断熱材の熱特性 断熱材の熱特性 ~熱伝導率および比熱測定~ ~熱伝導率および比熱測定~ ニチアス㈱ 浜松研究所 大村 高弘
断熱材の熱特性断熱材の熱特性~熱伝導率および比熱測定~~熱伝導率および比熱測定~
ニチアス㈱浜松研究所
大村 高弘
講演内容講演内容
l熱伝導率測定における問題点とそれに対する取り組み
l各種熱伝導率測定方法と測定結果の比較
l熱伝導率の推定式
l断熱材の比熱測定
断熱材の熱伝導率測定に関する問題点断熱材の熱伝導率測定に関する問題点
l標準物質がない→装置間の誤差
精度確認ができない。
l広い温度領域における断熱材の熱伝導率や比熱が正確に示されていない。
特に800℃以上の高温や真空下のデータ。
300 400 500 600 700 800-15
-10
-5
0
5
10
15
20
Temperature [K]
(λob
s-λ
calc
)×10
0/λ
calc
Fig. 1 Deviations of thermal conductivity round-robin test results from values calculated with the corrected equation for fibrous almina-
silica.
300 400 500 600 700 800-25-20-15-10
-505
1015
Temperature [K]
(λob
s-λ
calc)×
100/λ
calc
Fig. 2 Deviations of thermal conductivity round-robin test results from values
calculated with the corrected equation for calcium silicate.
熱伝導率の測定精度向上にた取り組み熱伝導率の測定精度向上にた取り組み
1. 各種測定法が可能な装置の開発:定常法と非定常法の比較 定 常 法:保護熱板法保護熱板法
非定常法:非定常熱線法、周期加熱法、ホットディスク法非定常熱線法、周期加熱法、ホットディスク法
2. 2. 精度の高い推定式の提案精度の高い推定式の提案::温度と嵩密度の関数温度と嵩密度の関数
1. 異種測定法による結果を比較
2. 測定結果と推定式による結果との比較
間接加熱法
直接加熱法
定常法 軸方向定常熱流 絶対法
比較法
経方向定常熱流
縦型絶対法
平板絶対法
可動間隙法
絶対法 同心円筒法
縦型比較法
平板比較法
同心球法
比較法 同心円筒法
軸方向非定常熱流非定常法
経方向非定常熱流
パルス状加熱法
ステップ状加熱法
波面分割干渉法
周期加熱法
光音響法
強制レーリー散乱法(パルス状加熱)
ラプラス変換法(平板)(任意加熱)
定速昇温法
熱線法(ステップ状加熱)
ラプラス変換法(円筒)
定常法
非定常法
軸方向熱流
軸方向熱流
径方向熱流
(Kohlrausch法, 積分法)
(Angell法)
(物性値同時測定法)
Fig. 3 Schematic of the Guarded Hot Plate method (GHP method)
(a) Solid figure of Double-side mode of operation
Guard heater
Specimen
Specimen
Cooling heater
Cooling heater
Gap
Metering sectionheater
Specimen
Guard heater
Cooling heater
Cooling heater
Heat flow
Metering section
SpecimenGuard heater
Auxiliary heater
Cooling heater
Heat flow
InsulationMetering section
heater heaterHeat flow
(b) Single-side mode of operation (c) Double-side mode of operation
Q =λ θ1-θ2
d
Hot Wire
Thermocouple
Specimen
Fig. 4 Schematic of the Hot Wire method
Polyimide sheet
Nickel
Heating part
Electrode
Fig. 5 Schematic of sensor in Hot Disk method.
Specimen
λ=4π
Q
θ2-θ1
ln t2/t1
λ=π3/2a
Q
ΔT τ
D τ
Specimen cross section
Tem
pera
ture
(℃) 1010
1000
990
Time (hour)
5~10℃
3~6℃
Thermal sensor1
Thermal sensor2
Thermal sensor3
Heat waves
Top half of specimen
Bottomhalf of specimen
Thermal sensor2
Thermal sensor1
Thermal sensor3
20
20
φ:time lag, T:period, κ:thermal diffusivity, ρ:densityλ:thermal conductivity.
φ=argsinhkL 1+isinhkx 1+i
A=As
Aj=
cosh2kL-cos2kL
cosh2kx-cos2kx
κ=2k2ω
ω=2πT
λ=ρcκ
熱伝導率測定装置
測定装置(測定装置(GHPGHP法)法)Water tank
Thermal insulation
Specimen
Auxiliary heater
円
筒
ヒ
-
タ
Metering
Guard heater
Cylindricalheater
Cooling unit
Bell glass
Vacuum pump
Temperature controller
Scanner
Digital multimeter
Computer
heatersection
Thermal insulation
Thermal insulation
120
200
250
Water tank
測定装置(周期加熱法、非定常熱線法)
Water tank
Insulation
Specimen
InsulationAuxiliary heater
円
筒
ヒ
-
タ
Cylindricalheater Cooling unit
Insulation
BellGlass
Vacuum pumpScanner
Digital Multimeter
Computer
Temperature Controller
Function Generator
Cyclic heaterSpecimen
Hot Wire
Table 2-3 Developped measuring apparatus. Apparatus Property Principle of measurement Temperature
range [℃] C 170 Thermal conductivity
Thermal diffusivity Specific heat
Transient hot-wire method Cyclic heat method Hot Disk method
-170~40
H1000 Thermal conductivity Thermal diffusivity
Transient hot-wire method Cyclic heat method
100~1000
HV1000 Thermal conductivity Thermal diffusivity
Transient hot-wire method Cyclic heat method
100~1000
H1300 Thermal conductivity Thermal diffusivity
Guarded hot plate method Cyclic heat method
100~1300
S1000 Specific heat Drop caloriemeter method 100~1000
Table 2-4 Measurment error of each method Method of
measurement Error [%]
Guarded hot plate method
6
Transient hot-wire method
5
Cyclic heat method Under 10 (depending on specimen)
Hot Disk method
Thermal conductivity :3 Thermal diffusivity :7 Specific heat :3
Drop caloriemeter method
8
0 200 400 600 800 10000
0.1
0.2
0.3
0.4
Temperature [℃]
Ther
mal
con
duct
ivity
[W/(m
K)]
・:Transient hot-wire method:Cyclic heat method
+10%
-10%
Least squares approximation by a quadratic equation
ρ=393 kg/m3
Fig. 6 Thermal conductivity of lightweight insulation with bulk
density ρ=393 kg/m3.
Al2O3:SiO2:Fe2O3=27:32:6
0 200 400 600 800 10000
0.1
0.2
0.3
0.4
Temperature [℃]
Ther
mal
con
duct
ivity
[W/(m
K)]
・:Transient hot-wire method:Cyclic heat method
+10%
-10%
Least squares approximation by a quadratic equation
ρ=458 kg/m3
Fig. 7 Thermal conductivity of lightweight insulation with bulk
density ρ=458 kg/m3.
0 500 10000
0.1
0.2
0.3
0.4
Least squares approximation by a quadratic equation
Temperature [℃]
Ther
mal
con
duct
ivity
[W/(m
K)]
・
+10%
+10%
-10%
-10%Atmosphericpressure
1.3 Pa
:GHP method under atmosferic pressure:Cyclic heat method under
atmosferic pressure:GHP method under 1.3 Pa:Cyclic heat method under 1.3 Pa
Fig. 8 Thermal conductivity of alumina fiber insulation with bulk density ρ= 205
kg/m3.
H1300を使った測定比較
0 500 10000
0.1
0.2
0.3
0.4
Temperature [℃]
Ther
mal
con
duct
ivity
[W/(m
K)]
Atmospheric pressure
1.3 Pa
+10%
+10%
-10%
-10%
:H1000(Atmospheric pressure):H1300(Atmospheric pressure):H1000(1.3Pa):H1300(1.3Pa)
・
Fig. 9 Comparison thermal conductivity of alumina fiber insulation (ρ= 205 kg/m3) by
H1000 with H1300 using cyclic heat method.
異種測定法間の差異種測定法間の差
l保護熱板法、非定常熱線法、周期加熱法、ホットディスク法に関して、同一試験体であれば、測定結果は±10%以内で一致する。
未知の材料に適用可能
推定式の結果と測定結果の推定式の結果と測定結果の比較による精度向上比較による精度向上
測定精度の高い高嵩密度断熱材のデータから推定式を作成
なぜ推定式が必要か?
低嵩密度(20kg/m3以下)断熱材は、ふく射エネルギーを透過させてしまうため、測定誤差が大きい。装置に依存してしまう。
異種測定法によるチェックが難しい
測定結果と推定結果を比較
精度向上
従来の推定式と問題点従来の推定式と問題点
最も実用的な式a, b, cは係数ρは嵩密度c
ba ++=ρ
ρλ
*その他の数多くの推定式
箇々の素材の熱物性値や素材同士の接触熱抵抗を必要としている
開発スピードについて行けず、実用性に欠ける
従来の推定式の問題点従来の推定式の問題点
1. 温度の関数になっていない
2. 嵩密度のみの関数:他の情報(固体、ふく射、気体による伝熱効果)が得られない
3. 高嵩密度試験体で推定式を作成すると、低嵩密度側は外挿になるため、推定精度が悪い
試験体ごとに、最小自乗法を使って係数a, b, c を導出しているため
根本的な原因
0 50 100 150 200 250 3000
0.05
0.10
0.15
0.20
0.25
0.30
Bulk density [kg/m3]
Ther
mal
con
duct
ivity
[W/(m
K)] :Measured values at 200℃
:Measured values at 300℃:Measured values at 400℃:Calculated line using all data at 200℃:Calculated line using all data at 300℃:Calculated line using all data at 400℃:Calculated line using 5 data at 200℃:Calculated line using 5 data at 300℃:Calculated line using 5 data at 400℃
・
Fig. 10 Calculated results by least square method.
係数係数UUおよびおよびVV00のの決定決定
真空下の熱伝導率λv:
λv
T 3Aρ
B /ρ
ρ
切片=Aρ切片
A
傾き=B/ρ傾き
B
1/ρ
3TBAv ρρλ +=
0 100 200 300 400 500 6000
0.01
0.02
0.03
0.04
0.05
Third power of absolute temperature [K3]
Ther
mal
con
duct
ivity
[W/(m
K)]
[×106]
:166kg/m3:293kg/m3:288kg/m3:227kg/m3
・
Fig. 11 Thermal conductivity of rock wool with four kinds of bulk density under evacuated condition (2 Pa).
0 100 200 3000
0.005
0.010
0.015
Bulk density [kg/m3]
Inte
rcep
t of s
olid
line
in F
ig. 5
-8
[W
/(m K
)]
・
Least squares approximation by a linear equation
Fig. 12 Intercepts of each line in Fig. 11 vs. bulk density.
0 0.002 0.004 0.006 0.0080
2
4
6
8
10
12
14
Reciprocal of bulk density [m3/kg]
Gra
dien
t of s
olid
line
in F
ig. 5
-8
[
W/(m・
K4 ]
[×105]
Least squares approximation by a linear equation
Fig. 13 Gradients of each line in Fig. 11 vs. reciprocal of bulk density.
0 50 100 150 200 250 3000.02
0.03
0.04
0.05
0.06
0.07
0.08
Bulk density [kg/m3]
Ther
mal
con
duct
ivity
[W/(m
K)]
:Measured values at 20℃:Measured values at 60℃:Measured values at 100℃:Calculated line by Eq.(5-36) at 20℃:Calculated line by Eq.(5-36) at 60℃:Calculated line by Eq.(5-36) at 100℃
・
Fig. 14 Thermal conductivity of rock wool.
0 50 100 150 200 250 3000
0.05
0.1
0.15
0.2
0.25
0.3
Bulk density [kg/m3]
Ther
mal
con
duct
ivity
[W/(m
K)]
:Measured values at 200℃:Measured values at 300℃:Measured values at 400℃:Calculated line by Eq.(5-36) at 200℃:Calculated line by Eq.(5-36) at 300℃:Calculated line by Eq.(5-36) at 400℃
・
Fig. 15 Thermal conductivity of rock wool.
0 50 100 150 200 2500
0.05
0.10
0.15
0.20
0.25
0.30
Bulk density [kg/m3]
Ther
mal
con
duct
ivity
[W/(m
K)]
100℃200℃300℃
400℃
500℃
600℃・
Fig. 16 Comparison of reference data with calculated results.
真比熱と平均比熱真比熱と平均比熱
( )basesss
st HHdd
mc −= 1
1
1θ真比熱
21
211
ss
ss
ssm
HHm
cθθ −
−=平均比熱
① Cylindrical heater
② Specimen
③ Digital multimeter
④ Temperature controller
⑤-1 Thermocouple
⑥ Measuring water tank
⑦ Monitoring water tank
⑧ Support plate⑨ Personal computer
①②
③
④
⑥
⑦
⑤-2
⑧
⑨
⑤-1152
275
140
7 00
250
600
φ89
φ191
⑤-2 Thermocouple
Fig. 17 Schematic of specific heat measuring apparatus (Type: S1000)
0 200 400 600 800 1000 12000
200
400
600
800
1000
1200
1400
Temperature [℃]
Enth
alpy
[kJ/
kg]
:Measured values :Eq.(2-90)
+10%
-10%
Fig. 18 Enthalpy of the standard specimen SRM720 Synthetic
Sapphire (α-Al2O3)
0 200 400 600 800 1000 120000.20.40.60.81.01.21.41.6
Temperature [℃]
Mea
n sp
ecifi
c he
at [k
J/kg
/K]
:Measured values :Eqs.(2-15) and (2-90)
+10%
-10%
Fig. 19 Mean specific heat of the standard specimen SRM720
Synthetic Sapphire (α-Al2O3)
0 200 400 600 800 1000 120000.20.40.60.81.01.21.41.6
Temperature [℃]
Spec
ific
heat
[kJ/
kg/K
]+5%-5%
SiC refractory materialρ=2800kg/m3Ts1=290~1000℃
:Measured values (Mean specific heat):Mean specific heat by Eq. (6-9):True specific heat
Fig. 20 Mean and true specific heats of SiC refractory.
0 200 400 600 800 1000 120000.20.40.60.8
11.21.41.6
Rockwoolρ=100kg/m3Ts1=100~700℃
+5%-5%
Temperature [℃]
Spec
ific
heat
[kJ/
kg/K
] :Measured values (Mean specific heat):Mean specific heat Eq. (6-9):True specific heat
Fig. 21 Mean and true specific heats of rock wool.
0 200 400 600 800 1000 120000.20.40.60.8
11.21.41.6
Temperature [℃]
Spec
ific
heat
[kJ/
kg/K
]
Alumina silica fiber insulationρ=130kg/m3Ts1=100~1000℃
+5%-5%
:Measured values (Mean specific heat):Mean specific heat by Eq. (6-9):True specific heat
Fig. 22 Mean and true specific heats of alumina silica fiber.
0 200 400 600 800 1000 120000.20.40.60.81.01.21.41.6
Temperature [℃]
Spec
ific
heat
[kJ/
kg/K
]+5%-5%
Calcium-silicate insulationρ=130kg/m3Ts1=120~1000℃
:Measured values (Mean specific heat):Mean specific heat by Eq. (6-9):True specific heat
Fig. 23 Mean and true specific heats of calcium-silicate insulation.
0 200 400 600 800 1000 120000.20.40.60.81.01.21.41.6
Temperature [℃]
Spec
ific
heat
[kJ/
kg/K
]
+5%-5%
SiO2-glassρ=2465kg/m3Ts1=200~600℃
:Measured values (Mean specific heat):Mean specific heat by Eq. (6-9):True specific heat
Fig. 24 Mean and true specific heats of SiO2-glass.
0 50 100 150 200 250 30000.20.40.60.81.01.21.41.6
+5%-5%
Temperature [℃]
Spec
ific
heat
[kJ/k
g/K
]
Fluoro rubberρ=1858kg/m3Ts1=100~200℃
:Measured value (Mean specific heat):Mean specific heat by Eq. (6-9):True specific heat
Fig. 25 Mean and true specific heats of Fluoro rubber.