Concentrated Evacuated Tubes for Solar-Thermal
Energy Generation using Stirling Engine
Achintya Madduri Member, IEEE, Denise Loeder, Nic Beutler, Mike He Member, IEEE, Seth
Sanders Fellow, IEEE
Abstract—In this study a commercial evacuated tube solar hot- the solar-thermal collection system, which is generated by
water system was modiﬁed to be used as a thermal-power source the evacuated tube system. Tests were conducted on various
for a thermodynamic engine. Commercial hot-water systems topologies using evacuated tubes for increasing the efﬁciency
are meant to operate at temperatures that are close to the
boiling point of water. Single-tube non-imaging concentrators of solar-heat collection.
were built in order to increase the input solar-radiation per
tube and therefore supply thermal-power at temperatures of
180 − 220 ◦ C. Simulations and experiments show that it is
possible to use concentrators to increase the temperature range
of thermal power extracted from a commercial evacuated tube
system and use this modiﬁed system to increase the efﬁciency of
solar-thermal energy generation.
Index Terms—Solar-Thermal Energy Generation, Non-imaging
Concentrators, Evacuated-tube Solar-Thermal Generators
I. I NTRODUCTION
ENEWABLE energy technology will need to address Figure 1. A system representation of a solar thermal electricity generation
R important challenges in order to be adopted at high pen-
etrations in a modern electric grid. These challenges include
scheme using a Stirling-cycle engine.
achieving low enough cost to be economically attractive and The Carnot efﬁciency can be calculated using equation 1.
mitigating the variability inherent in renewable energy sources,
a problem most directly addressed by energy storage. There- ηcarnot = 1 − (1)
fore, there exists a need for an electric generation technology
that easily incorporates low-cost energy storage. A Stirling The heat engine is expected to operate at fraction of the
engine based system for distributed generation of electricity is Carnot cycle (Equation 2) .
a renewable energy technology that addresses the challenges 2
described above . The proposed system, as shown in Figure ηengine = · ηcarnot (2)
1, is comprised of a passive solar collector, a hot thermal
storage subsystem, a Stirling engine for energy conversion, The total system efﬁciency of a heat engine is deﬁne as the
and a waste heat recovery system to implement combined product of the thermal-conversion efﬁciency and the engine
heat and power. The hot-ﬂuid storage tank can be implemented thermodynamic efﬁciency (Equation 3).
with commercially available residential hot-water tanks or with
ηtotal = ηthermal · ηengine (3)
low cost thermal storage ﬂuids, such as mineral or vegetable
oils. However, synthetic thermal storage ﬂuids or phase-change
materials (PCMs) can also be deployed in order to achieve
higher energy storage density. The system as envisioned would A. Evaluation Criteria
be appropriate for residential solar generation or on a small The evaluation criteria for comparing the performance of
commercial building scale. The focus of this paper is on unconcentrated evacuated tubes to concentrated evacuated
achieving high-efﬁciency performance from a commercially tubes is the power output from an ideal Carnot engine per
available solar hot-water system at temperatures in the range unit of installed solar-collector area. An insolation level of
of 180 − 220 ◦ C. Qin = 1000 W/m2 is often used as a way to standardize
It is of particular interest to have a high-temperature input performance metrics for solar-collectors. Since the input in-
to a thermodynamic engine, because the efﬁciency of a ther- solation is normalized per unit area, it is also informative to
modynamic cycle is related to the temperature change, ∆T , normalize the thermal-power output by installed solar-collector
between the hot and cold sides of the engine. In this speciﬁc area, i.e. report Qout in units of W/m2 as well. By multiplying
case the cold-side temperature of the engine is determined by the thermal-power output, Qout , by the idea Carnot efﬁciency,
rejection to ambient Temperature, Tamb . The input temperature ηcarnot (Equation 1), one achieves a measure of the theoretical
is determined by the temperature of the hot supply from output mechanical power from a solar-powered heat engine per
Unconcentrated evacuated tube
With concentration ratio A = 2.22
@ Qin = 1000 W/m2
Figure 2. A representation of an Apricus evacuated tube system .
0 50 100 150 200 250 300
∆T = Tabsorber−Tambient (°K)
unit installed solar-collector area. A reason to compare solar- Figure 3. Theoretical output thermal-power per unit installed solar-collector
collection systems over the same installed collector area is area curves of an Apricus evacuated tube system. The red line represents the
that the available area is often the limiting factor. While cost efﬁciency of the system with concentration. Equation 4 is used with input
insolation of Qin = 1000 W/m2 to generate these curves.
of the components is also important, there is not much of a
difference in material cost between an unconcentrated and a
concentrated evacuated tube system.
C. Non-Imaging Concentrators
B. Evacuated Tube System The foundations of non-imaging optics and concentrators
The solar-collector system is comprised of evacuated tube are described in the classical work done by Winston et. al. ,
absorbers with non-imaging concentrators to achieve the tem- . The concentration ratio of a concentrator is described as
peratures required to maximize efﬁcient operation at low the area of the input aperture to the area of the absorber. The 2-
cost. A commercially-available evacuated-tube solar-hot-water dimensional Compound Parabolic Concentrator (CPC) , has
collection system distributed by Apricus Inc., Figure 2 was been shown to have the maximum theoretical concentration-
used for the experiments described in this paper. The evacuated ratio, wherein, all rays that fall within the entrance aperture
tube system is a simple technology where thermal-power is and acceptance angle are reﬂected out from the exit aperture.
collected by a vacuum insulated solar-radiation absorber and The 2-D CPC is also described as being an “ideal” concentra-
transferred to a working ﬂuid by a heat-pipe. The evacuated tor due to a few other important characteristics:
tube absorber has a thermal-power output curve that is shown 1) Since the CPC is a non-imaging concentrator there is
in Figure 3. The thermal-power output curve is normalized by no need for diurnal tracking. A CPC with an acceptance
the aperture area of the evacuated tubes. The industry standard angle of 56◦ (a concentration ratio of 1/sin 56◦ ≈ 1.21)
for modeling performance of evacuated tube absorbers is to can accept direct solar radiation for 6-8 hours a day
use a quadratic model shown in Equation 4. without adjusting for seasonal variation.
Qout = ao · Qin − a1 · ∆T − a2 · ∆T 2 (4) 2) The performance of a non-imaging concentrator is much
better than that of an imaging one in the case of diffuse
For the Apricus absorbers, the model parameters are: a0 = radiation. This also increases the ability of the solar-
0.687, a1 = 1.505 W/m2 ·◦ K , and a2 = 0.011 W/m2 ·◦ K 2 . collector to perform well over a wider range of weather
The coefﬁcients are normalized such that Qout is in units of conditions.
thermal-power generated per unit of installed evacuated tube 3) The high tolerance of non-imaging concentrators to
area (W/m2 ). It is necessary to minimize the losses per tube in aberrations is also very beneﬁcial in allowing for ease
order to maximize ηthermal (Equation 3). It is easily possible in manufacturing.
to increase ηthermal by increasing the solar radiation input into
each tube while reducing the number of tubes used—the mag-
nitude of the tube loss coefﬁcients (a1 , a2 ) is a function of the II. T HEORETICAL D ESIGN
number of evacuated tubes used per unit of installation area.
A comparison of output thermal-power per unit installed-area In order to characterize the effectiveness of using concen-
of normal evacuated tubes to concentrated evacuated tubes is trated evacuated tubes as a thermal-power source for a heat
shown in Figure 3. One concentrated evacuated tube replaces engine, single-tube concentrators for the Apricus evacuated
three unconcentrated tubes, therefore, concentrating the solar tube system were designed and built. A test setup was cre-
input to an individual tube while reducing the number of tubes ated to compare the relative performance of concentrated to
used overall decreases the surface area, thereby increasing the unconcentrated evacuated tubes. Both the concentrator design
system efﬁciency at ∆T = Thot − Tamb > 100 ◦ C. and the experimental setup are described in the sections below.
factor of 1.21 × π ≈ 3.77 on a per-tube basis.
2) The evacuated tubes are housed in a copper header with
ﬁxed inter-tube spacing as shown in Figure 2. The design
for concentration should be adaptable to the commercial
design without major redesign. A concentrator with
a 56 ◦ acceptance angle is the right size such that
every third tube position could be used to hold the
concentrated-tubes without unused spaces or overlaps.
3) The height of the concentrators is approximately equal to
the the diameter of the collecting aperture divided by the
tangent of collecting angle. This leads to a substantial
increase in height with decrease in acceptance angle.
While it is possible to truncate and still preserve higher
concentration ratios, the loss of acceptance angle and
hence time-of-day for direct radiation was considered
sub-optimal for this experiment.
4) As was discussed above in Section I, the important met-
Figure 4. Proﬁle of a CPC with concentration ratio of 3 for a cylindrical
absorber  ric in determining the value of adding concentrators to
the evacuated tubes is achieving a greater engine output
for the same installed roof-top area of solar-collectors
in the case where three unconcentrated evacuated tubes
are replaced with one concentrated evacuated tube. The
power output for a concentrated evacuated tube system
ao · A · Qin − a1 · ∆T − a2 · ∆T 2
Wout = · ηcarnot
where A is the solar radiation gain to the absorber—i.e.
increased solar ﬂux due to a single tube concentrator
with acceptance angle of θmax .
The comparison of the normalized power output of a Carnot
Figure 5. Representation of the concentrator used in this experiment. It has
an acceptance angle of 56 ◦ which translates to a concentration ratio of 1.21
engine is shown in Figure 6. Based on the comparison, the
case for using fewer concentrated tubes and operating at a
higher temperature T = 150 + Tamb ≈ 180 ◦ C is clear for
A. Concentrator Design even a concentration ratio of 2.22. (Note: This concentration
ratio corresponds to the simulated gain in incident radiation
Concentrators for the evacuated tubes were designed based
for a CPC with an acceptance angle of 56◦ as shown below
on the ideas from . The main consideration was to design
in Section III.)
a concentrator cross-section that was meant for the cylindrical
The concentrators were manufactured using a vacuum ther-
absorber architecture. The original CPC is designed for a
moforming process. Vacuum thermoforming provides accurate
planar absorber. In order to be suitable for a non-planer
plastic shapes that can be coated with a thin layer of reﬂective
absorber, the CPC design has to be adapted , . The
mylar sheeting. An example test concentrator is shown in
required modiﬁcation is to have a section deﬁned by the
involute of the absorber surface meet the proﬁle of a CPC.
The meeting point of the two proﬁles is where the extreme
ray entering a CPC meets the surface of the CPC after one III. S IMULATION S ETUP AND R ESULTS
reﬂection. The general proﬁle of a CPC for a cylindrical The evacuated tubes were simulated in LightTools using
aperture is shown in Figure 4. materials that incorporated all the optical properties speciﬁed
The concentrator proﬁle that was used in this experi- by Apricus Inc. An overview of the optical properties imple-
ment is shown in Figure 5. An acceptance angle of 56 ◦ — mented in the simulations can be seen in Table I. A forward
concentration ratio of 1.21—was chosen for the concentrators. 3-dimensional ray trace analysis was used in order to obtain
The motivations behind the relatively low concentration ratio simulated results of the absorbed radiation at the absorber
were the following: surface. Further, the sun was modeled not only to portray the
1) In the normal operating case for the evacuated tubes, AM1.5G spectrum of the sun, but also to trace the arc that
the acceptance aperture is equal to the diameter of the the sun traces in the sky over the course of a day due to local
tube—the area that is exposed to incident solar radiation. latitude and time of year. A characteristic day in Phoenix, AZ
Hence the theoretical gain with a CPC with concentra- was chosen to model a day with peak incident radiation of
tion ratio of 1.21 is an increase of solar radiation by a 1000 W/m2 .
Unconcentrated evacuated tube
@ Qin = 1000 W/m2 With concentration ratio A = 2.22
Figure 8. Picture of 30-tube Apricus hot-water system integrated with a
storage tank. The system is setup as a thermosyphon to operate without the
0 need of a pump. The heat transfer ﬂuid is Soybean oil.
0 50 100 150 200 250 300
∆T = Tabsorber−Tambient (°K)
Figure 6. Theoretical comparison of power output from an ideal Carnot heat In order to analyze the effect of the highly reﬂective roof
engine per unit area of installed solar-collectors given an insolation level of of our test site simulations of an evacuated tube without
Qin = 1000 W/m2 . Equations 1 and 4 were used to generate these curves. a reﬂective roof-surface were compared to simulations of
an evacuated with a representative roof-surface with optical
reﬂection properties corresponding to a “bitumen” roof . For
simulating the performance of the CPC, a SolidWorks model
with an acceptance angle of 56 ◦ (Figure 5) was imported into
the LightTools simulation environment.
There is a gain-factor of 1.41 in incident solar-radiation
due to the radiation reﬂected onto the back of an evacuated
tube installed on a highly reﬂective roof. (Note: gain-factor in
simulations is a measure of the increase in net solar ﬂux on
an absorber over a period of 6 hours centered at midday.)
The measured gain-factor of a concentrated evacuated tube
in comparison to an unconcentrated evacuated tube with a
highly reﬂective roof is 1.57. In comparison, without a reﬂec-
tive roof, the measured gain-factor of a concentrated tube in
comparison to an unconcentrated evacuated tube is 2.22. The
deviation of this gain-factor from the theoretical concentration
ratio of 1.2 × π ≈ 3.77 can be explained by the variation in
the incident angle of solar radiation due to the arc of the sun
in the sky. Further deviance from the ideal can be explained
by the realistic modeling of the glass cover, the absorber and
the CPC wall coating.
Figure 7. Picture of ﬁnished single-tube concentrator formed using a plastic
thermoforming process and coated with reﬂective mylar. IV. E XPERIMENTAL R ESULTS AND A NALYSIS
A full test system with integrated storage, as shown in
Figure 8, was built to measure the performance of a stock
30-tube Apricus solar hot-water system. The heat storage
Component Material Ref Trans Abs ﬂuid was chosen based on a cost and performance basis. The
Absorber Al/Al-N 0.02 0.02 0.96 important characteristics desired were low vapor pressure and
Cover Borosilicate 3.3 0.04 0.92 0.04 low viscosity at temperatures in the range of 200 − 300 ◦ C.
CPC coating Al Mylar 0.98 N/A 0.02 Due to these considerations, soybean oil was used .
Table I Temperature measurements of the ﬂuid were made at var-
O PTICAL PROPERTIES IMPLEMENTED FOR THE SIMULATIONS OF THE CPC ious points in the system loop. While collecting data for
AND EVACUATED TUBES WHERE R EF =R EFLECTANCE ,
T RANS =T RANSMITTANCE , AND A BS =A BSORPTION . the entire system, it was determined that the thermosyphon
dynamics were too complicated to extract an effective compar-
ison of the performance of unconcentrated evacuated tubes to
concentrated evacuated tubes. Therefore, for the experimental
data used in this paper, the individual tubes were disconnected
from the ﬂuid loop. The heat-pipes (Figure 2) of the tubes
were connected to thermocouples and were insulated using
two inches of ﬁberglass sheeting and Al foil, which corre-
sponds to an R-value of 11. The temperature measurements
were made with thermocouples placed directly on the heat-
pipe bulb and underneath the ﬁberglass insulation—time-series
measurements were collected every 30 seconds for two hours.
A. Evacuated Tube Thermal Analysis
The dynamics of the individual evacuated tubes are based on
the heat balance (Equation 6). The temperature was measured
at the heat-pipe bulb since it is the dominant thermal mass
of the system. Equation 6 expresses the rate of temperature
change of the heat-pipe.
mtube · T = Qin − C · (T − Tamb ) − R · (T 4 − Tsky ) (6)
This model is a simpliﬁed version from . The terms in
the equation are as follows:
1) C is the conductive loss term (W/◦ K ), which is mainly
from the bulb, where it is not vacuum sealed.
2) R is the radiative loss term (W/◦ K 4 ), which is primarily
from the absorber surface. This is a small term, but
becomes important at higher-temperatures.
3) Tsky is the sky temperature that can be derived from
the dry bulb temperature and the dew point ambient
temperature as follows :
Tsky = (ǫsky )0.25 · Tamb (7)
tdp tdp 2
ǫsky = 0.711 + 0.56 · ( ) + 0.73 · ( ) (8)
4) mtube is the thermal mass of an evacuated tube, which is Figure 9. Temperature vs. Time and Temperature vs. ∆T for an experiment
effectively the thermal mass of the heat-pipe (inclusive comparing the performance of an unconcentrated vs. a concentrated evacuated
of bulb and working ﬂuid). The thermal mass was
estimated to be mtube = 330 J/◦ K using a differential Date Measured Concentration Ratio
mass measurement described in the appendix. July 15th , 2011 1.3
5) Qin is the solar radiation ﬂux (W/m2 ) measure July 19th , 2011 (1) 1.2
July 19th , 2011 (2) 1.4
B. Single-Tube Concentrator Performance July 27th , 2011 1.44
Multiple experiments were conducted to measure the in-
crease in performance due to the concentrators. The data Table II
O BSERVED CONCENTRATION RATIO MEASURED AS THE RATIO OF THE
analysis procedure was to ﬁrst use time-series temperature data ESTIMATED INPUT SOLAR RADIATION FOR CONCENTRATED VS .
and extract a plot of ∆T (rate of change of bulb temperature) UNCONCENTRATED EVACUATED TUBES WITH HIGHLY REFLECTIVE
vs. Tamb . Once ∆T is available, a constrained linear-least-
squares algorithm was used to estimate the model parameters
of Equation 6. As can be seen in Figure 9, the extracted model
parameters ﬁt the time-series data very accurately.
Concentration ratio is determined as the ratio of measured
increase in solar ﬂux, Qin , extracted from the experimental The theoretical concentration ratio for the single-tube con-
data. The concentration ratios comparing a concentrated evac- centrators is 1.21 × π ≈ 3.77. In experiments, the measured
uated tube to an unconcentrated evacuated tube on a reﬂective gain-factor in solar radiation input from concentrated evacu-
roof (Table II) corresponded very closely to the simulations— ated tubes in comparison to unconcentrated evacuated tubes on
a gain-factor of 1.57 from simulation results. The average a highly reﬂective roof was 1.33. As is explained in Section
concentration ratio was measured from experimental data to be III, where this increase was measured from simulations to be
1.33, this is based on four experiments conducted in Berkeley, 1.57, the deviation from theory is due to the non-ideal arc that
California around the time of maximum solar altitude for each the Sun follows during a day based on local latitude and time
of those days. of year. Also, there are losses from the non-ideal reﬂective
surfaces of the concentrators used for the above experiments. Achintya Madduri is a Ph. D. student at the Department of Electrical
Engineering and Computer Science at the University of California, Berkeley.
He is working under Professor Seth Sanders on designing thermal collectors
for use in solar-thermal generation and also on developing architecture for
V. C ONCLUSIONS “smart” DC micro-grids.
The focus of this paper was to characterize the importance Denise Loeder is a visiting student researcher from Technische Universtät
of using concentrators for achieving high-efﬁciency solar- München at the Department of Electrical Engineering and Computer Science
at the University of California, Berkeley. She is working under Professor Seth
thermal conversion from a commercial evacuated tube system Sanders on thermal collectors for use in solar-thermal generation.
supplying input thermal-power at temperatures of 180−220 ◦ C
to a heat-engine. As is shown in Figures 3 and 6, the thermal
Nic Beutler is a visiting student researcher from Technische Universtät
and mechanical efﬁciency of using concentrated evacuated München at the Department of Electrical Engineering and Computer Science
tubes at this temperature range are 35% and 12% respectively. at the University of California, Berkeley. He is working under Professor Seth
This is based on simulation results of a concentrator with an Sanders on thermal storage for use in solar-thermal generation.
acceptance angle of 56◦ over the course of 6 hours in a day
with peak insolation of 1000 W/m2 . Experiments with custom Seth Sanders is a Professor in the Department of Electrical Engineering and
manufactured concentrators and a commercial evacuated tube Computer Science at the University of California - Berkeley. He joined the
UC Berkeley faculty in 1989. His research interests are in high-frequency
system prove that simulations are accurate and useful in pre- power conversion circuits and components, in design and control of electric
dicting thermal performance of a concentrated evacuated tube machine systems, and in nonlinear circuit and system theory as related to the
system. Both simulations and experiments show that using power electronics ﬁeld.
a concentrated evacuated tube system will convert incident
solar radiation to thermal-power more efﬁciently at higher Mike He is a Ph.D. student in the Department of Electrical Engineering and
temperatures and therefore increase the mechanical power Computer Science at the University of California - Berkeley. He is working
under Professor Seth Sanders on Stirling engines for distributed solar thermal
output from a heat-engine per unit of installed solar-collector electric generation. He is an NSF Graduate Fellow.
In order to get a measure of the thermal mass of the evacu-
ated tube heat-pipe, a known mass of (600 g) or (231 J/◦ K ) of
copper was added to a tube in the form of multiple layers of
.005 ” thick copper foil. This copper mass was tightly wrapped
around the heat-pipe bulb. Time-series measurements of the
temperatures of an evacuated tube with an additional thermal
mass and one without were collected with the same input
solar irradiance. The temperature data was analyzed to extract
the thermal mass of the Apricus evacuated tubes, which was
estimated as mtube = 330 J/◦ K .
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