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1 断熱材の熱特性 ~ 熱伝導率および比熱測定 ~ ニチアス浜松研究所大村高弘

4 講演内容熱伝導率測定における問題点とそれに対する取り組み各種熱伝導率測定方法と測定結果の比較熱伝導率の推定式断熱材の比熱測定

5 断熱材の熱伝導率測定に関する問題点標準物質がない装置間の誤差精度確認ができない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 8 以上の高温や真空下のデータ

6 (λ obs -λ calc ) 1/λ calc Temperature [K] Fig. 1 Deviations of thermal conductivity round-robin test results from values calculated with the corrected equation for fibrous alminasilica. (λ obs -λ calc ) 1/λ calc Temperature [K] Fig. 2 Deviations of thermal conductivity round-robin test results from values calculated with the corrected equation for calcium silicate.

7 熱伝導率の測定精度向上にた取り組み 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 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 : 保護熱板法非定常法 : 非定常熱線法周期加熱法ホットディスク法 2. 精度の高い推定式の提案 : 温度と嵩密度の関数

8 間接加熱法定常法軸方向定常熱流絶対法縦型絶対法平板絶対法可動間隙法比較法縦型比較法経方向定常熱流絶対法平板比較法同心円筒法同心球法比較法同心円筒法非定常法軸方向非定常熱流パルス状加熱法経方向非定常熱流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 ) 直接加熱法定常法軸方向熱流 (Kohlrausch 法, 積分法 ) 径方向熱流 (Angell 法 ) 非定常法軸方向熱流 ( 物性値同時測定法 )

9 Coolingheater Specimen Guardheater Meteringsection heater Specimen Coolingheater Gap Q = λ θ1-θ2 d (a) Solid figure of Double-side mode of operation Auxiliaryheater Insulation Meteringsection heater Coolingheater Heatflow Meteringsection heater Specimen Specimen Heatflow Guardheater Heatflow Guardheater Coolingheater Coolingheater (b) Single-side mode of operation (c) Double-side mode of operation Fig. 3 Schematic of the Guarded Hot Plate method (GHP method)

10 HotWire Specimen Thermocouple Q λ= 4 π ln t2/t1 θ2-θ1 Fig. 4 Schematic of the Hot Wire method Specimen Heatingpart Nickel Electrode Polyimidesheet Q λ= π 3/2 a D τ ΔT τ Fig. 5 Schematic of sensor in Hot Disk method.

11 Thermalsensor1 5~1 T e m p e r a tu r e ( ) 11 Thermalsensor1 2 Tophalfofspecimen Thermalsensor2 3~6 2 Bottomhalfofspecimen 1 Thermalsensor2 Thermalsensor3 99 Thermalsensor3 Specimencrosssection sinhkx 1+i φ=arg sinhkl 1+i A= As A j = cosh2kx-cos2kx cosh2kl -cos2kl φ:time lag, κ:thermal diffusivity, λ:thermal conductivity. ω κ= 2k 2 ω= 2 π T T:period, ρ:density Time(hour) Heatwaves λ=ρcκ

12 熱伝導率測定装置

13 測定装置 (GHP( 法 ) Guardheater 2 12 Watertank Metering section heater Cylindrical heater Bellglass 円筒ヒ - タ Thermalinsulation Coolingunit Specimen Thermalinsulation Auxiliaryheater 2 5 Thermalinsulation Vacuumpump Scanner Watertank Temperaturecontroller Digitalmultimeter Computer

14 測定装置 ( 周期加熱法非定常熱線法 ) Watertank Cylindrical heater Bell Glass 円筒ヒ - タ Insulation Coolingunit Specimen Specimen Cyclic heater Insulation Auxiliary heater Insulation Hot Wire Vacuumpump Temperature Controller FunctionGenerator Scanner Digital Multimeter Computer

15 Table 2-3 Developped measuring apparatus. Apparatus Property Principle of measurement Temperature range [ ] C 17 Thermal conductivity Transient hot-wire method -17~4 Thermal diffusivity Specific heat Cyclic heat method Hot Disk method H1 Thermal conductivity Transient hot-wire method 1~1 Thermal diffusivity Cyclic heat method HV1 Thermal conductivity Transient hot-wire method 1~1 Thermal diffusivity Cyclic heat method H13 Thermal conductivity Guarded hot plate method 1~13 Thermal diffusivity Cyclic heat method S1 Specific heat Drop caloriemeter method 1~1 Table 2-4 Measurment error of each method Method of measurement Guarded hot plate method Transient hot-wire method Cyclic heat method Hot Disk method Drop caloriemeter method Error [%] Under 1 (depending on specimen) Thermal conductivity :3 Thermal diffusivity :7 Specific heat :

16 Thermal conductivity [W/(m K)] :Transient hot-wire method :Cyclic heat method Temperature [ ] ρ=393 kg/m 3 +1% -1% Least squares approximation by a quadratic equation Fig. 6 Thermal conductivity of lightweight insulation with bulk density ρ=393 kg/m 3. Thermal conductivity [W/(m K)] :Transient hot-wire method :Cyclic heat method Temperature [ ] ρ=458 kg/m 3 +1% -1% Least squares approximation by a quadratic equation Fig. 7 Thermal conductivity of lightweight insulation with bulk density ρ=458 kg/m 3. Al 2 O 3 :SiO 2 :Fe 2 O 3 =27:32:6

17 H13 を使った測定比較 Thermal conductivity [W/(m K)] :GHP method under atmosferic pressure :Cyclic heat method under atmosferic pressure :GHP method under 1.3 Pa :Cyclic heat method under 1.3 Pa Least squares approximation by a quadratic equation Atmospheric pressure 5 1 Temperature [ ] 1.3 Pa +1% -1% +1% -1% Fig. 8 Thermal conductivity of alumina fiber insulation with bulk density ρ= 25 kg/m 3. Thermal conductivity [W/(m K)] :H1(Atmospheric pressure) :H13(Atmospheric pressure) :H1(1.3Pa) :H13(1.3Pa) Atmospheric pressure 5 1 Temperature [ ] 1.3 Pa +1% -1% +1% -1% Fig. 9 Comparison thermal conductivity of alumina fiber insulation (ρ= 25 kg/m 3 ) by H1 with H13 using cyclic heat method.

18 異種測定法間の差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 ±1% 以内で一致する未知の材料に適用可能

19 推定式の結果と測定結果の比較による精度向上なぜ推定式が必要か? 低嵩密度 (2kg/m 3 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精度の高い高嵩密度断熱材のデータから推定式を作成測定結果と推定結果を比較精度向上

20 従来の推定式と問題点最も実用的な式 λ = b a ρ + + ρ c a, b, c は係数 ρ は嵩密度 * 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

21 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根本的な原因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

22 Thermal conductivity [W/(m K)] :Measured values at 2 :Measured values at 3 :Measured values at 4 :Calculated line using all data at 2 :Calculated line using all data at 3 :Calculated line using all data at 4 :Calculated line using 5 data at 2 :Calculated line using 5 data at 3 :Calculated line using 5 data at Bulk density [kg/m 3 ] Fig. 1 Calculated results by least square method.

23 係数 Uおよび V の決定真空下の熱伝導率 λ v : λ = Aρ + v B T ρ 3 λ v B /ρ 切片切片 =Aρ Aρ T 3 傾き傾き =B/ρ A B ρ 1/ρ

24 Thermal conductivity [W/(m K)] :166kg/m 3 :293kg/m 3 :288kg/m 3 :227kg/m [ 1 6 ] Third power of absolute temperature [K 3 ] Fig. 11 Thermal conductivity of rock wool with four kinds of bulk density under evacuated condition (2 Pa).

25 Intercept of solid line in Fig. 5-8 [W/(m K)] Least squares approximation by a linear equation Bulk density [kg/m 3 ] Gradient of solid line in Fig. 5-8 [W/(m K 4 ] [ 1 5 ] Least squares approximation by a linear equation Reciprocal of bulk density [m 3 /kg] Fig. 12 Intercepts of each line in Fig. 11 vs. bulk density. Fig. 13 Gradients of each line in Fig. 11 vs. reciprocal of bulk density.

26 Thermal conductivity [W/(m K)] :Measured values at 2 :Measured values at 6 :Measured values at 1 :Calculated line by Eq.(5-36) at 2 :Calculated line by Eq.(5-36) at 6 :Calculated line by Eq.(5-36) at Bulk density [kg/m 3 ] Fig. 14 Thermal conductivity of rock wool. Thermal conductivity [W/(m K)] :Measured values at 2 :Measured values at 3 :Measured values at 4 :Calculated line by Eq.(5-36) at 2 :Calculated line by Eq.(5-36) at 3 :Calculated line by Eq.(5-36) at Bulk density [kg/m 3 ] Fig. 15 Thermal conductivity of rock wool.

27 Thermal conductivity [W/(m K)] Bulk density [kg/m 3 ] Fig. 16 Comparison of reference data with calculated results.

28 真比熱と平均比熱真比熱 c st 1 d = s1 ms dθ s1 ( H H ) base 平均比熱 c sm = 1 m s H s1 H θ θ s1 s2 s2

29 φ φ Cylindricalheater 2 Specimen 3 Digitalmultimeter 4 Temperaturecontroller 5-1Thermocouple 5-2Thermocouple 6 Measuringwatertank 7 Monitoringwatertank 8 Supportplate 9 Personalcomputer Fig. 17 Schematic of specific heat measuring apparatus (Type: S1)

30 Enthalpy [kj/kg] :Measured values :Eq.(2-9) +1% -1% Temperature [ ] Mean specific heat [kj/kg/k] Temperature [ ] +1% -1% :Measured values :Eqs.(2-15) and (2-9) Fig. 18 Enthalpy of the standard specimen SRM72 Synthetic Sapphire (α-al 2 O 3 ) Fig. 19 Mean specific heat of the standard specimen SRM72 Synthetic Sapphire (α-al 2 O 3 )

31 Specific heat [kj/kg/k] :Measured values (Mean specific heat) :Mean specific heat by Eq. (6-9) :True specific heat +5% -5% SiC refractory material ρ=28kg/m 3 T s1 =29~ Temperature [ ] Fig. 2 Mean and true specific heats of SiC refractory. Specific heat [kj/kg/k] Specific heat [kj/kg/k] :Measured values (Mean specific heat) :Mean specific heat by Eq. (6-9) :True specific heat :Measured values (Mean specific heat) :Mean specific heat Eq. (6-9) :True specific heat +5% -5% Rockwool ρ=1kg/m 3 T s1 =1~ Temperature [ ] Fig. 21 Mean and true specific heats of rock wool. +5% -5% Alumina silica fiber insulation ρ=13kg/m 3 T s1 =1~ Temperature [ ] Fig. 22 Mean and true specific heats of alumina silica fiber.

32 Specific heat [kj/kg/k] :Measured values (Mean specific heat) :Mean specific heat by Eq. (6-9) :True specific heat +5% -5% Calcium-silicate insulation ρ=13kg/m 3 T s1 =12~ Temperature [ ] Fig. 23 Mean and true specific heats of calcium-silicate insulation. Specific heat [kj/kg/k] :Measured values (Mean specific heat) :Mean specific heat by Eq. (6-9) :True specific heat +5% -5% SiO 2 -glass ρ=2465kg/m 3 T s1 =2~ Temperature [ ] Fig. 24 Mean and true specific heats of SiO 2 -glass. Specific heat [kj/kg/k] % -5% Fluoro rubber ρ=1858kg/m 3 T s1 =1~2 :Measured value (Mean specific heat) :Mean specific heat by Eq. (6-9) :True specific heat Temperature [ ] Fig. 25 Mean and true specific heats of Fluororubber.

レーザフラッシュ熱拡散率測定に関する標準の整備状況

レーザフラッシュ熱拡散率測定に関する標準の整備状況平成 1 年度固体熱物性クラブ全体会合 010. 1. 6 於 : 秋葉原コンベンションホール固体熱物性標準整備の現状と開発計画熱拡散率 / 熱伝導率 ( 独 ) 産業技術総合研究所計測標準研究部門熱物性標準研究室阿子島めぐみ熱の伝導に関連する物性値熱伝導率 λ [W/(m K)] 定常的な温度勾配が存在する時の熱エネルギーが伝わる割合熱拡散率 α [m /s] 温度分布が緩和して熱的な平衡状態になる速さ