136
3 Experiments in Pebble Bed Heat Transfer
to retrieve the thermal diffusivity from the measured temperatures. The calculated
results have proven that it is an effective algorithm for data processing, and the
analyses of sensitivity and uncertainty also illustrate its desirable characteristics on
robustness and uncertainty. All of these explorations are beneficial to guide the practical experiments in later work. Furthermore, the effective thermal conductivity can
also be derived through the known volume-averaged density and specific heat capacity of the graphite elements in this method.
Through the dynamic temperature data of one-dimensional heat transfer, the effective thermal diffusivity is retrieved by the inverse method in the bulk region of the
pebble bed. Then, the effective thermal conductive is calculated through the effective
thermal diffusivity, bulk density, and specific heat capacity of graphite. The stable
result is consistent with previous researches in effective thermal conductivity of a
pebble bed. The decrease in the effective thermal conductivity near the wall is also
observed in this test.
The uncertainty analysis reveals that statistical errors of thermocouples make a
little influence in the inverse method. However, a constant systematic error should
be treated carefully. Although this facility has sufficient circumferential symmetry,
the position error is regarded as the statistical uncertainty of the five circumferential
temperature series to study the effect of the installation position of thermocouples.
This study preliminarily verifies the inverse method to determine the effective
thermal diffusivity and conductivity of a pebble bed with a well-symmetry experimental facility. This method avoids measuring the heat flow in a large facility with
high-temperatures, which gives rise to lots of unmeasurable error in heat loss of high
temperatures.
3.3 Effective Thermal Diffusivity and Conductivity
At the present stage, four heating tests have been conducted up to 1,200
◦ C. Two
of them are vacuum tests at an absolute pressure 20 Pa, and another two are helium
tests at the constant atmospheric pressure from 105 kPa to 108 kPa during the whole
heating and cooling process. The vacuum condition is maintained by two sets of
four mechanical vacuum pumps alternately. The helium pressure is monitored and
stabilized by a helium pressurizer. Figures (3.9a, b) show the average temperature
processes by the five sets of azimuthal thermocouples at the middle level. In the
vacuum tests, the heating process is divided into two stages to alleviate temperature
variation in the first test, and the heating is set as only one stage in the second
test. Two heating processes of helium tests are similar. The whole experimental
periods of four tests are 433 h, 400 h, 265 h, and 240 h. The difference in the heating
processes can prove the experimental repeatability and robustness, and the results of
these tests will be compared with the results of helium SANA and vacuum HTTU.
Moreover, although the highest temperature is about 1,200
◦ C in all tests, the less
time consumption in helium tests implies the effective thermal diffusivity in helium
condition is higher than that in the vacuum condition.
3 Experiments in Pebble Bed Heat Transfer
to retrieve the thermal diffusivity from the measured temperatures. The calculated
results have proven that it is an effective algorithm for data processing, and the
analyses of sensitivity and uncertainty also illustrate its desirable characteristics on
robustness and uncertainty. All of these explorations are beneficial to guide the practical experiments in later work. Furthermore, the effective thermal conductivity can
also be derived through the known volume-averaged density and specific heat capacity of the graphite elements in this method.
Through the dynamic temperature data of one-dimensional heat transfer, the effective thermal diffusivity is retrieved by the inverse method in the bulk region of the
pebble bed. Then, the effective thermal conductive is calculated through the effective
thermal diffusivity, bulk density, and specific heat capacity of graphite. The stable
result is consistent with previous researches in effective thermal conductivity of a
pebble bed. The decrease in the effective thermal conductivity near the wall is also
observed in this test.
The uncertainty analysis reveals that statistical errors of thermocouples make a
little influence in the inverse method. However, a constant systematic error should
be treated carefully. Although this facility has sufficient circumferential symmetry,
the position error is regarded as the statistical uncertainty of the five circumferential
temperature series to study the effect of the installation position of thermocouples.
This study preliminarily verifies the inverse method to determine the effective
thermal diffusivity and conductivity of a pebble bed with a well-symmetry experimental facility. This method avoids measuring the heat flow in a large facility with
high-temperatures, which gives rise to lots of unmeasurable error in heat loss of high
temperatures.
3.3 Effective Thermal Diffusivity and Conductivity
At the present stage, four heating tests have been conducted up to 1,200
◦ C. Two
of them are vacuum tests at an absolute pressure 20 Pa, and another two are helium
tests at the constant atmospheric pressure from 105 kPa to 108 kPa during the whole
heating and cooling process. The vacuum condition is maintained by two sets of
four mechanical vacuum pumps alternately. The helium pressure is monitored and
stabilized by a helium pressurizer. Figures (3.9a, b) show the average temperature
processes by the five sets of azimuthal thermocouples at the middle level. In the
vacuum tests, the heating process is divided into two stages to alleviate temperature
variation in the first test, and the heating is set as only one stage in the second
test. Two heating processes of helium tests are similar. The whole experimental
periods of four tests are 433 h, 400 h, 265 h, and 240 h. The difference in the heating
processes can prove the experimental repeatability and robustness, and the results of
these tests will be compared with the results of helium SANA and vacuum HTTU.
Moreover, although the highest temperature is about 1,200
◦ C in all tests, the less
time consumption in helium tests implies the effective thermal diffusivity in helium
condition is higher than that in the vacuum condition.