Energy Loss by Thermal Conduction and Natural Convection in Annular Solar Receivers

TL;DR: In this paper, a parabolic-cylindrical solar collector with a circular receiver tube enclosed by a concentric glass envelope and situated along the focal line of the parabolic trough reflector is described.

Abstract: An effective device for the collection of solar energy is the so-called parabolic-cylindrical solar collector. In this device, a circular receiver tube is enclosed by a concentric glass envelope and situated along the focal line of a parabolic trough reflector. The heat transfer processes which occur in the annular space between the receiver tube and the glass envelope are important in determining the overall heat loss from the receiver tube. In typical high temperature receiver tube designs the rate of energy loss by combined thermal conduction and natural convection is of the same order of magnitude as that due to thermal radiation, and can amount to approximately 6% of the total rate at which energy is absorbed by the solar collector. The elimination of conduction and natural convection losses can significantly improve the performance of a large collector field.

Summary

INTRODUCTION

• An effective device for the collection of solar energy is the so called parabolic-cylindrical solar collector.
• The heat transfer processes which occur in the annular space between the receiver tube and the glass envelope are important in determining the overall heat loss from the receiver tube.
• In typical high temperature receiver tube designs the rate of energy loss by combined thermal conduction and natural convection is of the same order of magnitude as that due to thermal radiation, and can amount to approximately 6% of the total rate at which energy is absorbed by the solar collector.
• '.lhe receiver configuration chosen for study is typical of those used in the Solar Total Energy System at Sandia Laboratories.
• The receiver tube has a "black chrome" selective coating and is 2.54 em in outside diameter.

CONDUCTION HEAT LOSS

• Of the three modes of heat transfer, the most significant heat loss savings for an annular receiver can be accomplished by limiting conduction losse~.
• Convection losses are negligible so long as the annular space is properly sized.
• Radiation losses, being_ primarily fixed by the receiver tube selective surface properties, are more difficult to reduce.
• Variations in electroplating parameters to reduce the receiver thermal emittance properties may result in lower solar absorptivity and perhaps poor durability _properties.
• Attempts to limit heat transfer through the annular space will :be discussed in the f6llowing sections.

•Effect of Vacuum

• For a given gas, the relative magnitudes of the molecular mean free path and the annulus gap determines whether the effective heat transfer coefficient for thermal conduction is (1) .independent of annulus pressure, (2) a function of the annulus pressure, or (3) negligible.
• The analysis assumed steady state conditions and utilized standa~~correlations for the effects of pressure, wind, geometry, and temperature on the conduction and convection terms.
• Heat inp~t was provided by a ChromaloxR resistance heater element centered inside the receiver tube.
• All vacuums were maintained with a CEC Sampling Probe and Sargent-Welch single stage vacuum pump.
• Variations in receiver tube coating properties necessitated bracketing the experimental data with analytical results calculated for receiver tube emissivities of 0.2 and 0.3 at 589 K, with the emissivities decreasing linearly with temperature to 0.15 at 373 K.

Effect of Annulus Gap Sizing

• Optimum sizing of the annular space for operation at atmospheric prassure requires that the energy transferred across the gap be by thermal conduction and radiation heat transfer.
• By decreasing the pressure, the Rayleigh number is reduced below 1000 through lowering the annulus gas density.
• Hg and oversizing the gap, heat loss savings of between 15 and 30 W/m may be obtained over that lost by a receiver design sized to eliminate convection heat transfer at atmospheric pressure.
• Since the reduction of heat loss by 30 W/m for the "correctly" sized annular space necessitates using vacuums below 0.1 mm.

\ Effect Of Gases Other Than Air

• Utilization of gases other than air in the receiver annulus should reduce the conduction heat loss so long as (1) the gas thermal conductivity is less than that of air and (2) the.
• Calculations were performed for argon a.nd carbon dioxide.
• The insulating effect of the lower thermal conductivity is.
• The resulting methodology ~been incorporated, by Gartling [8] , into a user-oriented, f~ite element, computer program called NACHOS.
• The program is quite versatile and cc;tn be used for the analysis of both free and forced convection heat transfer as well as for isothermal flows.

Heat Transfer Between• Concentr•ic Cylinders

• In order to demonstrate that the results of the numerical analysis are compatible with existing experimental results, an initial series of calculations was performe~ for horizontal, concentric, circular cylinders with uniform temperatures.
• ~ the Rayleigh number, where the heat loss ratio is defined to be the ratio of the energy loss per unit length due to natural convection -10to that due to thermal conduction acting alone.
• When the highest temperature occtirred on the lower surface of the inner cylinder,-the calculated results were virtually indistinguishable from those obtained with uniform wall temperatur~s as plotted in Figure 5 .
• The results for this nonuniform case nre not plotted.

Eccen~ric Cylinders

• The geometry chosen for the study of eccentric cylinders consisted of inner and outer cylinde~s of radii 1.27 em and 2.79 em, with the inner cylinder displaced downward a distance equal to onehalf the gap width yielding an eccentricity of 0.76 em.
• R was held at a 1.1niform temperature, also known as Each cylinde.
• The selection of the case chosen for study was influ~nced by certain practical considerations.
• First, a downward displacement of the inner cylinder enhances the ~ convection process more than an upward displacement.
• Secondly, an eccentricity of one-half the gap width is greater than that encountered in practical receiver designs.

Figures

Figure 3. Receiver Annulus Oversizing for Reducing Heat Loss

Figure 4. Summary Data on Heat Loss Reduction Techniques

Figure 1. Receiver Tube Temperature as a Function of Annulus Pressure

Figure 6. Steamlines .and Isotherms for Natural Convection Between Concentric, Circular Cylinders, Uniform Temperature, NRa = 12,142 ~

Full text

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ENERGY
LOSS
BY
THERMAL
CONDUCTION
AND
NATURAL
CONVECTION
IN
ANNULAR
SOLAR
RECEIVERsl
by
1
. k d
1'
2
A.
C.
Ratze
,
C.
E.
H1c
ox,
an
D.
K.
Gart
1ng
Fluid
and
Thermal
Sciences
Department
Sandia
Laboratories
Albuquerque,
NM
87115
USA
presented
at
Fifteenth
International
Thermal
Conductivity
Conference
Ottawa,
Ontario,
Canada
The
work
discussed
in
this
paper
was
supported
by
the
United
States
Energy
Research
and
Development
Administion.
Member~
u[
Llu.:!
Technicu.l
St.:1ff
~
ASTE
R
OIS
T
RIBhJT.IO
.N
OF
THIS
DOCU
ME C b
.
NT
IS
UNLJMIT£0

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INTRODUCTION
An
effective
device
for
the
collection
of
solar
energy
is
the
so
called
parabolic-cylindrical
solar
collector.
In
this
device,
a
circular
r.eceiver
tube,
with
a
suitable
selective
coating,
is
en-
closed
by
a
concentric
glass
envelope
and
situated
along
the
focal
line
of
a
parabolic
trough
reflector.
The
heat
transfer
processes
which
occur
in
the
annular
space
between
the
receiver
tube
and
the
glass
envelope
are
important
in
determining
the
overall
heat
loss
from
the
receiver
tube.
In
typical
high
temperature
receiver
tube
designs
the
rate
of
energy
loss
by
combined
thermal
conduction
and
natural
convection
is
of
the
same
order
of
magnitude
as
that
due
to
thermal
radiation,
and
can
amount
to
approximately
6%
of
the
total
rate
at
which
energy
is
absorbed
by
the
solar
collector.
The
elimination
of
conduction
and
natural
convection
losses
can
signifi-
c·antly
improve
the
performance
of
a
large
collector
field.
In
this
paper,
several
techniques
useful
for
the
reduction
of
energy
loss
by
thermal
conduction
and
natural
convection
are
considered.
'.lhe
receiver
configuration
chosen
for
study
is
typical
of
those
used
in
the
Solar
Total
Energy
System
at
Sandia
Laboratories.
The
receiver
tube
has
a
"black
chrome"
selective
coating
and
is
2.54
em
in
outside
diameter.
The
inside
diameter
of
the
glass
envelope
is
approximately
4.4
em.
Typical
operating
temperatures
of
the
receiver
tube
and
glass
envelope
are
approximateli
573
K
and
373
K,
respectively.
CONDUCTION
HEAT
LOSS
Of
the
three
modes
of
heat
transfer,
the
most
significant
heat
loss
savings
for
an
annular
receiver
can
be
accomplished
by
limiting

..
-2-
conduction
losse~.
Convection
losses
are
negligible
so
long
as
the
annular
space
is
properly
sized.
Radiation
losses,
being_
pri-
marily
fixed
by
the
receiver
tube
selective
surface
properties,
are
more
difficult
to
reduce.
Variations
in
electroplating
parameters
to
reduce
the
receiver
thermal
emittance
properties
may
result
in
lower
solar
absorptivity
and
perhaps
poor
durability
_properties.
Attempts
to
limit
heat
transfer
through
the
annular
space
will
:be
discussed
in
the
f6llowing
sections.
Techniques
studied
include
{1)
evacuation
of
the
annulus
gas,
(2)
oversizing
the
arinular
space,
.and
(3)
using
gases
other
than
air
for
the
heat
transfer
medium.
·Effect
of
Vacuum
A
revie\v
of
the
literature
on
vacuum
technology
indicates
that
the
thermal
conductivity
of
a
gas
i~
a
function
of
the;
mean
free
p·ath
of
the
gas
molecule~
[1,
2,
3].
An
expression
relating
the
mean
free
path
of
a
gas
to
the
enclosure
pressure
and
gas
temperature
is
where
T,
P,
and
o
are
given
in
deg
K,
mm
Hg,
and
em,
respectively.
For
a
given
gas,
the
relative
magnitudes
of
the
molecular
mean
free
path
and
the
annulus
gap
determines
whether
the
effective
heat·
transfer
coefficient
for
thermal
conduction
is
(1)
.independent
of
annulus
pressure,
(2)
a
function
of
the
annulus
pressure,
or
(3)
negligible.
The
governing
equation
for
the
effective
heat
transfer
coefficient
for
the
annular
space
is
[1]
k
kef~
r.Ln(r
/r.)
+.bA(r./r
+
lf
~
0
~ ~
0
(2)