152
3 Experiments in Pebble Bed Heat Transfer
where u p j,m is the type B standard uncertainty of p j,m obtained from Eq. (3.48) in
each set. Here the degree of freedom of the type B standard uncertainty is chosen as
infinity.
v B, ¯
p j = ∞.
(3.50)
3.3.5.2 Statistical Error of Experimental Setting (Type a Uncertainty)
From the discussion of Sect. (3.3.4), it is found that some disparities of installation
positions of different azimuthal sensors still exist in the present facility and cause the
different results of five sets from C1 to C5. The subtle difference of local packing
structure at each sensor also gives rise to a small change of measured temperature.
Moreover, the different heating processes also give some differences between the
first and second tests.
Although the improved inverse method of Sect. (3.3.4), is used to alleviate this
kind of error from the facility effectively, the differences can not be eliminated
entirely by the present method. Therefore, this error should be considered as the
type A uncertainty by involving the ten results of C1–C5 of two repeated tests into
uncertainty analysis, under helium and vacuum conditions.
First, for instance, two vacuum repeatability tests were conducted at different
times, and five results were obtained at the same time. According to the recommendation of report JCGM 100:2008 of Joint Committee for Guides in Metrology [26],
the standard deviation of each test p j is calculated by the following procedure:
¯
p j, f =
1
5
5
m = 1
p m, f
(3.51)
σ j, f =
1
4
5
m = 1
p m, j, f − ¯
p j, f
2
(3.52)
Here m indicates the different set from C1 to C5, and j is the index of vector P. The
subscript f denotes the first test, and n will be used to denote the next or second test.
¯
p j, f is an average p j of five sets in the first test. σ f is the standard deviation of five
results in the first test. σ n is calculated by the same equation. In addition, the degrees
of freedom of the two tests are v f = 4 and v n = 4. To combine the results of the
two tests, the pooled experimental standard deviation σ j, p should be used as
σ j, p =
v f σ
2
j, f +v n σ
2
j,n
v f +v n
(3.53)
Then, the type A standard uncertainty of ¯
p j from the ten results is
u A, ¯
p j =
σ j, p
√
10
(3.54)
3 Experiments in Pebble Bed Heat Transfer
where u p j,m is the type B standard uncertainty of p j,m obtained from Eq. (3.48) in
each set. Here the degree of freedom of the type B standard uncertainty is chosen as
infinity.
v B, ¯
p j = ∞.
(3.50)
3.3.5.2 Statistical Error of Experimental Setting (Type a Uncertainty)
From the discussion of Sect. (3.3.4), it is found that some disparities of installation
positions of different azimuthal sensors still exist in the present facility and cause the
different results of five sets from C1 to C5. The subtle difference of local packing
structure at each sensor also gives rise to a small change of measured temperature.
Moreover, the different heating processes also give some differences between the
first and second tests.
Although the improved inverse method of Sect. (3.3.4), is used to alleviate this
kind of error from the facility effectively, the differences can not be eliminated
entirely by the present method. Therefore, this error should be considered as the
type A uncertainty by involving the ten results of C1–C5 of two repeated tests into
uncertainty analysis, under helium and vacuum conditions.
First, for instance, two vacuum repeatability tests were conducted at different
times, and five results were obtained at the same time. According to the recommendation of report JCGM 100:2008 of Joint Committee for Guides in Metrology [26],
the standard deviation of each test p j is calculated by the following procedure:
¯
p j, f =
1
5
5
m = 1
p m, f
(3.51)
σ j, f =
1
4
5
m = 1
p m, j, f − ¯
p j, f
2
(3.52)
Here m indicates the different set from C1 to C5, and j is the index of vector P. The
subscript f denotes the first test, and n will be used to denote the next or second test.
¯
p j, f is an average p j of five sets in the first test. σ f is the standard deviation of five
results in the first test. σ n is calculated by the same equation. In addition, the degrees
of freedom of the two tests are v f = 4 and v n = 4. To combine the results of the
two tests, the pooled experimental standard deviation σ j, p should be used as
σ j, p =
v f σ
2
j, f +v n σ
2
j,n
v f +v n
(3.53)
Then, the type A standard uncertainty of ¯
p j from the ten results is
u A, ¯
p j =
σ j, p
√
10
(3.54)