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Proceedings of the 20th National

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                                                                      Proceedings of the 20 National and 9th International
                                                                         ISHMT-ASME Heat and Mass Transfer Conference
                                                                                          January 4-6, 2010, Mumbai, India




                                                                                                         10HMTC271


                       DETERMINING THE SPECIFIC HEAT OF POWDERED INSULATION


               Peter W. Higgins                         Christopher Olson                         Mingli He
          Metropolitan State College of            Gas Compressor Consultants,           Metropolitan State College of
                     Denver                                    Inc.                                 Denver
              Denver, CO, 80217                         Denver, CO, 80202                    Denver, CO, 80217
                      USA                                      USA                                  Country
              phiggin1@mscd.edu                        colson31@mscd.edu                       he@mscd.edu



ABSTRACT                                                              powder with a known specific heat value, Aerogel beads, and
    A technique is presented for the determination of specific        3M glass bubbles as shown in Figure 1.
heat of a new generation of powdered insulation suitable for
the annular space of a large cryogenic storage tank. The
method uses a copper sensing cup into which a small amount
of heated insulation powder is poured. J, and K-type
thermocouples measure the temperature loss of the powder
and the corresponding temperature gain of the cup. In order
for the energy gain of the cup to equal the energy loss of the
powder, the entire cell is wrapped with a cryogenic blanket,
and for some of the tests, subject to a partial vacuum.
Equating the energy loss from the powder to the energy gain
of the cup over a short period of about 60 seconds yields the
specific heat of the powder. The results of applying this
method to the study of 10-70 micron glass spheres and aerogel
beads are presented and discussed. Study of this material
becomes timely since these products may find application in                            Figure 1 a. 3 M BUBBLES
efficient cryogenic storage of fuel cell products made by wind        3M Series K1 Glass bubbles (Soda Lime Borosilicare Glass,
and solar plants located in areas not connected to a power            Amorphus Silica). Mean diameter is 65 microns with a bulk
                                                                                        3
grid. This work was done by undergraduate students at                 density of 70 kg/m . Recommended for use in the 15 millitorr
Metropolitan State College of Denver.                                 cryogenic tank vacuum.



INTRODUCTION
    Large, 3,200,000-liter cryogenic tanks exist at NASA's
shuttle launch facilities for LH2 and LO2 storage. Currently,
these use Perlite insulation material in a 1.5 meter annular
space between the inner and outer walls of these tanks which
is maintained at a vacuum of 15 millitorr. Daily hydrogen
boiloff substancially exceeds design specifications, and the
insulation material is nearing its useage lifetime, so NASA is
considering replacing the Perlite with better insulation. Two
materials are now under consideration: 3M glass beads, and
Aerogel beads. Since the specific heat of these materials is
not precisely known, NASA investigators have sent samples
for our students to study. This paper is a result of their efforts.                   Figure 1 b. AEROGEL BEADS
                                                                      Cabot Corporation Nanogel Aerogel beads. 1-mm spherical
                                                                                                               3
                                                                      particle having a bulk density of 80 kg/m . Recommended for
                                                                      use in an ambient pressure.
MATERIALS TESTED
   Three powdered insulation samples were provided by the
Kennedy Space Center, NASA for analysis: Expanded Perlite
                     Figure 1 c. PERLITE
Ryolex Grade #39 made by Silbrico Corporation having a bulk
                           3
density of from 60-220 kg/m .
                                                                                               †
                                                                                    Figure 2 . FINAL METHOD LAYOUT
    Although the specific heats for the glass beads and bubbles      †
                                                                      This apparatus is an original piece of lab equipment built in Philadelphia by
are not known, NASA has tested the thermal performance of            the Queen Company circa 1880. Its use here honors Otto von Guericke,
these 3 materials for boundary temperatures of 78 / 293 K as         German Mayor of Maydeburg, who invented the check value hand vacuum
shown in Table 2.                                                    pump in 1654, and whose Maydeburg spheres astonished onlookers for a
                                                                     century. This type vacuum pump, improved by Boyle, was instrumental in the
                                                                     development of gas laws. (Wikipedia.org)
      Table 2. APPARENT THERMAL CONDUCTIVITY

    Insulation            Apparent Thermal Conductivity
     Material                       (mW/mK)
                         High Vacuum         Ambient
                                            Pressure
     Perlite                  0.9              36
 Glass Bubbles                0.6              27
 Aerogel Beads                1.8              14


TESTING APPARATUS AND METHODOLOG


Final Method
    A test cell was constructed in which a small quantity of
heated power cools in a 2.83 cm diameter, 2.3 cm tall copper
cup. The cup is equipped with 2 thermocouples, one in the
center sense powder temperature, the other on the side of the
cup to measure cup temperature. A data acquisition system
samples these thermocouples twice a second. The test cell sits                         Figure 3. LABVIEW INTERFACE
on, and is surrounded by a 1.5 cm thick, Aspen Cryogel Z
cryogenic blanket held in place by a velcro strap.
    In the first series of tests of all three powders the isolated   Early unsuccessful Methods
cell was placed inside a PVC 2 inch coupling and topped by               The test procedure and apparatus described above evolved
another piece of cryogenic blanket. In the second tests of the       from earlier attempts to make this measurement which failed
3M powder only, the test cell was additionally placed in a           to yield the results expected for expanded perlite. Perlite was
vacuum jar vacuum pumped down to 17 inches Hg, thus                  our calibrating standard since it has a known average specific
removing about 60 % of the air around the test cell. This            heat¹ of 1090 J/Kg K. In these previous attempts a large
second configuration is shown in Figure 2.                           aluminum billet having a cavity for the powder was heated in
    In both series of tests the thermocouple leads are               an oven to about 100 C. The temperature of the cavity and of
connected to an Omega 6018 data acquisition module pictured          the aluminum block was measured with thermocouples. A
inside the wooden box shown in the picture. Powder is placed         measured amount of room temperature powder was poured
in a small beaker and heated on a hot plate. During the              into the cavity, and the whole cell was quickly tightly wrapped
heating process the powder is frequently stirred and tumbled         in aerogel blanket (sides, top and bottom) and the test cell was
to assure uniform heating throughout.                                subject to partial vacuum. An energy balance equating energy
    The DAQ is connected to the serial port of a laptop              loss from the aluminum block to that gained by the powder
running LabView 8. A LabView program was written to read             yielded results at least a factor of 2 from the expected result.
the incoming data stream, to parse the data to a chart object        This was attributed to two factors: the aluminum block was
and to write an ASCII text file with the timestamp and channel       too massive, hence the temperature change needed to heat the
values. The user interface is shown by Figure 3.                     powder was too small for accurate measurement by the
                                                                     thermocouples, and secondly, heat loss from the large surface
                                                                     area billot to its environment could not be adequately
                                                                     controlled.
The Successful Experiments                                                                                                                     3M Bubbles Test
  Following details the experiments made using the heated                                                                                                                                          Cup, run 1

powder and room temperature cup:                                                            100.00                                                                                                 Pow der, run 1
                                                                                                                                                                                                   Cu cup, run 2
                                                                                             90.00
                                                                                                                                                                                                   Pow der, run 2
                                                                                             80.00

                                                                                             70.00
  Data: In the first series of tests temperature data was




                                                                      Temperature, C
                                                                                             60.00
obtained from J-type thermocouples welded by the students                                    50.00
using a carbon bar extracted from a 6 volt lantern battery and                               40.00
connected to the negative side of a sealed 6 volt lead acid                                  30.00

battery. The positive side of the battery was then connected to                              20.00

within 1/2 inch of the juction wires to be welded. The wires                                 10.00

were momentarily touched to the carbon bar shorting the                                       0.00




                                                                                                     1

                                                                                                          8

                                                                                                               15

                                                                                                                         22

                                                                                                                               29

                                                                                                                                      36

                                                                                                                                             43

                                                                                                                                                   50

                                                                                                                                                            57

                                                                                                                                                                        64

                                                                                                                                                                               71

                                                                                                                                                                                      78

                                                                                                                                                                                             85

                                                                                                                                                                                                         92

                                                                                                                                                                                                                99

                                                                                                                                                                                                                           106

                                                                                                                                                                                                                                       113
battery and producing just enough arc for a very fine bead                                                                                              Tim e, s

weld. Each thermocouple was subsequently tested in ice
water and in boiling water where phase change temperatures
are known. A 3/16 roughly circular thin solder bead was                                                              Figure 5. 3M BUBBLES TEST
added to the thermocouple used to measure the powder
temperature to increase the thermocouple's sensing surface in
contact with the powder.                                                                                                                     Aerogel Beads Test
    The thermocouples were connected to two channels of an                                                                                                                                    Pow der, run 1

Omege 6018 data acquisition module and calibrated with a                                    60.00
                                                                                                                                                                                              Cup, run1
                                                                                                                                                                                              Pow der, run2
Transmation 1045 precision millivolt calibrator. A LabView 8                                                                                                                                  Cup, run 2
                                                                                            50.00
program was written using the low level Instrument Assistant
object that acquired the continuous string data stream. The                                 40.00


                                                                           Temperature, C
stream was then parsed into analog channel data then digitized
                                                                                            30.00
and fed to both a chart display and a user-selected text file.
Sampling was accomplished by a system timer object that                                     20.00

released the CPU to look at the data according to user-
                                                                                            10.00
specified intervals.
    Shown in figures 4-6 are the temperature signals obtained                                0.00
                                                                                                     1
                                                                                                         12
                                                                                                              23
                                                                                                                    34
                                                                                                                          45
                                                                                                                                 56
                                                                                                                                       67
                                                                                                                                             78
                                                                                                                                                   89
                                                                                                                                                          100
                                                                                                                                                                  111
                                                                                                                                                                         122
                                                                                                                                                                                133
                                                                                                                                                                                      144
                                                                                                                                                                                             155
                                                                                                                                                                                                     166
                                                                                                                                                                                                              177
                                                                                                                                                                                                                     188
                                                                                                                                                                                                                                 199
                                                                                                                                                                                                                                         210
from the powder-embedded thermocouple and from the                                                                                                      Tim e, s

thermocouple measuring the copper cup temperature. Figure 4
shows the data from the Perlite test when the powder was
heated to about 60 C. The most repeatable results were                                                        Figure 6. AEROGEL BEADS TEST
obtained by taking the heat losses and gains over a 60 second
interval starting slightly after the peak powder temperature.

                                                                                                                                            3M Vacuum Test

                                                                                            120.00                                                                             Cup, #1
                                                                                                                                                                               Powder, #1
                                                                                            100.00
                                                                                                                                                                               Cup, #2
                                                                    Temperature, C




                                                                                             80.00                                                                             Powder, #2
                                                                                             60.00
                                                                                             40.00

                                                                                             20.00
                                                                                               0.00
                                                                                                         1
                                                                                                              41
                                                                                                                     81
                                                                                                                               121
                                                                                                                                      161
                                                                                                                                             201
                                                                                                                                                    241
                                                                                                                                                                281
                                                                                                                                                                         321
                                                                                                                                                                                361
                                                                                                                                                                                       401
                                                                                                                                                                                                   441
                                                                                                                                                                                                              481




                                                                                                                                             Time, sx2



                                                                                                                         Figure 7. 3M VACCUM TEST

                  Figure 4. PERILITE TEST
                                                                    Analysis: Analysis of the data recorded by the Omega
    Two runs were then made examining the energy balance          6018 thermocouple module in a text file was performed in
on the 3M bubbles: the first in which the bubbles were heated     Excel after the raw data was imported and parsed into
to over 90 C, the second with the bubbles heated to about 40      columns. An energy balance yields:
as shown in figure 5 Figure 6 shows the two test runs made
on the Aerogel beads.                                                                  Ein  Eout  dE / dt sys                                                                                                                                (1)
Figure 7 shows the data taken from a retest of the 3M bubbles
using the vacuum apparatus shown in Figure 2 with a vacuum
of 17 inches hg.                                                      Applied to the copper cup over a time period dt, the energy
                                                                  in comes from the energy lost from the heated powder.
                                                                  Energy out of the copper cup is minimized by insulation and a
                                                                  partial vacuum; therefore the energy lost from the powder
                                                                                                                5
results in internal energy gain of the cup since no work is          Comment on Measurement Error : Error associated
done. The energy lost from the powder in a time dt is:             with the time constant of the J and K type thermocouples are
                                                                   minimal since the time constant for the very small welded
    Ein  m p  c p  Tp                                   (2)    junctions are in the order of a second. The DAQ was properly
                                                                   calibrated in mV for each thermocouple used, and each
                                                                   welded thermocouple was tested in ice water and boiling
   wherein cp is the epecific heat of the powder, mp is its mass   water.      Since all temperatures used were temperature
and ΔTp is its temperature change in the time period dt. This      differences, a slight bias in value or size of a degree would
equates to the internal energy increase of the small copper cup    cancel. Likewise weights of the powder and cup were made to
given by:                                                          within a few percent using laboratory grade digital scales.
                                                                   Since specific heat is a property of the material, its distribution
    dE  mc  c pc  Tc                                    (3)    about a mean value is small so the Gauss error function
   wherein mc is the mass of the cup, cpc the specific heat and    pertaining to this distribution would not show a large
ΔTc is the temperature change of the cup in dt. Combining          statistical variation in sample value. Thus the major unknown
equations the unknown powder specific heat is therefore:           in our experiments is the amount of heat escaping from the
                                                                   powder on its top surface through the aerogel blanket and into
                                                                   the surrounding still air, and from the sides and bottom of the
    c pp  mc  c pc  Tc /(m p  Tp )                    (4)
                                                                   cupper cup into the blanket and surrounds, all during the
                                                                   approximately 60 second sample period.
   Specific heats so computed are shown in Table 3.                    The maximum amount of this extraneous heat transfer for
                                                                   the 3M bubbles test in the bell jar can be approximated as due
                      Table 3. RESULTS                             to conduction through the Aspen Cryogel Z, 1.5 cm thick
                                                                   blanket followed by natural convection into the partially
Material/      mcu    mp     cpcu     cpp    dTp     dT    Tim     evacuated (17 inches Hg) air in the bell jar:
 Run #          g     G     J/Kg     J/Kg     C       c     e
                              K        K             C      S
                                                                       t  T / Rth  Q                                         (6)
3M            28.8    2.1   385      494     6.90   .66    60
bubbles/1     5       5
                                                                       wherein the sum of the thermal resistances include the
3M                                   490     33.8   3.2    73
                                                                   blanket resistance and the film resistance on both sides of the
bubbles/2                                    1      1
                                                                   surface of the blanket to the partially evacuated air in the bell
3M                                   461     22.4   2      57      jar. (see www.aspen.com for Aerogel Cryogel Z properties)
bubbles,                                                           This is computed for both the powder top surface and for the
vacuum/3                                                           sides and bottom of the copper cup. In the case of the high
3M                                   514     28.1   2.8    60      temperature 3M bubbles case, the heat gained by the cup was
bubbles,                                                           31J while the maximum extraneous loss from the powder was
vacuum/4                                                           5.5J and from the cup was 2J resulting in a maximum error of
Aerogel/1     28.8    1.3   385      1078    9.82   1.3    105     24%. Tests done at the lower temperatures would have about
              5       9                             1              half this error.
Aerogel/2             1.4            1075    14.8   2.0    161
                                             3      1
Perlite       28.8    1.0   385      1009    17.2   1.5    60         Summary Results : The final results of the specific
              5                              6      6              heat testing done by the heat transfer undergraduate students at
                                                                   Metro State College of Denver is presented in Table 4. It is
                                                                   possible that these values are underestimated by between 10 to
                                                                   24% if extraneous heat loss is accounted for.
  Fourier Number: The Fourier number is a dimensionless
time equal to the diffusivity of the sample times the sample                          Table 4. FINAL RESULTS
time divided by the radius squared of the cup, i.e.:
                                                                                                      Calculated       Calculated
                                                                                     Expected
                                                                                                          cp               cp
      t /l   2
                                                            (5)      Material         Value
                                                                                                       J/Kg K           J/Kg K
                                                                                      J/Kg K
                                                                                                        Run 1            Run 2
    wherein the diffusivity is thermal conductivity divided by     Expanded
heat capacity (density times specific heat). For expanded                               1090              1009             1014
                                                                     Perlite
perlite whose density ranges from 32 to 66 kg/m3, thermal          3M Glass
conductivity runs from .039 to .045 and whose nominal                                 Unknown             494               490
                                                                    Bubbles
specific heat is 1090 J/Kg/K, the Fourier Number ranges from       3M Glass
0.23 to 0.42 when the sample period is 60 s. This is consistant    Bubbles,           Unknown             461               514
with requiring a minimum Fourier number of 0.2 for using the        vacuum
one term approximation for the analytical solution of heat
                                                                    Aerogel
conduction as presented by the Heisler charts. It is also                             Unknown             1078             1075
                                                                     Beads
consistant with the results obtained by Ponder² when studying
thermal conductivity of tissues, and with the parameter
estimation process used by Božičević³.
                                                                   CONCLUSIONS
                                                                      Students at Metropolitian State College of Denver were
                                                                   able to devise a testing methodology for determining the
specific heat of unknown insulation powders that produced
reasonable and repeatable results using inexpensive lab
materials and instruments. Since this methodology relied on
an enegy balance between heat dissipated from the insulation
powder and heat gained by a copper cup it was essential that
heat losses from the cup to its surroundings be significantly
reduced. This was accomplished by surrounding the test cell
by an aerogel cryogenic blanket supplied to us by the
Cryogenics Test Laboratory at KSC. In a second test series on
the 3B bubbles, a low level vacuum helped eliminate heat loss
to air. It was found that good, repeatable results were possible
when the sample period was about 60 seconds, which is
consistant with a Fourier number greater than 0.2. This was
long enough for heat to dissipate from the powder into the
cup, but short enough to render the test cell adiabatic. The
maximum error associated with the measured values is
estimated to be 24%. There are sophisticated, automated
methods for performing this same experiment, but these suffer
from the same extraneous heat loss errors that our team
worked to eliminate4.


REFERENCES
   [1] Cengel, Yuns A., 2007. Heat and Mass Transfer. 3rd
       Edition, McGrawHill,.
   [2] Ponder, Eric., 1962. "The Coefficient of Thermal
       Conductivity of Blood and of Various Tissues", The
       Journal of General Physiology, Vol 45, pp545-551.
   [3] Božičević, Juraj; 2003. "Determination of Thermal
       Conductivity in Liquids by Monitoring Transient
       Phenomenon", XVII IMEKO World Congress,
       Metrology in the 3rd Millennium.
   [4] Anter Corporation (www.anter.com); "Discussion on
       Measuring Specific Heat Capacity Using the Flash
       Method", (Technical Note #71)
   [5] Pfaffenberger,     Pattersn,    1981.     "Statistical
       Methods",Richard D Irwin, Inc.