132
3 Experiments in Pebble Bed Heat Transfer
Table 3.1 Optimal solutions of different polynomials
Order
S( P)
p 1
p 2
p 3
e rel
0th
12633.12 2.0167 × 10 −5
0
0
83.96%
1th
4780.83
−4.2235 × 10 −7 1.3204 × 10 −8
0
23.97%
2th
3.38
1.7035 × 10 −6
−7.2257 × 10 −10
1.1653 × 10 −11 0.03%
Exact
6.84
1.7115 × 10 −6
−7.5176 × 10 −10
1.1671 × 10 −11 0.00%
Note The polynomial forms are written as α(T ) = p 1 + p 2 T + p 3 T 2 uniformly. The units of
S, p 1 , p 2 , and p 3 are the same with definitions in the context
3.2.3 Preliminary Tests in Vacuum
The preliminary results of effective thermal diffusivity and conductivity from a lowtemperature test, which was mainly conducted to find and correct the malfunctions
in the facility. Since it accompanied by some failures of the temperature acquisition
system in this test, only a brief result given by the above inverse method is presented.
The more discussions about experimental details and errors would be arranged in the
following sections for normal experiments.
In Eq. (3.10), the relationship between diffusivity and conductivity has been
defined. The density and specific heat capacity of graphite are measured by other
methods. The density is 1,846 kg/m
3 , and the volume-expansion thermal coefficient
is 4.5 × 10
−6 1/K, which gives 0.7% in density variation between 30
◦ C and 1,650
◦ C.
Besides, in the definitions of Eqs. (3.1) and (3.10), the relative volume expansion of
graphite doesn’t change the term . Therefore, the density of graphite is regarded as a
constant in the inverse method. The specific heat capacity is measured by STA449F3
(DSC) of Netzsch, whose accuracy is 3% of the value. The specific heat capacity is
measured twice up to 1,400
◦ C at two individual samples, and the result can be fitted
by a piecewise function. Also, since the apparatus can only measure up to 1,400
◦ C,
the data between 1,400
◦ C and 1,600
◦ C is extrapolated by this piecewise function,
which gives a 10% uncertainty of these data in this region.
Therefore, through Eq. (3.10), effective thermal conductive in bulk pebble bed is
obtained, and the result is compared with the near-vacuum result of HTTU at the
North-West University of South Africa [10]. Four main differences exist between
their test and the test at Tsinghua University. The four main differences are different batch of graphite, different scale of annular bed, 10kPa nitrogen used in their
near-vacuum condition, and the steady-state method used in their data processing.
However, the research team at Tsinghua University still gives a comparable result
obtained by T2–T5 within the reachable temperature region in Fig. (3.6). It should
be noted that the peak at 1,000
◦ C of Rousseau’s result is caused by the wall effect in
their measurement [11].
In addition, the near-wall temperatures, T1 and T6, are not used in the present
section since the wall effect [11], is also observed in this test. In the annular region of
T2–T5, the porosity is regarded as a constant. If the variable porosity is considered in
Eqs. (3.1) and (3.10), with different positions, i.e., the variable density of pebble bed,
3 Experiments in Pebble Bed Heat Transfer
Table 3.1 Optimal solutions of different polynomials
Order
S( P)
p 1
p 2
p 3
e rel
0th
12633.12 2.0167 × 10 −5
0
0
83.96%
1th
4780.83
−4.2235 × 10 −7 1.3204 × 10 −8
0
23.97%
2th
3.38
1.7035 × 10 −6
−7.2257 × 10 −10
1.1653 × 10 −11 0.03%
Exact
6.84
1.7115 × 10 −6
−7.5176 × 10 −10
1.1671 × 10 −11 0.00%
Note The polynomial forms are written as α(T ) = p 1 + p 2 T + p 3 T 2 uniformly. The units of
S, p 1 , p 2 , and p 3 are the same with definitions in the context
3.2.3 Preliminary Tests in Vacuum
The preliminary results of effective thermal diffusivity and conductivity from a lowtemperature test, which was mainly conducted to find and correct the malfunctions
in the facility. Since it accompanied by some failures of the temperature acquisition
system in this test, only a brief result given by the above inverse method is presented.
The more discussions about experimental details and errors would be arranged in the
following sections for normal experiments.
In Eq. (3.10), the relationship between diffusivity and conductivity has been
defined. The density and specific heat capacity of graphite are measured by other
methods. The density is 1,846 kg/m
3 , and the volume-expansion thermal coefficient
is 4.5 × 10
−6 1/K, which gives 0.7% in density variation between 30
◦ C and 1,650
◦ C.
Besides, in the definitions of Eqs. (3.1) and (3.10), the relative volume expansion of
graphite doesn’t change the term . Therefore, the density of graphite is regarded as a
constant in the inverse method. The specific heat capacity is measured by STA449F3
(DSC) of Netzsch, whose accuracy is 3% of the value. The specific heat capacity is
measured twice up to 1,400
◦ C at two individual samples, and the result can be fitted
by a piecewise function. Also, since the apparatus can only measure up to 1,400
◦ C,
the data between 1,400
◦ C and 1,600
◦ C is extrapolated by this piecewise function,
which gives a 10% uncertainty of these data in this region.
Therefore, through Eq. (3.10), effective thermal conductive in bulk pebble bed is
obtained, and the result is compared with the near-vacuum result of HTTU at the
North-West University of South Africa [10]. Four main differences exist between
their test and the test at Tsinghua University. The four main differences are different batch of graphite, different scale of annular bed, 10kPa nitrogen used in their
near-vacuum condition, and the steady-state method used in their data processing.
However, the research team at Tsinghua University still gives a comparable result
obtained by T2–T5 within the reachable temperature region in Fig. (3.6). It should
be noted that the peak at 1,000
◦ C of Rousseau’s result is caused by the wall effect in
their measurement [11].
In addition, the near-wall temperatures, T1 and T6, are not used in the present
section since the wall effect [11], is also observed in this test. In the annular region of
T2–T5, the porosity is regarded as a constant. If the variable porosity is considered in
Eqs. (3.1) and (3.10), with different positions, i.e., the variable density of pebble bed,