluid; recuperator
1. Introduction
Global energy use is predicted to continue to grow over the coming decades. Diminishing fossil
fuel reserves and concerns about climate change mean that this extra energy demand will have to be
supplied from non-conventional sources, many of which provide heat at temperatures too low to be
exploited with traditional methods. Steam power plants become uneconomical for heat sources with
temperatures below 400 ◦ C due to declining efficiency combined with increasing component sizes
due to low-pressure operation [1,2]. Several alternative methods exist for exploiting heat sources at
such low temperatures, including the Stirling Cycle, Organic Rankine Cycle (ORC), and Kalina Cycle.
However, Bianchi and De Pascale [3] have identified the Organic Rankine Cycle as the most promising
technology for their utilisation. Typical heat sources for the Organic Rankine Cycle include solar,
geothermal, biomass and industrial waste heat [4]. These heat sources have temperatures ranging
from 80 ◦ C for solar ponds, to over 500 ◦ C for high-grade industrial waste heat [4], of which most exist
at temperatures between 100 ◦ C and 300 ◦ C [5,6].
Energies 2017, 10, 440; doi:10.3390/en10040440
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Organic Rankine Cycles replace water with an organic working fluid, which can exhibit superior
thermal characteristics at low temperatures [7]. Most cycles use pure, single-component working
fluids [8,9], however, there is also the potential to use a working fluid mixture. Organic Rankine
Cycles are a relatively mature technology, with some market penetration, especially for geothermal
applications. Their efficiency is often improved by the utilisation of a recuperative cycle [10,11],
in which an internal heat exchanger is used to recover thermal energy from the expander exhaust
that would otherwise be rejected in the condenser and use it to preheat the working fluid before it
enters the evaporator. In this way, the heat that would otherwise be rejected from the cycle through
the condenser is used to reduce the demand for input energy in the evaporator.
Drescher and Brüggemann [12] performed an in-depth analysis of working fluids for biomass
ORCs, between temperatures of 90 ◦ C and 350 ◦ C, finding a maximum efficiency of 25% for a
recuperative cycle operating towards the higher end of this range. Andreasen et al. [13] performed a
working fluid screening for lower heat source temperatures of 90 ◦ C and 120 ◦ C, with a maximum
efficiency of 10.3% for the higher temperature heat source. Bruno et al. [14] analysed solar powered
ORCs for reverse osmosis desalination, and found that the efficiency of the cycle strongly depended
on the selection of working fluid, and also the heat source temperature, varying from 7% to over 30%
at the highest heat source temperatures.
Organic Rankine Cycles do suffer from several issues. Firstly, the constant temperature during
phase change increases the temperature mismatch in the heat exchangers, increasing exergy destruction,
and reducing the utilisation of the heat source for non-isothermal heat sources and sinks [15].
Yu et al. [16] identified a linear relationship between the integrated average temperature difference
in the heat exchanger and the rate of exergy destruction. Secondly, the choice of pure working
fluid is limited, meaning that not every application has an ideal working fluid. Organic Rankine
Cycles are generally designed with a working fluid to match the temperatures of the heat source and
heat sinks. Xu and Yu [17] showed that the efficiency of a subcritical ORC is related to the critical
temperature of the working fluid. They found that the cycles tended to be less efficient when the
difference between the heat source temperature and the critical temperature of the fluid becomes
greater. Single-component working fluids have a particular critical temperature, and so if the critical
temperature doesn’t match the operational conditions, a loss in efficiency will result. Thirdly, the small
temperature differential provided by a low-enthalpy heat source means that the cycles are very
sensitive to changing temperature of coolant, which can be proportionally significant compared to
the cycle’s driving temperature differential. This has been identified as a problem hindering thermal
cycles across the world [18]. It is of particular concern for cycles using air-cooled condensers, which are
common for applications where portability or modularity is considered important, or where cooling
water is too scarce or expensive. The heat sink for these cycles is the ambient air which, in continental
climates, can vary in temperature by over 50 ◦ C between summer and winter, and also a significant
amount between day and night, as shown in previous research by the authors [19].
A cycle designed to operate in such conditions must ensure that liquid working fluid is fed to the
pump at all times, as to allow vapour to be ingested into the pump compromises its efficiency and can
even lead to damage due to cavitation. This requires a high condenser pressure, which means that
when the ambient air is at a lower temperature, the cycle must either reduce the flow rate of coolant,
or operate with significant subcooling at the pump outlet, which increases the heat energy required in
the evaporator without any corresponding increase in expander work, reducing the cycle’s efficiency.
This means that for much of the year, the cycle is operating at off-design conditions.
The authors have recently proposed that these issues can be solved by the concept of a dynamic
ORC, capable of adjusting the composition of the working fluid during operation to match the changing
ambient conditions [20]. When two working fluids are combined, they can generally form what is
known as a zeotropic mixture [21]. This means that, instead of undergoing phase change at a constant
temperature, like pure, single-component fluids, they instead exhibit a temperature change during
phase change, known as “glide”. The lower temperature end of the phase change is known as the
Energies 2017, 10, 440
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bubble point, and the higher temperature end is known as the dew point. The bubble and dew points
of a zeotropic mixture lie between the boiling points of its two constituent parts. This means that with
two components having different boiling points, a zeotropic mixture with a specific bubble or dew
point temperature in between these two points can be formed by mixing them together. Given the
right working fluid components, this can ensure that the pump in an Organic Rankine Cycle system is
fed liquid for any ambient temperature between these two points. Several sources have concerned
themselves with the efficiency of cycles using zeotropic mixtures as the working fluids, and found that
they only cause a slight drop in cycle first law efficiency, while resulting in an increase in other metrics,
such as heat source utilisation [22–24].
The proposed dynamic ORC system builds on this concept, by allowing the working fluid’s
composition to be actively tuned during operation of the rig, using R245fa and R134a as the two
components of the working fluid. These fluids are two commonly-selected ones for conventional
Organic Rankine Cycles [25–27], are miscible with each other [28], and the difference between their
boiling points is roughly equal to the annual variation in temperature in a continental climate, making
them the most suitable for an initial analysis of this cycle. However, both of these fluids are HFCs
(Hydrofluorocarbons), and this class of refrigerants has recently been subject to a phase-out decision
over the coming decades due to their high Global Warming Potential. For a dynamic cycle, the key
factor in the choice of fluids is an appropriate difference between their boiling points. Alternatives to
HFCs do exist, and are presented below.
Alkanes are a promising class of working fluid, and in particular pentane and isopentane have
been used in real-world cycles [2]. Alkanes tend to be relatively dry working fluids, meaning that they
are particularly suitable to the presence of a recuperator. They are also flammable, which means that
special care must be taken with their handling, Alkanes are a large class of refrigerants and this means
that working fluid pairs for a great variety of ambient conditions can be selected.
HFOs (Hydrofluoro-olefins) are another fluid group under consideration in literature as a direct
replacement for HFCs. R1233zd-E is the HFO replacement for R245fa [29], and R1234yf and R1234ze
have been considered as replacements for R134a [27,30]. HFOs have very similar properties to HFCs,
often being considered as “drop-in” replacements. R1233zd has been shown to give slightly higher
thermal efficiencies than R245fa under the same operating conditions, whereas R1234yf showed slightly
reduced power output due to lower density at the expander inlet. Overall they are likely to be no
less suited to use in a dynamic ORC than the HFCs considered in this paper, but an investigation of
alternative working fluids is an interesting avenue of further research.
The cycle is initially designed to operate on the hottest day of the year with the working fluid
composed entirely of R245fa, the fluid component with the higher boiling point. As the temperature
drops from summer to autumn, the temperature of the coolant available to the cycle also drops.
This gives excess cooling capacity. The composition of the working fluid is then adjusted by removing
fluid from the receiver and replacing it with pure R134a, shifting the overall composition towards
R134a. This lowers the bubble point of the fluid, and allows better utilisation of the coolant. As the
temperature drops further, the composition is shifted further towards R134a. The fluid mixture
removed from the system is separated by distillation to produce pure R134a and R245fa, which can
then be used in further composition tuning operations. In the spring, when temperatures begin to rise
again, the available coolant is no longer cold enough to ensure the working fluid is liquid at the pump
inlet. Now the composition of the working fluid is shifted back towards R245fa, raising the bubble
point of the fluid and ensuring the liquid condition at the pump inlet.
The previous paper [19] considered a cycle using a turbine as the expander, and assumed that
such a cycle can relatively simply adjust its evaporating pressure in operation by changing the shaft
load on the turbine and increasing the pump power accordingly, with little change in the turbine’s
isentropic efficiency. This allows the pressure ratio of the cycle to be changed in operation, increasing
the evaporator pressure when the working fluid is mostly composed of R134a to minimise excess
superheat. The results of this paper [19] showed a significant increase in the year-round electricity
Energies 2017, 10, 440
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generation of a dynamic cycle compared to a conventional one. An economic analysis of the dynamic
cycle was also carried out, using the Chemical Engineering Plant Cost Index (CEPCI). This revealed
that the additional cost of a composition tuning system capable of distilling the system’s entire charge
of working fluid in 12 h was roughly 0.4% of the total cost of the system, and that the greatest increase
in the capital cost of a dynamic system would come from the need to have a supply of extra working
fluid for tuning purposes, which would add a further 6% to the cost of the cycle. The increased cost of
the system was offset by increased electricity generation. For any increase greater than 7% the payback
period of the cycle was shortened and the 20-year return on investment increased.
However, turbines become uneconomical for smaller-scale applications below a few hundred
kilowatts, and are outcompeted by positive displacement expansion devices, such as scroll, screw,
and rotary vane expanders [30]. Quoilin et al. [31] have calculated the minimum economical operating
power for a turbine in an ORC system to be roughly 40 kW for solar thermal applications, rising to
over 100 kW for geothermal. This leaves a large amount of microgeneration applications for which
turbines are unsuited as expanders.
Positive displacement devices generally have an inbuilt volume ratio, which is constrained
by their geometry. The isentropic efficiency of these devices drop off sharply if a pressure ratio
different to that defined by an adiabatic expansion process between these volumes is imposed [32–34].
This pressure ratio is hereafter referred to as the “designed pressure ratio”. The working fluid in the
expander is enclosed in an expansion chamber. In each case, the enclosed volume of working fluid
will reach the discharge stage at a pressure defined primarily by the geometry of the expander. If this
pressure is not equal to the condenser pressure, the fluid will undergo an isochoric pressure drop
(i.e., under-expansion) or increase (i.e., over expansion). In the case of under-expansion, when the
in-built volume ratio of the expander could provide a pressure ratio less than the actual pressure ratio
between the evaporator and condenser, this will result in unused potential of the working fluid. In the
case of over-expansion, when the in-built volume ratio of the expander could provide a pressure ratio
greater than the actual pressure ratio between the evaporator and condenser, work will have to be
expended by the expander to repressurise the fluid to the condenser pressure. Therefore, the previous
approach to the dynamic cycle using a turbine as the expansion device is not applicable to small-scale
ORC systems.
As the considerations for designing ORC systems with positive displacement expanders are
significantly different from those with turbines, this paper expands on the previous work by investigating
whether the dynamic ORC concept can be applied to systems using a positive displacement expander
which is constrained to a specific expansion ratio (ultimately pressure ratio). It analyses the system
under a variety of ambient conditions, heat source temperatures and cycle configurations, both
recuperative and non-recuperative to determine the feasibility of the development of dynamic Organic
Rankine Cycle systems using positive displacement expanders having a fixed expansion ratio. It also
adds an analysis of recuperative cycles applied to this dynamic concept, as well as an analysis of the
specific power of the cycle and how this is affected by the changing working fluid composition in
response to changing ambient temperature.
2. Numerical Modelling
As shown in Figure 1, a dynamic Organic Rankine Cycle consists of the same major components
as a standard Organic Rankine Cycle, namely the evaporator, expander, condenser, recuperator,
and pump. In addition to these, the dynamic cycle has a composition tuning system attached to it.
In order to simplify the analysis in this paper, the composition tuning system was considered to be a
“black box”, capable of separating the working fluid into its two component parts, and reintroducing
measured amounts of these pure components into circulation in the system. It was assumed to have
no significant transient effects on the performance of the system as a whole apart from the change in
working fluid composition. In practice such a system would most likely be a small distillation column,
which is well-established technology. Previous research from the authors showed that the extra power
Energies 2017, 10, 440
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required for a distillation system to keep up with changing ambient conditions is negligible compared
to the overall power output of the cycle, as the average parasitic power required for separating and
compressing
Energies 2017, 10,the
440 distillate would be 23 W for a 1 MW system [19].
5 of 22
Figure
in this
this paper.
paper.
Figure 1.
1. Schematic
Schematic Diagram
Diagram of
of Dynamic
Dynamic Organic
Organic Rankine
Rankine Cycle
Cycle considered
considered in
There was assumed to be no pressure losses as the fluid passed through heat exchangers. This
There was assumed to be no pressure losses as the fluid passed through heat exchangers. This is a
is a common assumption, but does not entirely reflect real world systems accurately. Real-world
common assumption, but does not entirely reflect real world systems accurately. Real-world systems
systems will experience pressure drops, especially in heat exchangers. The primary effect of this is
will experience pressure drops, especially in heat exchangers. The primary effect of this is that the
that the pressure ratio at the expander inlet is reduced compared to the ideal case. A preliminary
pressure ratio at the expander inlet is reduced compared to the ideal case. A preliminary investigation
investigation assuming a 5% pressure drop in each heat exchanger, as was carried out in [34],
assuming a 5% pressure drop in each heat exchanger, as was carried out in [34], indicating that in a
indicating that in a recuperative cycle this would cause an 18% decrease in pressure ratio, and a 14%
recuperative cycle this would cause an 18% decrease in pressure ratio, and a 14% decrease in expander
decrease in expander power, while the evaporator heat load remained relatively constant. For a nonpower, while the evaporator heat load remained relatively constant. For a non-recuperative cycle,
recuperative cycle, the pressure ratio decreased by 14%, causing a 10% drop in expander power.
the pressure ratio decreased by 14%, causing a 10% drop in expander power. These pressure losses
These pressure losses must be carefully considered in the design of real-world systems. However, for
must be carefully considered in the design of real-world systems. However, for comparison of the
comparison of the dynamic and non-dynamic ORCs, the pressure losses will not have a major effect
dynamic and non-dynamic ORCs, the pressure losses will not have a major effect on the differences
on the differences caused by the working fluid composition.
caused by the working fluid composition.
Further assumptions were that there was no heat transfer to and from the system outside of heat
Further assumptions were that there was no heat transfer to and from the system outside of heat
exchangers (i.e., a perfectly insulated system), and no effects due to changes in velocity, elevation, or
exchangers (i.e., a perfectly insulated system), and no effects due to changes in velocity, elevation, or
compressibility. The work required to pump heat transfer fluids through the heat exchangers was
compressibility. The work required to pump heat transfer fluids through the heat exchangers was
neglected in this research. Based on these assumptions, a standard steady-state numerical model was
neglected in this research. Based on these assumptions, a standard steady-state numerical model was
built using MATLAB R2016a (Mathworks, Natick, MA, USA) and REFPROP 9.1 (National Institute
built using MATLAB R2016a (Mathworks, Natick, MA, USA) and REFPROP 9.1 (National Institute of
of Standards and Technology: Gaithersburg, MD, USA) [35]. REFPROP 9.1 was used to provide
Standards and Technology: Gaithersburg, MD, USA) [35]. REFPROP 9.1 was used to provide values
values for the thermophysical properties of the working fluid, and can be called via MATLAB
for the thermophysical properties of the working fluid, and can be called via MATLAB function. Given
function. Given a state defined by two fluid properties, this function can calculate most other
a state defined by two fluid properties, this function can calculate most other important thermal and
important thermal and physical properties of a fluid at this state.
physical properties of a fluid at this state.
Figure 2 shows the numbering convention for the points of the cycle, which are the same as those
Figure 2 shows the numbering convention for the points of the cycle, which are the same as
shown in Figure 1. An external data file containing average monthly ambient temperature data for a
those shown in Figure 1. An external data file containing average monthly ambient temperature data
variety of locations in different climate types was linked to the numerical model. The ambient
for a variety of locations in different climate types was linked to the numerical model. The ambient
temperature data from this data file could be used to determine the temperature of coolant available
temperature data from this data file could be used to determine the temperature of coolant available
to the system over the course of the year, which was stored as an array in MATLAB. Beijing, China
to the system over the course of the year, which was stored as an array in MATLAB. Beijing, China
was chosen to use as a case study as it is an example of a continental climate with a high variation in
was chosen to use as a case study as it is an example of a continental climate with a high variation
temperature between winter and summer. The output power for the case study was selected as 10
in temperature between winter and summer. The output power for the case study was selected as
kW. The pinch point temperature difference in the heat exchangers was taken to be 5 °C which is
10 kW. The pinch point temperature difference in the heat exchangers was taken to be 5 ◦ C which is
consistent with previous research [36,37], and an additional 2 °C of subcooling was added to the cycle
consistent with previous research [36,37], and an additional 2 ◦ C of subcooling was added to the cycle
at State 1 to ensure an adequate Net Positive Suction Head was provided to the pump. This allowed
at State 1 to ensure an adequate Net Positive Suction Head was provided to the pump. This allowed
the condition of the working fluid at State 1 to be characterised using the equations
=
+5
the condition of the working fluid at State 1 to be characterised using the equations T1 = Tambient + 5
and
=
at( = + 2).
and P1 = Psat at ( T = T1 + 2).
Energies 2017, 10, 440
Energies 2017, 10, 440
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6 of 22
435
3
Temperature (K)
415
395
375
355
2b
335
315
295
275
1000
4
2
4b
1
1200
1400
1600
1800
2000
Specific Entropy (J/kg.K)
Figure 2.
2. T-s diagram
ORC,
with
thethe
recuperative
portion
of theofcycle
marked
in a thicker
Figure
diagramofofa azeotropic
zeotropic
ORC,
with
recuperative
portion
the cycle
marked
in a
green
line.
thicker green line.
Knowing
Knowing the
the temperature
temperature of
of the
the fluid
fluid and
and the
the required
required saturation
saturation temperature
temperature allows
allows the
the
condenser
pressure
to
be
determined
for
the
hottest
day
of
the
year,
which
is
also
when
the
working
condenser pressure to be determined for the hottest day of the year, which is also when the working
fluid
fluid is
is composed
composedentirely
entirely of
of the
the working
workingfluid
fluid component
component with
with the
the higher
higher boiling
boilingpoint,
point,in
inthis
thiscase
case
study
studyR245fa.
R245fa.REFPROP
REFPROP9.1
9.1can
canthen
thenbe
beused
usedto
tocalculate
calculatethe
theother
otherfluid
fluid properties,
properties,such
suchas
as specific
specific
entropy,
and specific
specificenthalpy.
enthalpy.For
For
a given
pressure,
REFPROP
can be
also
be to
used
to calculate
the
entropy, and
a given
pressure,
REFPROP
can also
used
calculate
the bubble
bubble
and
dewofpoints
fluid
as its composition
changes,aallowing
a set
of glide
curves
the
and dew
points
a fluidofasaits
composition
changes, allowing
set of glide
curves
for the
fluid for
pairing
fluid
drawn up.
Knowing
required pressure
condenser
pressure
andof
thethe
shape
of the
to bepairing
drawn to
up.beKnowing
the
requiredthe
condenser
and
the shape
bubble
linebubble
of the
line
ofcurve,
the glide
the required
fluid composition
satisfy
thecondition
liquid condition
at the inlet
pumpcan
inlet
glide
thecurve,
required
fluid composition
to satisfytothe
liquid
at the pump
be
can
be calculated
any ambient
temperature
provided
to the numerical
calculated
for anyfor
ambient
temperature
provided
to the numerical
model.model.
With
condenserpressure
pressureand
andfluid
fluid
composition
determined,
the cycle
can then
be analysed
With the condenser
composition
determined,
the cycle
can then
be analysed
using
using
theworld
real world
climate
data provided,
according
to well-established
thermodynamic
techniques
the real
climate
data provided,
according
to well-established
thermodynamic
techniques
[19,38].
[19,38].
Thepoint
pinchtemperature
point temperature
in the evaporator
is to
taken
beas5 before,
°C as before,
a further
5
The pinch
in the evaporator
is taken
be 5to◦ C
and a and
further
5 ◦ C of
°C
of
superheat
is
added
at
the
expander
inlet
to
ensure
a
pure
vapour
with
no
droplets
is
fed
into
superheat is added at the expander inlet to ensure a pure vapour with no droplets is fed into the
the
expander,
allowing
the evaporator
to be calculated
using the
expander,
allowing
the evaporator
pressurepressure
to be calculated
using the equations
T3 equations
= Theat source −=5
and
= − 5).
and Pevap −
= 5Psat
at ( T = =
T3 − 5at(
).
This
the
evaporator
pressure
onon
thethe
hottest
dayday
of the
year,year,
and and
as the
Thislast
lastwas
wasused
usedtotocalculate
calculate
the
evaporator
pressure
hottest
of the
as
cycle
in this
studystudy
uses uses
a positive
displacement
expander,
this evaporator
pressure
was held
the cycle
in case
this case
a positive
displacement
expander,
this evaporator
pressure
was
year-round.
The isentropic
efficiency
of the
andand
thethe
expander
were
setset
toto90%
held year-round.
The isentropic
efficiency
of pump
the pump
expander
were
90%and
and70%,
70%,
respectively.
Asthe
thepressure
pressure
ratio
of cycle
the cycle
wasconstant
held constant
year, the efficiencies
isentropic
respectively. As
ratio
of the
was held
over theover
year,the
the isentropic
efficiencies
ofand
the expander
pump andwere
expander
were also
to remain constant.
of the pump
also assumed
toassumed
remain constant.
For
Forthe
thepurposes
purposesof
ofanalysis,
analysis,the
thepumping
pumpingand
andexpansion
expansionprocesses
processeswere
wereinitially
initiallyassumed
assumed to
tobe
be
isentropic,
2,isentropic and
to be
determined
using
REFPROP.
isentropic, allowing hh2,isentropic
andh4,isentropic
h4,isentropic
to be
determined
using
REFPROP.These
Thesevalues
valuescan
canthen
then
be
used to
tofind
findthethe
actual
values
using
an isentropic
efficiency
less
thanaccording
100%, according
the
be used
actual
values
using
an isentropic
efficiency
less than
100%,
the equations:
equations:
h2,isentropic − h1
−ℎ )
ηpump = (ℎ ,
(1)
=
( h2 − h1 )
(1)
(ℎ − ℎ )
ηexpander =
− ℎh4)
( h3 −
(ℎ
h
−
h
(ℎ 3 − ℎ 4,isentropic
)
,
(2)(2)
The isentropic
the the
pump
and expander
were taken
be 90%toand
The
isentropicefficiencies
efficienciesof of
pump
and expander
weretotaken
be 70%,
90%respectively.
and 70%,
This
is
consistent
with
previous
published
literature.
For
this
research,
it
was
assumed
that the
respectively. This is consistent with previous published literature. For this research, it was assumed
expansion
device used
was
designed
with a volume
thatratio
would
cause
to operate
this efficiency
that
the expansion
device
used
was designed
with a ratio
volume
that
would
cause toatoperate
at this
at
the
imposed
pressure
ratio,
i.e.,
a
different
expander
would
be
required
for
a
cycle
operating
at a
efficiency at the imposed pressure ratio, i.e., a different expander would be required for a cycle
different
pressure
ratio.
The
ratio
of
specific
heats
of
the
working
fluids
varies
by
less
than
1%
as
the
operating at a different pressure ratio. The ratio of specific heats of the working fluids varies by less
fluid1%
composition
is composition
shifted from R245fa
to R134a,
so it was
assumed
that
there
wouldthat
be no
significant
than
as the fluid
is shifted
from R245fa
to R134a,
so it
was
assumed
there
would
Energies 2017, 10, 440
7 of 21
over- or under-expansion losses introduced due to changing fluid composition at a constant pressure
and volume ratio.
Knowing the evaporator and condenser pressures, and the enthalpies at states 2 and 4,
the temperatures and entropies at these states can now also be obtained using REFPROP.
The effect of a recuperator could also be investigated. The MATLAB program initially took the
case of zero heat transfer from the hot to the cold side, giving a pinch point temperature difference of
T4 -T1 . The program then gradually increased the amount of heat transferred while monitoring the
temperature difference at 100 different points inside the heat exchanger, taking the minimum value as
the new pinch point. When this pinch point reached 5 ◦ C, the corresponding value of heat transfer
could then be designated as Qrecuperator .
Once this has been done, all six points of the cycle have been characterized: pump outlet,
recuperator outlet cold, evaporator outlet, expander outlet, recuperator outlet hot and condenser outlet.
Equations (3)–(6) can then be used to calculate the efficiency of the cycle:
Wpump = h2 − h1
(3)
Wexpander = h3 − h4
(4)
Qevaporator = h3 − h2b
(5)
ηcycle =
Wexpander − Wpump
Qevaporator
(6)
This allows the efficiency of the cycle to be calculated for any value of ambient temperature.
Using real-world climate data as the values for ambient temperature allows, the performance of a
dynamic ORC under various climate conditions to be analysed. The program analysed several key
metrics. The first was the efficiency of the conventional ORC, η con , which was the efficiency of the cycle
η cycle on the hottest day of the year, when the working fluid had to be composed of 100% R245fa to
ensure the liquid condition at the pump inlet. This is also the year-round efficiency of a cycle utilizing
a fixed working fluid composition. The second was the efficiency of the dynamic ORC, η dyn , for a
given ambient temperature at a particular point in the year. Both of these were calculated according to
Equation (6).
The third metric was the average annual efficiency of the dynamic ORC over the course of the
year [19], η dyn. . This is defined as:
η dyn. =
∑1N ηdyn.
N
(7)
where N is the number of operational days in the year [19].
The fourth was the annual improvement in energy provision ψ. This was given by the equation
previously developed by the authors in [19]:
ψ=
η dyn. − ηcon
ηcon
× 100%
(8)
The pinch point in the heat exchangers could be analysed using an energy balance method. Using
the assumption that the heat exchangers were perfectly thermally insulated from the environment,
and that the temperature difference at the expander inlet was 10 ◦ C, a T-Q diagram could be set up.
As for the recuperator, the program took 100 points in the heat exchanger and calculated the
temperature difference between the hot and cold streams. The temperature of the thermal fluid
(assumed to be pressurised water in this case study) after transferring a certain amount of energy to
the working fluid could be calculated from the equation:
.
Q0 = mwater c p ∆T
(9)
Energies 2017, 10, 440
8 of 21
0
where mwater
. is the mass flow rate of the hot water and cp its specific heat capacity. The higher the
flow rate, the smaller the temperature change of the water as it exchanges energy with the working
fluid. The mass flow rate of water is therefore increased from zero until the pinch point reaches the
required 5 ◦ C in both the evaporator and condenser. Once the flow rate is known, the final and average
temperatures can be calculated using the lever rule, assuming that the specific heat capacity of the
thermal fluid remains constant, giving a straight line on the pinch point diagram.
Knowing the mass flow rate of the hot water, the specific power output of the cycle can be
calculated. The specific power is defined here as the power output from the expander per unit of mass
flow of hot fluid in the evaporator, or mathematically as:
W 0 specific =
10, 000
m0 water
(10)
where W’ is the specific power. This allowed a further performance metric to be defined, similar to the
increase in annual energy generation ψ. This was the increase in average annual specific power, given
the symbol φ and defined as:
W 0 specific,dyn − W 0 specific,con
φ=
(11)
W 0 specific,con
where W 0 specific,dyn . is the specific work of the dynamic cycle and where W 0 specific,con . is the specific
work of the conventional, non-dynamic cycle The exergy at a given state can be determined using
the equation:
X = h − h0 − T0 (s − s0 )
(12)
As the values for specific enthalpy h and specific entropies are known for all states in the system,
as is the temperature of the reference state T0 , the exergy at any point in the system can be calculated.
This can be used to calculate the exergy destruction rate in each component:
.
Id =
.
.
.
∑ Ein − ∑ Eout − W
(13)
For the pump, the exergy destruction rate can be given by:
.
.
.
.
I pump = ( E2 − E1 ) + (W pump )
For the recuperator by:
.
.
.
.
(14)
.
I regen = ( E2b − E2 ) − ( E4 − E4b )
(15)
For the evaporator by:
.
.
.
.
.
I evap = ( Ehw,in − Ehw,out ) − ( E3 − E2 )
For the expander by:
.
.
.
.
I expander = ( E3 − E4 ) − (W expander )
For the condenser by:
.
.
.
.
.
I cond = ( E4 − E1 ) − ( Ecw,in − Ecw,out )
(16)
(17)
(18)
The Overall Exergy Efficiency of the cycle is given by:
.
ηexergy =
I evaporator
.
W expander
(19)
A qualitative analysis of the effect of working fluid composition on the heat transfer process was
also carried out. The Nusselt number is the ratio of total to conductive heat transfer in a fluid, and is
Energies 2017, 10, 440
9 of 21
generally calculated for each case using empirical correlations to experimental data. Alimoradi and
Veysi [38] give a rough correlation for the Nusselt number in a shell-and tube heat exchanger of:
Nu = CRe0.7 Pr0.315
(20)
where Re is the Reynolds Number and Pr is the Prandtl Number of the fluid:
Energies 2017, 10, 440
Re =
ρuD
µ
Pr =
µc p
k
(21)
9 of 22
(22)
where ρ is fluid density, u is fluid velocity, D is the
viscosity,
= characteristic length, µ is the kinematic(22)
cp is the specific heat capacity, and k is the thermal conductivity. D was set to 1 cm and u to 1.5 m/s,
where is fluid density, u is fluid velocity, D is the characteristic length, μ is the kinematic viscosity,
and all
of the other information for the calculation could be obtained from REFPROP.
cp is the specific heat capacity, and k is the thermal conductivity. D was set to 1 cm and u to 1.5 m/s,
The cycle was analysed for several heat source temperatures, for recuperative and non-recuperative
and all of the other information for the calculation could be obtained from REFPROP.
cases, andThe
forcycle
five ambient
climate
eachtemperatures,
case, the dynamic
cycle wasand
compared
to
was analysed
for conditions.
several heat For
source
for recuperative
nonthe conventional,
non-dynamic
as climate
well asconditions.
comparing
effect
a recuperative
or
recuperative cases,
and for fivecycle,
ambient
Forthe
each
case,of
theusing
dynamic
cycle was
non-recuperative
dynamic
cycle.
compared to the conventional, non-dynamic cycle, as well as comparing the effect of using a
recuperative or non-recuperative dynamic cycle.
3. Results
3. Results
The MATLAB routine based on the equations given in the previous section was used to analyse a
routine
based Rankine
on the equations
given in3 the
previous
sectionvariation
was used in
to temperature,
analyse
case studyThe
forMATLAB
the dynamic
Organic
Cycle. Figure
shows
the annual
a
case
study
for
the
dynamic
Organic
Rankine
Cycle.
Figure
3
shows
the
annual
variation
in inlet
and the change in working fluid composition needed to ensure the liquid condition at the pump
temperature, and the change in working fluid composition needed to ensure the liquid condition at
for various climate conditions. It can be seen that in the colder winter months, a greater proportion of
the pump inlet for various climate conditions. It can be seen that in the colder winter months, a greater
R134a in the working fluid can be tolerated due to the lower ambient temperature. During the warmer
proportion of R134a in the working fluid can be tolerated due to the lower ambient temperature.
summer
months, more R245fa must be present to ensure the bubble point of the fluid is high enough
During the warmer summer months, more R245fa must be present to ensure the bubble point of the
to ensure
this
condition.
fluid is
high
enough to ensure this condition.
The The
conditions
forfor
Beijing
case study
studyfor
formore
more
in-depth
analysis,
has the
conditions
Beijingwere
weretaken
taken as
as a
a case
in-depth
analysis,
as it as
hasitthe
greatest
variation
between
summer
among
locations
considered.
greatest
variation
between
summerand
andwinter
winter temperatures
temperatures among
thethe
locations
considered.
It wasIt was
also used
in the
authors’
previousstudy
study[19],
[19], which
which enables
also used
in the
authors’
previous
enablescomparison.
comparison.
1.4
Ambient Temperature
310
R134a Proportion
1.2
1
300
0.8
290
0.6
280
0.4
270
260
Jan-13
R134a Proportion
Ambient Temperature (K)
320
0.2
0
Feb-13
Apr-13
May-13
Jul-13
Sep-13
Oct-13
Month
Figure 3. Annual temperature variation and associated changes in working fluid composition for Beijing.
Figure 3. Annual temperature variation and associated changes in working fluid composition for
Beijing.
Figure 4 shows the variation in the efficiency of the cycle depending on the ambient temperature.
◦ C. The of
shows the variation
in the
the cycle
depending is
oncold
the ambient
The heat Figure
source4temperature
is set as
100efficiency
winter
temperature
enoughtemperature.
for the working
The
heat
source
temperature
is
set
as
100
°C.
The
winter
temperature
is
cold
enough
for
the
working
fluid to be liquid at the pump inlet, even when it is 100% R134a. As the ambient temperature
increases,
fluid
to
be
liquid
at
the
pump
inlet,
even
when
it
is
100%
R134a.
As
the
ambient
temperature
the efficiency remains constant, until the point at which the ambient temperature becomes too high for
increases, the efficiency remains constant, until the point at which the ambient temperature becomes
too high for a 100% R134a working fluid to be a liquid at the pump inlet. At this point, R245fa must
be introduced. The cycle efficiency then drops off with increasing ambient temperature. The
recuperative cycle in a relatively linear fashion, whereas the basic cycle shows a concave shape.
Energies 2017, 10, 440
10 of 21
a 100% R134a working fluid to be a liquid at the pump inlet. At this point, R245fa must be introduced.
The cycle efficiency then drops off with increasing ambient temperature. The recuperative cycle in a
Energies
2017,
440
of 22
relatively
linear
fashion,
whereas the basic cycle shows a concave shape.
Energies
2017,
10,10,
440
10 10
of 22
20%
20%
19%
19%
Recuperative
Cycle
Recuperative
Cycle
Basic
Cycle
Basic Cycle
Cycle Efficiency
Cycle Efficiency
18%
18%
17%
17%
16%
16%
15%
15%
14%
14%
13%
13%
253253
263263
273273
283283
293293
303303
Ambient
Temperature
Ambient
Temperature
(K)(K)
Figure 4. Variation in Cycle Efficiency with ambient temperature for a heat source temperature of
Variation
in
Cycle
Efficiency
with
ambient
temperature
a heat
source
temperature
4. 4.
Variation
in ambient
Cycle
Efficiency
with
ambient
temperature
forfor
a heat
source
temperature
of of
◦Figure
100Figure
C under
Beijing’s
conditions.
under
Beijing’s
ambient
conditions.
100100
°C°C
under
Beijing’s
ambient
conditions.
Figure
5 shows
the
variation
enthalpy
change
evaporator,
condenser
and
Figure
5 5shows
the
variation
of
the
enthalpy
change
inexpander,
the expander,
evaporator,
condenser
Figure
shows
the
variation
of of
thethe
enthalpy
change
in in
thethe
expander,
evaporator,
condenser
and
recuperator
as
the
ambient
temperature
changes.
It
can
be
seen
that
the
amount
of
energy
transferred
andrecuperator
recuperator
asambient
the ambient
temperature
changes.
It that
canthe
be amount
seen that
the amount
of energy
as the
temperature
changes. It
can be seen
of energy
transferred
evaporator
and
condenser
increases
relatively
linearly
the
evaporator
the
ambientas the
in in
thethe
evaporator
and
condenser
relatively
linearly
forfor
thelinearly
evaporator
as as
the
ambient
transferred
in the evaporator
and increases
condenser
increases
relatively
for the
evaporator
temperature
decreases,
and
a slightly
convex
shape
the
condenser.
This
can
explain
the
shape
temperature
decreases,
and
in in
a and
slightly
shape
forfor
the
condenser.
can
explain
shape
ambient
temperature
decreases,
in aconvex
slightly
convex
shape
for the This
condenser.
Thisthe
can
explain
the
of
the
response
curve
for
the
non-recuperative
cycle
seen
in
Figure
4.
of the response curve for the non-recuperative cycle seen in Figure 4.
shape of the response curve for the non-recuperative cycle seen in Figure 4.
350350
Enthalpy Change (kJ/kg)
Enthalpy Change (kJ/kg)
300300
250250
200200
150150
100100
Expander
Expander
Evaporator
Evaporator
Condenser
Condenser
Regenerator
Regenerator
50 50
0 0
250250
260260
270270
280280
290290
300300
310310
Ambient
Temperature
Ambient
Temperature
(K)(K)
Figure
5. Comparison
of enthalpy
change
in each
each major
majorcycle
cyclecomponent
component
with
varying
ambient
Figure
Comparison
enthalpy
change
with
varying
ambient
Figure
5. 5.
Comparison
of of
enthalpy
change
in in
each◦ major
cycle component
with
varying
ambient
temperature
for
a
heat
source
temperature
of
100
C
in
Beijing’s
ambient
conditions.
temperature for a heat source temperature of 100 °C in Beijing’s ambient conditions.
temperature for a heat source temperature of 100 °C in Beijing’s ambient conditions.
The
response
curve
Figure
5has
has
a steeper
steeper
slope
evaporator
than
for
expander
The
response
curve
in in
Figure
55has
a asteeper
slope
forfor
thethe
evaporator
than
for
thethe
expander
The
response
curve
in
Figure
slope
for
the
evaporator
than
for
the expander
towards
the
right
hand
side
of
the
graph,
i.e.,
for
operation
under
higher
temperature
ambient
towards
the
right
hand
side
of
the
graph,
i.e.,
for
operation
under
higher
temperature
ambient
towards the right hand side of the graph, i.e., for operation under higher temperature ambient
conditions.
This
means
that
the
evaporator
enthalpy
change
is
more
sensitive
to
changing
ambient
conditions.
This
means
that
the
evaporator
enthalpy
change
is
more
sensitive
to
changing
ambient
conditions. This means that the evaporator enthalpy change is more sensitive to changing ambient
temperature
this
region.
temperature
drops,
evaporator
enthalpy
change
will
therefore
temperature
in in
this
region.
AsAs
thethe
temperature
drops,
thethe
evaporator
enthalpy
change
will
therefore
temperature
in this
region.
Asthe
theexpander
temperature
drops,
the This
evaporator
enthalpy
change
willcycle
therefore
increase
more
quickly
than
enthalpy
change.
means
that
efficiency
increase
more
quickly
than
the expander
enthalpy
change.
This means
that
thethe
efficiency
of of
thethe
cycle
increase
more
quickly
than
the
expander
enthalpy
change.
This
means
that
the
efficiency
of
the cycle
is relatively
insensitive
changing
ambient
temperature
higher
ambient
temperature
regions.
is relatively
insensitive
to to
changing
ambient
temperature
in in
thethe
higher
ambient
temperature
regions.
is relatively
insensitive
to
changing
ambient
temperature
in
the
higher
ambient
temperature
regions.
Any
increase
expander
enthalpy
change
is cancelled
out
a corresponding
increase
evaporator
Any
increase
in in
expander
enthalpy
change
is cancelled
out
byby
a corresponding
increase
in in
evaporator
enthalpy
change.
lower
temperatures,
example
from
270
to
280
curve
Figure
5 for
Any
increase
in
expander
enthalpy
change
isexample
cancelled
out
by
increase
in5evaporator
enthalpy
change.
AtAt
lower
temperatures,
forfor
from
270
KaK
tocorresponding
280
K,K,
thethe
curve
in in
Figure
for
Energies 2017, 10, 440
Energies 2017, 10, 440
11 of 21
11 of 22
enthalpy change. At lower temperatures, for example from 270 K to 280 K, the curve in Figure 5 for
expander
steeper
thanthe
thecurve
curvefor
forthe
theevaporator.
evaporator.This
Thismeans
means that
that the
the efficiency of the
thethe
expander
is is
steeper
than
the cycle
cycle is
is
more
sensitive
to
changing
ambient
temperature
in
this
region,
resulting
in
a
steeper
slope
for
this
more sensitive to changing ambient temperature in this region, resulting in a steeper slope for this
part
of the response
curve
in Figure
4.
of part
the response
curve in
Figure
4.
For
the
recuperativecycle,
cycle,the
theresponse
response curve
curve for
show
thethe
same
For
the
recuperative
for efficiency
efficiencyininFigure
Figure4 4does
doesnot
not
show
same
convex
shape.
This
can
also
be
explained
using
the
data
presented
in
Figure
5.
The
curve
in
Figure
5 5
convex shape. This can also be explained using the data presented in Figure 5. The curve in Figure
for
the
recuperator
has
a
convex
shape,
with
a
steep
section
at
high
ambient
temperatures,
a
peak
at
for the recuperator has a convex shape, with a steep section at high ambient temperatures, a peak
recovered
in in
thethe
at about
about 275
275 K,
K, then
then aa decrease
decreasetotoaasteady
steadyvalue
valuebelow
belowabout
about265
265K.K.The
Theenergy
energy
recovered
recuperator is subtracted directly from the energy required in the evaporator, thereby increasing
recuperator is subtracted directly from the energy required in the evaporator, thereby increasing
efficiency. The convex shape of the recuperator curve in Figure 5 works to cancel out the factors
efficiency. The convex shape of the recuperator curve in Figure 5 works to cancel out the factors
causing the concave shape of the efficiency curve for the non-recuperative cycle, as seen in Figure 4.
causing the concave shape of the efficiency curve for the non-recuperative cycle, as seen in Figure 4.
This results in the relatively straight line seen for the efficiency plot for the recuperative cycle seen in
This results in the relatively straight line seen for the efficiency plot for the recuperative cycle seen in
Figure 4. This can be explained by a combination of the temperature glide caused by a zeotropic fluid,
Figure
4. This
can be
a combination
and the
principle
ofexplained
operation by
of the
recuperator.of the temperature glide caused by a zeotropic fluid,
and theFigure
principle
of operation this
of the
6 demonstrates
byrecuperator.
comparing T-s diagrams for the cycle operating under high
Figure
6
demonstrates
this
by
T-s diagrams
for the
cycle
operating
high
temperature and low temperature comparing
ambient conditions.
The thick
green
section
of theunder
T-s plot
temperature
low transferred
temperatureinambient
conditions.
The
of the T-s plot ambient
represents
represents and
the heat
the recuperator.
It can
bethick
seen green
that insection
the low-temperature
theconditions
heat transferred
in thehand
recuperator.
It can
be seen that
in the low-temperature
conditions
in the right
plot, there
is significant
superheat
at the expanderambient
outlet. This
means in
thethat
right
hand
plot,
there
is
significant
superheat
at
the
expander
outlet.
This
means
that
the
working
the working fluid exiting the expander is significantly warmer than the working fluid exiting
the
fluid
exiting
theaexpander
is significantly
warmer
than the
working
fluid exiting
theThis
pump,
giving
pump,
giving
greater driving
temperature
differential
for the
recuperator
to exploit.
tends
to
increasedriving
the amount
of heat transferred
in the
underto
low
temperature
conditions,
as seenthe
a greater
temperature
differential
forrecuperator
the recuperator
exploit.
This tends
to increase
in Figure
5. transferred in the recuperator under low temperature conditions, as seen in Figure 5.
amount
of heat
Figure
6. Comparison
of dynamic
Organic
Rankine
operating
under
high temperature
Figure
6. Comparison
of dynamic
Organic
Rankine
CyclesCycles
operating
under high
temperature
(290 K, left)
(290
K,
left)
and
low
temperature
(265
K,
right)
ambient
conditions.
and low temperature (265 K, right) ambient conditions.
Also to be noted is the fact that the left hand figure, representing higher temperature ambient
Also to be noted is the fact that the left hand figure, representing higher temperature ambient
conditions, also happens to be the T-s diagram for a zeotropic fluid, and therefore exhibits a
conditions,
alsoglide
happens
to be
the T-s
diagram
a zeotropic
thereforeinexhibits
a temperature
temperature
during
phase
change.
Thisfor
can
be seen tofluid,
causeand
an increase
the temperature
of
glide
phase
change.
can
be seen
to cause
increase
in thewill
temperature
ofincrease
the expander
the during
expander
outlet
relativeThis
to the
pump
outlet
due toan
this
glide, which
also tend to
the
outlet
relative
to the
pump outlet
due
to this glide,
which
will
also tend
to increase
thethe
amount
of of
heat
amount
of heat
transferred
in the
recuperator.
This
could
explain
the slight
drop in
amount
transferred
in the recuperator.
This could
explain
the slight
drop in
heatbecause
transferred
heat transferred
in the recuperator
at higher
proportions
of R134a
in the
the amount
working of
fluid,
as
in the
the recuperator
at higher
proportions
of R134a
in the
working
fluid, because
as the
workingand
fluid
working fluid
once again
approaches
a pure
fluid
composition,
the glide
decreases,
once
again approaches
a pure
fluid
composition,
the
decreases,due
andto
counteracts
the increase
counteracts
the increase
in heat
energy
transferred
inglide
the recuperator
increasing superheat
to in
heat
energy
transferred
in theofrecuperator
to increasing
superheat
some degree.
The response
some
degree.
The response
the dynamicdue
cycle
with changing
ambienttotemperature
clearly
shows
the cyclecycle
has improved
performance
a conventional
Rankine
Cycle
when
the
of that
the dynamic
with changing
ambientover
temperature
clearlyOrganic
shows that
the cycle
has
improved
temperatureover
is lower.
performance
a conventional Organic Rankine Cycle when the temperature is lower.
It can
seenfrom
fromFigure
Figure77that
thatthe
thedynamic
dynamic cycle
cycle performs
cycle
It can
bebe
seen
performsbetter
betterthan
thanthe
theconventional
conventional
cycle
both
recuperative
non-recuperative
cases,
the greatest
improvement
occurring
forfor
both
thethe
recuperative
andand
non-recuperative
cases,
withwith
the greatest
improvement
occurring
during
colder
winterasmonths,
as by
predicted
by thecurves
response
curves
shown4.inAs
Figure
4. As the
theduring
colderthe
winter
months,
predicted
the response
shown
in Figure
the conventional
Energies
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2017,10,
10,440
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12
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of21
22
conventional ORC efficiency is based on the highest annual temperature, the lowest point of the
ORC efficiency is based on the highest annual temperature, the lowest point of the monthly average
monthly average for the dynamic cycle is still higher than this, as even during the hottest months, the
for the dynamic cycle is still higher than this, as even during the hottest months, the temperature is
temperature is generally lower than the maximum most of the time. The non-recuperative cycle
generally lower than the maximum most of the time. The non-recuperative cycle increases in efficiency
increases in efficiency extremely slowly in response to decreasing temperature at the higher end of
extremely slowly in response to decreasing temperature at the higher end of the temperature range,
the temperature range, so the non-recuperative dynamic cycle only begins to significantly outperform
so the non-recuperative dynamic cycle only begins to significantly outperform the conventional cycle
the conventional cycle at the beginning and end of the year when the temperature is a great deal
at the beginning and end of the year when the temperature is a great deal colder than the maximum.
colder than the maximum. The efficiency of the recuperative dynamic cycle increases far more
The efficiency of the recuperative dynamic cycle increases far more sharply with increasing temperature,
sharply with increasing temperature, and so the improvement can be seen even during the summer
and so the improvement can be seen even during the summer months, when the temperature is still
months, when the temperature is still close to the maximum used in the design of the conventional cycle.
close to the maximum used in the design of the conventional cycle.
14%
Dynamic RegenerativeCycle
Dynamic Non-Regenerative Cycle
Conventional Regenerative Cycle
12%
Efficiency
Conventional Non-Regenerative Cycle
10%
8%
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Month
◦ C under Beijing’s
Figure
Figure7.7.Annual
Annualvariation
variationin
incycle
cycleefficiency
efficiencyfor
foraaheat
heatsource
sourcetemperature
temperatureofof100
100 °C
under Beijing’s
ambient
conditions.
Graph
shows
monthly
averages.
ambient conditions. Graph shows monthly averages.
Thevalue
valueof
ofψψchanges
changesdepending
dependingon
onthe
theannual
annualvariation
variation in
in temperature,
temperature, as
as shown
shown in
in Figure
Figure 8.
8.
The
TheMATLAB
MATLABroutine
routinewas
wasrun
runusing
usingclimate
climatedata
datafrom
fromseveral
severallocations
locationsworldwide,
worldwide,for
forheat
heatsource
source
The
temperatures of
of 100
100 ◦°C
and 150
150 ◦°C.
A steady
steady increase
increase in
in ψψ can
can be
be seen
seen as
as the
the amplitude
amplitude of
of the
the
temperatures
C and
C. A
temperature variations
variations increases. This
asas
thethe
greater
thethe
temperature
variation,
the
temperature
Thisisistotobebeexpected,
expected,
greater
temperature
variation,
greater
thethe
difference
between
thethe
hot
the Carnot
Carnot
the
greater
difference
between
hotand
andcold
coldreservoirs,
reservoirs,and
and therefore
therefore the greater the
efficiency. The
The plot
plot deviates
deviates slightly
slightly from
from the
the linear
linear increase
increase in
in Carnot
Carnot efficiency,
efficiency, however,
however,due
dueto
to
efficiency.
severalfactors,
factors,most
mostnotably
notablythe
thecomposition
compositionofof
the
working
fluid.
When
temperature
variation
several
the
working
fluid.
When
thethe
temperature
variation
is
is small,
only
a small
amount
R134a
neededtotokeep
keepup
upwith
withthe
thechanging
changingheat
heatsink
sink temperature.
temperature.
small,
only
a small
amount
ofof
R134a
is is
needed
Whenthe
thetemperature
temperaturevariation
variationisismuch
muchlarger,
larger,the
theworking
workingfluid
fluidcan
canbe
be100%
100%R134a,
R134a,and
andstill
stillhave
have
When
excesscooling
coolingcapacity
capacityititisisnot
notutilising.
utilising.Some
Somesmall
smalldeviations
deviationsfrom
fromthe
thetheoretical
theoreticalsmooth
smoothincrease
increase
excess
canbe
beseen.
seen.For
Forexample,
example,Phoenix
Phoenix has
has aa higher
higher average
average temperature
temperature than
than any
any of
of the
the other
other locations,
locations,
can
andtherefore
thereforeaareduced
reducedconventional
conventionalcycle
cycleefficiency.
efficiency.This
Thismeans
meansthat
thatthe
thedynamic
dynamiccycle
cycleisisslightly
slightly
and
more
effective
here
than
the
idealised
case
would
predict.
more effective here than the idealised case would predict.
Thetrend
trendfor
forthe
thenon-recuperative
non-recuperative
cycles
is aofslightly
a slightly
different
shape,
slowly
at then
first,
The
cycles
is of
different
shape,
risingrising
slowly
at first,
then increasing
in This
slope.
This is because,
Figure
4, the of
efficiency
of non-recuperative
increasing
in slope.
is because,
as shownasinshown
Figure in
4, the
efficiency
non-recuperative
cycles only
cycles only
increase
slowly
when the
ambient temperature
decreases
from the
annual maximum.
increase
very
slowlyvery
when
the ambient
temperature
decreases from
the annual
maximum.
At lower
At lower
annual temperature
the temperature
heat sink temperature
nevercold
becomes
cold
to
annual
temperature
variations,variations,
the heat sink
never becomes
enough
to enough
cause the
cause the non-recuperative
cycle
enter the
region
of itscurve
response
curve
where
a sharp
in
non-recuperative
cycle to enter
thetoregion
of its
response
where
a sharp
increase
inincrease
efficiency
efficiency
can
be seen.can be seen.
Energies 2017, 10, 440
Energies 2017, 10, 440
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13 of 22
Energies 2017, 10, 18%
440
14% 16%
150°C, regenerator
150°C, no regenerator
100°C,
regenerator
150°C,
regenerator
100°C,
nono
regenerator
150°C,
regenerator
12% 14%
100°C, regenerator
100°C, no regenerator
16%
18%
13 of 22
ψ
10% 12%
ψ
8% 10%
6% 8%
4%
2%
0%
6%
4%
2%
0%
0
0
5
10
5
10
15
20
15
25
20
25
30
Annual Temperature Variation (°C)
30
35
35
Annual Temperature Variation (°C)
Figure 8. Variation in ψ for five case studies for annual temperature variation. From left to right,
Figure
8. Variation
in
ψinfor
five
case
studies
temperaturevariation.
variation.
From
to right,
Figure
8. Variation
ψ for
five
case
studiesfor
for annual
annual temperature
From
left left
to right,
Mumbai,
Ushuaia,
Glasgow,
Phoenix,
Beijing.
Mumbai,
Ushuaia,
Glasgow,
Phoenix,
Beijing.
Mumbai,
Ushuaia,
Glasgow,
Phoenix,
Beijing.
TheThe
variation
in ψ ψ
with
changing
heat
sourcetemperature
temperature
was also
investigated,
and the results
variation
with
changing
heatsource
sourcetemperature
was
andand
the results
The variation
in ψinwith
changing
heat
wasalso
alsoinvestigated,
investigated,
the results
for the the
casecase
study
of of
Beijing’s
climate
conditions
plotted
in Figure
9. It can
be seen
thatboth
for the
both the
study
Beijing’s
climate
conditionsplotted
plotted
in
bebe
seen
thatthat
for
for theforcase
study
of Beijing’s
climate
conditions
in Figure
Figure9.9.ItItcan
can
seen
for both
the
recuperative
and
non-recuperative
dynamic
cycles,
the
improvement
in
annual
energy
provision
ψ
recuperative
and
non-recuperative
dynamic
cycles,
the
improvement
in
annual
energy
provision
ψ
recuperative and non-recuperative dynamic cycles,
improvement in annual energy provision ψ
◦ C,the
increases
gradually
until
a
temperature
of
150
whereat
it
peaks,
and
then
begins
to
drop
away.
increases gradually until a temperature of 150 °C, whereat it peaks, and then begins to drop away.
increases gradually until a temperature of 150 °C, whereat it peaks, and then begins to drop away.
in contrast
to results
the results
previously
obtained
by the
authors
a similar
dynamic
ORC
ThisThis
is iniscontrast
to the
previously
obtained
by the
authors
for for
a similar
dynamic
ORC
concept
This is in contrast to the results previously obtained by the authors for a similar dynamic ORC
concept
using
turbine
as the[19],
expander
[19],the
in value
whichofthe
value of ψdecreased
smoothly decreased
with heat
using
a turbine
as athe
expander
in which
ψ smoothly
with increasing
concept
using aheat
turbine
astemperature
the expander
in which
the Carnot
value of
ψ smoothly
decreased with
increasing
source
as the[19],
resulting
increased
of the conventional
source
temperature
as the
resulting increased
Carnot
efficiency
of efficiency
the conventional
cycle made the
increasing
heat
source
temperature
as
the
resulting
increased
Carnot
efficiency
of
the
conventional
cycle made the gains caused by the dynamic cycle proportionally smaller.
gains
caused by the dynamic cycle proportionally smaller.
cycle made the gains caused by the dynamic cycle proportionally smaller.
14%
14%
12%
12%
10%
ψ
10% 8%
Regenerative Cycle
6% 4%
Regenerative Cycle
Non-Regenerative Cycle
ψ
8% 6%
4%
2%
0%
Non-Regenerative Cycle
2%
0%
75
95
115
135
155
175
195
Heat Source Temperature (°C)
75
95
115
135
155
175
195
Figure
9. Variation
ininψψwith
heatsource
sourcetemperature
temperature
under
Beijing’s
ambient
conditions.
Figure
9. Variation
withchanging
changing heat
under
Beijing’s
ambient
conditions.
Heat Source Temperature (°C)
is significant
that
peakininthe
theplot
plotof
of Figure
Figure 99 occurs
critical
point
of R245fa,
It isItsignificant
that
thethe
peak
occursatatroughly
roughlythe
the
critical
point
of R245fa, at
at
a
temperature
of
154
°C.
As
stated
in
the
previous
section,
the
MATLAB
routine
ensured
that the
◦
Figure
9.
Variation
in
ψ
with
changing
heat
source
temperature
under
Beijing’s
ambient
conditions.
a temperature of 154 C. As stated in the previous section, the MATLAB routine ensured that
the cycle
cycle was subcritical, by selecting the evaporator pressure either to produce zero superheat at the
was subcritical, by selecting the evaporator pressure either to produce zero superheat at the expander
inlet when
the peak
working
fluidplot
wasof100%
R245fa, or to at
5 K below the
temperature
of
Itexpander
is significant
that the
in 100%
the
Figure
thecritical
critical
point of
inlet
when
the working
fluid was
R245fa,
or to9 5occurs
K belowroughly
the critical
temperature
of R245fa,
the fluid,
the
fluid,
whichever
was
the
lower.
at a temperature of 154 °C. As stated in the previous section, the MATLAB routine ensured that the
whichever was the lower.
cycle was
subcritical,
selecting
theinevaporator
pressure
to produce
zero as
superheat
the
Figure
10 showsbythe
variation
the evaporator
andeither
condenser
pressures
the heatatsource
expander
inletiswhen
theInworking
fluid
wasincreasing
100% R245fa,
or to
5 K below
the critical
temperature
of
temperature
varied.
the lower
range,
the heat
source
temperature
allows
the evaporator
the fluid, whichever was the lower.
Energies 2017, 10, 440
14 of 22
Energies 2017, 10, 440
14 of 21
Figure 10 shows the variation in the evaporator and condenser pressures as the heat source
temperature is varied. In the lower range, increasing the heat source temperature allows the
pressure to be increased, increasing the efficiency of the cycle. This trend continues until the critical
evaporator pressure to be increased, increasing the efficiency of the cycle. This trend continues until
point of R245fa is reached, at which point the pressure ratio cannot be increased any further without
the critical point of R245fa is reached, at which point the pressure ratio cannot be increased any
the cycle
becoming
supercritical.
After
this point, After
the cycle
then shows
the
same
trend
thetrend
previous
further
without the
cycle becoming
supercritical.
this point,
the cycle
then
shows
the as
same
cycle as
considered
by
the
authors,
with
the
increase
in
annual
energy
provision
dropping
off
as
the
the previous cycle considered by the authors, with the increase in annual energy provisiongains
caused
by
the off
dynamic
cyclecaused
become
proportionally
significant.
dropping
as the gains
by less
the dynamic
cycle become
less proportionally significant.
35
Condenser Pressure
Evaporator Pressure
30
Pressure (bar)
25
20
15
10
5
0
75
95
115
135
155
175
195
Heat Source Temperature (°C)
Figure
10. Variation
in Evaporator
Condenserpressure
pressurewith
withchanging
changing heat
heat source
Figure
10. Variation
in Evaporator
andand
Condenser
sourcetemperature
temperature for
for
Beijing’s
ambient
conditions.
Beijing’s ambient conditions.
The previous analysis has been a first-law treatment of the dynamic ORC. However, First Law
The
previous
analysis
has by
been
a first-law
treatment
of the
ORC.
However,
First Law
Efficiency
is only
one metric
which
a cycle can
be analysed.
Fordynamic
waste heat
sources,
for example,
Efficiency
is only
one is
metric
bymetric
whichbyawhich
cycle to
can
be analysed.
the specific
power
a better
judge
the cycle. For waste heat sources, for example,
Figure
11 is
shows
the metric
variation
the specific
power
of the cycle as the ambient temperature
the specific
power
a better
byinwhich
to judge
the cycle.
changes.
Two
things
are
immediately
apparent
from
the
graph.
Firstly,
power increases
Figure 11 shows the variation in the specific power of the
cyclethe
asspecific
the ambient
temperature
with
decreasing
ambient
temperature.
Secondly,
the
curves
for
the
recuperative
and increases
nonchanges. Two things are immediately apparent from the graph. Firstly, the specific power
recuperative cycles are identical.
with decreasing ambient temperature. Secondly, the curves for the recuperative and non-recuperative
The
first point can be explained by examining the pinch point diagrams for the evaporator15ofofthe
Energies
2017, 10, 440
22
cycles
are identical.
Specific Power (W.s/kg)
ORC. Figure 12 shows the evaporator pinch point diagrams for a high ambient temperature case, i.e.,
with the fluid composed of mostly R245fa, and a low ambient temperature case, i.e., with the fluid
90
composed mostly of R134a. The lower boiling point of the R134a has resulted in a far greater degree
80 expander inlet, allowing a much steeper line for the evaporator. The steeper line
of superheat at the
means a lower necessary
mass flow rate of thermal fluid. The ORC has its output fixed at 10 kW, so
70
the reduced mass flow rate observed in Figure 12 means that the specific power increases for the
60
lower heat sink temperatures represented by the leftmost pinch point diagram.
50
40
30
20
10
0
250
260
270
280
290
300
310
320
Ambient Temperature (K)
Figure 11. Variation in specific power for recuperative and non-recuperative dynamic cycles over the
Figure 11. Variation in specific power for recuperative and non-recuperative dynamic cycles over the
course of the year for Beijing’s ambient conditions, and a heat source temperature of 100 ◦ C. The specific
course of the year for Beijing’s ambient conditions, and a heat source temperature of 100 °C. The
power
of thepower
cycleofdoes
not vary
on whether
a recuperator
is present,
so these
two
curves
specific
the cycle
does depending
not vary depending
on whether
a recuperator
is present,
so these
two
are identical.
curves are identical.
Specific Power
50
40
30
Energies 2017, 10, 440 20
15 of 21
10
The first point0can be explained by examining the pinch point diagrams for the evaporator of the
250the evaporator
260
270 point
280
290for a high
300ambient
310temperature
320 case, i.e.,
ORC. Figure 12 shows
pinch
diagrams
Temperature
(K)
with the fluid composed of mostly R245fa,Ambient
and a low
ambient temperature
case, i.e., with the fluid
composed mostly of R134a. The lower boiling point of the R134a has resulted in a far greater degree
of superheat
the expander
inlet,
allowing
a much steeper
line for the evaporator.
The over
steeper
Figure 11.atVariation
in specific
power
for recuperative
and non-recuperative
dynamic cycles
the line
means
a lower
necessary
flowambient
rate of thermal
fluid.
ORC
has its
output fixed
at 10°C.
kW,
so the
course
of the
year formass
Beijing’s
conditions,
andThe
a heat
source
temperature
of 100
The
reduced
mass
flow
rate
observed
in
Figure
12
means
that
the
specific
power
increases
for
the
lower
specific power of the cycle does not vary depending on whether a recuperator is present, so these two
heat sink
temperatures
curves
are identical. represented by the leftmost pinch point diagram.
Figure 12.
12. Evaporator
Evaporator Pinch
heat source
source temperature
temperature of
of 100
100 ◦°C
and heat
heat sink
sink
Figure
Pinch Point
Point Diagrams
Diagrams for
for aa heat
C and
temperatures
of
−11
°C
(left)
and
25
°C
(right).
◦
◦
temperatures of −11 C (left) and 25 C (right).
The second point, the fact that the recuperative and non-recuperative curves are identical, can
The second point, the fact that the recuperative and non-recuperative curves are identical, can
be explained by the fact that the pinch point in both cases is at the bubble point of the working fluid,
be explained by the fact that the pinch point in both cases is at the bubble point of the working fluid,
and that the recuperator does not cause a phase change in the evaporator. Even though the energy
and that the recuperator does not cause a phase change in the evaporator. Even though the energy
transferred in the evaporator will be less in the recuperative case, meaning the first law efficiency
transferred in the evaporator will be less in the recuperative case, meaning the first law efficiency
increases, this does not necessarily translate into an increase in specific power, as the expander work
increases, this does not necessarily translate into an increase in specific power, as the expander work is
is still held constant, and the thermal fluid line must still satisfy the pinch point condition. This means
still held constant, and the thermal fluid line must still satisfy the pinch point condition. This means
that unless the pinch point position changes, there can be no change in the flow rate on the hot side
that unless the pinch point position changes, there can be no change in the flow rate on the hot
of the evaporator, and the specific power will not change. In no cases analysed was there a phase
side of the evaporator, and the specific power will not change. In no cases analysed was there a
change in the recuperator, meaning that there was no difference between the recuperative and nonphase change in the recuperator, meaning that there was no difference between the recuperative and
recuperative plots.
non-recuperative plots.
Figure 13 shows the variation in the increase in annual heat source utilization φ as the heat
source temperature changes. It can be seen that the value initially drops off slowly as the heat source
temperature is increased, due primarily to the increase in the minimum value of the specific power.
As the heat source temperature approaches the critical temperature, the value of φ drops off more
sharply. Figure 14 shows how the specific power of the non-dynamic cycle varies with heat source
temperature for Beijing’s ambient conditions. It can be seen that the specific power of the non-dynamic
cycle begins to increase at amount this point as well, due to the fact that after the critical temperature
of R245fa at 154 ◦ C there will be a superheat at the expander inlet for the non-dynamic cycle, allowing
an increased slope on the T-Q diagram for the thermal fluid and reducing its required flow rate.
temperature for Beijing’s ambient conditions. It can be seen that the specific power of the nontemperature
forbegins
Beijing’s
ambientatconditions.
It point
can beasseen
specific
power
thecritical
nondynamic cycle
to increase
amount this
well,that
duethe
to the
fact that
afterofthe
dynamic
cycleofbegins
at amount
point as well,
to the inlet
fact that
after
the critical
temperature
R245fatoatincrease
154 °C there
will bethis
a superheat
at thedue
expander
for the
non-dynamic
temperature
of R245fa
at 154 slope
°C there
willT-Q
be adiagram
superheat
expander
the non-dynamic
cycle, allowing
an increased
on the
for at
thethe
thermal
fluidinlet
andfor
reducing
its required
cycle,
allowing an increased slope on the T-Q diagram for the thermal fluid and reducing its required
flow rate.
Energies 2017, 10, 440
16 of 21
flow rate.
300%
300%
250%
250%
200%
200%
Ф Ф
150%
150%
100%
100%
50%
50%
0%
0% 75
75
95
95
115
135
155
115 Source135
155 (°C )
Heat
Temperature
175
175
195
195
Heat Source Temperature (°C )
Specific
Power
(W/kg)
Specific
Power
(W/kg)
Figure13.
13. Variation
Variationin
inφϕwith
withvarying
varyingheat
heatsource
sourcetemperature
temperaturefor
forBeijing’s
Beijing’sambient
ambientconditions.
conditions.
Figure
Figure 13. Variation in ϕ with varying heat source temperature for Beijing’s ambient conditions.
80
80
70
70
60
60
50
50
40
Regenerative Cycle
Regenerative Cycle
40
30
30
20
20
10
100
0 75
75
95
95
115
115
135
135
155
155
Heat Source Temperature (°C)
Heat Source Temperature (°C)
175
175
195
195
Figure 14. Variation in the Specific Power of the Non-Dynamic Cycle with varying heat source
temperature with Beijing’s ambient conditions.
Figure 14. Variation in the Specific Power of the Non-Dynamic Cycle with varying heat source
Figure
14. Variation
in the Specificconditions.
Power of the Non-Dynamic Cycle with varying heat source
Beijing’s
Atemperature
brief caveatwith
with
regardambient
to the analysis of specific power: Optimising the specific power output
temperature with Beijing’s ambient conditions.
is a complex task. Reducing the evaporator pressure will increase expander inlet superheat, and tend
A brief caveat with regard to the analysis of specific power: Optimising the specific power
to increase specific power, while reducing first law efficiency of the cycle. Reduced first law efficiency
A
caveat with
to the
of specific
Optimising
the inlet
specific
power
outputbrief
is a complex
task.regard
Reducing
the analysis
evaporator
pressurepower:
will increase
expander
superheat,
tends to increase the installed cost per kW of the cycle. The optimum point will depend on the exact
output
is atocomplex
Reducing
evaporator
will increase
expander
inlet superheat,
and tend
increasetask.
specific
power,the
while
reducingpressure
first law efficiency
of the
cycle. Reduced
first law
application of the cycle and the details of the heat source. Such a specific analysis is outside the scope of
and
tend totends
increase
specific the
power,
whilecost
reducing
first
lawcycle.
efficiency
of the cycle.
Reduced
first law
efficiency
to increase
installed
per kW
of the
The optimum
point
will depend
on
the general treatment applied in this paper, but the analysis presented serves to show the general trend.
efficiency tends to increase the installed cost per kW of the cycle. The optimum point will depend on
Figure 15 shows the variation in superheat over the course of the year. Figures 16 and 17 show
the exergy destruction in each component over the course of the year. Although some irreversibility
occurred in the pump, resulting in exergy destruction, its effect was negligible in comparison to other
components, and therefore has been left out of the following plots in the interest of clarity. It can
be seen that with a recuperator present, the evaporator is by far the greatest contributor to exergy
destruction. This exergy destruction is greatest during the winter months. This seems primarily to
be caused by the greater degree of superheat introduced at the expander inlet by the shifting of the
working fluid composition to one rich in R134a, which reduces its dew point.
The exergy efficiency of the cycle over the course of the year was also analysed. Figure 18 shows
this variation for a heat source temperature of 75 °C. It can be seen that the exergy efficiency is higher
year-round for the recuperative cycle, and that the recuperative and basic cycles diverge in the winter
months as the recuperator takes up the excess heat at the expander inlet. All cycles show high second
law efficiency in the summer months, which drops off slightly as the ambient temperature drops, the
Energies 2017, 10, 440
17 of 21
fluid composition changes, and the temperature mismatch in the evaporator increases.
Superheat at Expander Inlet (K)
60
50
40
30
20
10
0
Jan-13 Jan-13 Mar-13 Apr-13 May-13 May-13 Jun-13 Jul-13 Aug-13 Sep-13 Oct-13 Nov-13
Month
Figure 15. Superheat at expander inlet over the course of the year for a heat source temperature of
15. Superheat at expander inlet over the course of the year for a heat source temperature of
◦ CFigure
Energies
2017,
1818ofof2222
75
under
Beijing’s
ambient conditions.
Energies
2017,10,
10,440
440
75 °C under Beijing’s ambient conditions.
SpecificExergy
ExergyDestruction
Destruction(J/kg)
(J/kg)
Specific
100000
100000
10000
10000
1000
1000
100
100
Dec-12
Dec-12
Evaporator
Evaporator
Expander
Expander
Condenser
Condenser
Regenerator
Regenerator
Jan-13
Jan-13 Mar-13
Mar-13 May-13
May-13 Jun-13
Jun-13 Aug-13
Aug-13 Oct-13
Oct-13 Nov-13
Nov-13 Jan-14
Jan-14
Month
Month
16.
ininexergy
destruction
each
cycle
component
course
ofofthe
year
for
FigureFigure
16. Variation
in exergy
destruction
ininin
each
cycle
overthe
the
course
of
year
Figure
16.Variation
Variation
exergy
destruction
each
cyclecomponent
componentover
over
the
course
thethe
year
forafor
a a
heat
temperature
ofof◦75
aarecuperator.
heatsource
source
temperature
75°C
°Cwith
with
recuperator.
heat source
temperature
of 75
C
with
a recuperator.
SpecificExergy
ExergyDestruction
Destruction(J/kg)
(J/kg)
Specific
40000
40000
35000
35000
30000
30000
25000
25000
20000
20000
15000
15000
10000
10000
Evaporator
Evaporator
Expander
Expander
Condenser
Condenser
5000
5000
00
Dec-12
Dec-12 Jan-13
Jan-13 Mar-13
Mar-13 May-13
May-13 Jun-13
Jun-13 Aug-13
Aug-13 Oct-13
Oct-13 Nov-13
Nov-13 Jan-14
Jan-14
Month
Month
FigureFigure
17. Variation
in exergy destruction
in each cycle
componentover
over the
course of the
yearafor a
Figure17.
17.Variation
Variationininexergy
exergydestruction
destructioninineach
eachcycle
cyclecomponent
component overthe
thecourse
courseofofthe
theyear
yearfor
for a
◦
heat source
temperature
of 75
C
without
a arecuperator.
heat
temperature
ofof75
heatsource
source
temperature
75°C
°Cwithout
without
arecuperator.
recuperator.
Energies 2017, 10, 440
18 of 21
The recuperator shows the lowest exergy destruction rate, indicating the highest recuperator
efficiency, during the winter months, as was noted in the previous section. Figure 17 shows the similar
results for the case of a non-recuperative cycle. The specific exergy destruction in the evaporator is
higher in this case, reaching 37 kJ/kg, as opposed to 33 kJ/kg in the recuperative cycle. The exergy
destruction in the condenser is also noticeably higher, reaching almost 14 kJ/kg during the winter
months, which are when the recuperator is at its most effective.
The exergy efficiency of the cycle over the course of the year was also analysed. Figure 18 shows
this variation for a heat source temperature of 75 ◦ C. It can be seen that the exergy efficiency is higher
year-round for the recuperative cycle, and that the recuperative and basic cycles diverge in the winter
months as the recuperator takes up the excess heat at the expander inlet. All cycles show high second
law efficiency in the summer months, which drops off slightly as the ambient temperature drops,
Energies
2017, 10, 440 changes, and the temperature mismatch in the evaporator increases.19 of 22
the fluid
composition
Energies 2017, 10, 440
19 of 22
55%
55%
Exergy
ExergyEfficiency
Efficiency
50%
50%
45%
45%
40%
40%
Regenerative Cycle
Regenerative Cycle
Basic Cycle
Basic Cycle
Conventional ORC
Conventional ORC
35%
35%
30%
30%
Dec-12 Jan-13
12月-12 1月-13
Mar-13 May-13 Jun-13
3月-13 5月-13 6月-13
Aug-13 Oct-13 Nov-13 Jan-14
8月-13 10月-13 11月-13 1月-14
Month
Month
Figure
18. 18.
Variation
Efficiencyover
over
heat temperature
source temperature
of 75 ◦ C
Figure
VariationininExergy
Exergy Efficiency
the the
yearyear
for a for
heatasource
of 75 °C under
Figure
18. Variation
in Exergy
Efficiency
overRecuperative,
the year for a heat
source temperature and
of 75 Conventional
°C under
under
Beijing’s
ambient
conditions
Non-Recuperative,
Beijing’s
ambient
conditions
for for
thetheRecuperative,
Non-Recuperative,
and Conventional
Beijing’s ambient conditions for the Recuperative, Non-Recuperative, and Conventional
(Non-Dynamic)
cycles.
(Non-Dynamic)
cycles.
(Non-Dynamic) cycles.
An analysis of how the heat transfer coefficients in the heat exchangers varied depending on
An analysis
of how
thethe
heat
inthe
theheat
heatexchangers
exchangers
varied
depending
An analysis
of how
heattransfer
transfercoefficients
coefficients in
varied
depending
on on
working fluid composition was also carried out. Figure 19 shows how the Nusselt numbers for liquid
working
composition
was
alsocarried
carriedout.
out. Figure
Figure 19
thethe
Nusselt
numbers
for liquid
working
fluidfluid
composition
was
also
19shows
showshow
how
Nusselt
numbers
for liquid
and vapour varied depending on the working fluid composition.
and vapour
varied
depending
theworking
working fluid
fluid composition.
and vapour
varied
depending
ononthe
composition.
300
300
Liquid Nusselt Number
Liquid Nusselt Number
Nusselt
NusseltNumber
Number
250
250
Vapour Nusselt Number
Vapour Nusselt Number
200
200
150
150
100
100
50
50
0
0
0
0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
Mass Proportion of R134a in working fluid
Mass Proportion of R134a in working fluid
1
1
Figure
19. Variation
in Nusselt
Numberin
inthe
the evaporator
evaporator for
source
temperature
of 100
Figure
19. Variation
in Nusselt
Number
fora aheat
heat
source
temperature
of °C.
100 ◦ C.
Figure 19. Variation in Nusselt Number in the evaporator for a heat source temperature of 100 °C.
It can be seen in Figure 19 that the Nusselt number is around 270 for the pure R245fa, drops to
It can be seen in Figure 19 that the Nusselt number is around 270 for the pure R245fa, drops to
110 for the vapour Nusselt number and 165 for the liquid Nusselt number. Even for a situation with
110 for the vapour Nusselt number and 165 for the liquid Nusselt number. Even for a situation with
minimal superheating of the working fluid, this implies that an oversized heat exchanger will be
minimal superheating of the working fluid, this implies that an oversized heat exchanger will be
needed for the dynamic cycle compared to a non-dynamic cycle using R245fa as the working fluid.
needed for the dynamic cycle compared to a non-dynamic cycle using R245fa as the working fluid.
This will add to the capital cost of the dynamic cycle compared to a non-dynamic equivalent.
This will add to the capital cost of the dynamic cycle compared to a non-dynamic equivalent.
4. Conclusions
Energies 2017, 10, 440
19 of 21
It can be seen in Figure 19 that the Nusselt number is around 270 for the pure R245fa, drops
to 110 for the vapour Nusselt number and 165 for the liquid Nusselt number. Even for a situation
with minimal superheating of the working fluid, this implies that an oversized heat exchanger will be
needed for the dynamic cycle compared to a non-dynamic cycle using R245fa as the working fluid.
This will add to the capital cost of the dynamic cycle compared to a non-dynamic equivalent.
4. Conclusions
This paper investigates if the recently developed dynamic ORC cycle can be applied to small-scale
systems based on positive-displacement expanders with fixed expansion ratios. The results show
that the dynamic ORC is capable of increasing the system’s annual average efficiency for a given
heat source. However, such an improvement is much less than that of the large scale system using
turbine expanders with variable expansion ratios. Furthermore, such benefit strongly depends on heat
recovery via the recuperator. The higher the heat recuperation, the higher the efficiency improvement.
This is because an expander with a fixed expansion ratio approximately has a constant pressure ratio
between its inlet and outlet. The increase of pressure ratio between the evaporator and condenser by
tuning the condensing temperature to match colder ambient condition in winter cannot be utilized by
such expanders. However, with the recuperator in place, the higher discharging temperature of the
expander could increase the heat recovery and consequently reduce the heat input at the evaporator,
ultimately increasing the thermal efficiency.
The dynamic cycle also showed an improvement in specific power, implying better heat source
utilization. This was caused by increasing expander inlet superheat as the working fluid composition
changed, allowing for the same amount of electricity to be generated from a smaller flow rate of
thermal fluid.
An exergy analysis has also been conducted, and it was found that the exergy destruction in the
cycle was dominated by the evaporator. The exergy efficiency was improved by the dynamic cycle,
particularly in the winter months, as the recuperator and increased superheat caused by the change in
working fluid composition made better use of the increased available driving temperature differential,
compared to the conventional, non-dynamic cycle.
Acknowledgments: This research is funded by Royal Society (RG130051) and EPSRC (EP/N005228/1 and
EP/N020472/1) in the United Kingdom, and a joint Programme “Royal Society–National Natural Science
Foundation of China (Ref: IE150866)”.
Author Contributions: Zhibin Yu developed the initial concept. Peter Collings and Zhibin Yu performed the
literature review and collaborated on the introduction. Peter Collings produced the mathematical model and
MATLAB program. Peter Collings and Zhibin Yu analysed the results and interpreted the data. Peter Collings
and Zhibin Yu wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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