Mean thermal conductivity of VIPs during service life time R. Caps va-Q-tec AG, Würzburg Annex 65 meeting Grenoble, 11th/12th Sept. 2014

Increase of thermal conductivity λ with time t essentially depends on - permeation rate P air of air through envelope - permeation rate P H2O of moisture through envelope Permation is dependent on temperature T and relative humidity φ, which in construction both vary with time t depending on climate Quality of vacuum insulation can be described by a mean thermal conductivity λ mean during service life time t s λ mean = 0 ts ʃ λ(T(t), φ(t)) dt/t s (1) λ(t) = f(P air (T(t)), P H2O (T(t), φ(t))) VIP mean thermal conductivity

Permeation measurement Air permeation P air (cm³/m²d): Measurement of permeation of envelope including flanges and crinkles -increase of gas pressure in thin VIP with time -change of thermal conductivity of thin VIP with special core as function of time -measurement conditions : different temperatures T Moisture permeation P H2O (g/m²d): Measurement of permeation of envelope including flanges and crinkles -weight increase within closed envelope with time -measurement conditions : different temperatures T and humidities φ

Influence on thermal conductivity VIPs filled with fumed silica change of thermal conductivity λ with relative moisture content X H2O [%] change of thermal conductivity with gas pressure (air) and water vapour pressure change of relative humidity φ with moisture content X H2O (adsorption isotherm) make it simple: use linear relationships as first approximation: ∂λ/∂X H2O = 0.5 mW/mK /%(from ZAE measurement) ∂λ/∂p= 0.04 mW/mK / mbar(from e.g. λ(1000 mbar), λ(0 mbar)) ∂X H2O /∂φ = 0.06 % / % r.h.(from adsorption isotherm of silica) (p << p 1/2, φ < 50 %, X H2O < 10 %) rel. humidity φ(X H2O ) and steam pressure p s (T) => p H2O => λ H2O

mean VIP thermal conductivity λ D adsorption iso- therm ΔX H20 / Δφ VIP thickness d moisture permeation P H2O (T; r.h.) air permeation P air (T; r.h.) initial conduc- tivity λ 0 ; 90/90 total gas pressure p(t) water content X H20 (t) Input parameters for calculation of mean conductivity for silica VIP heat bridges Δλ eff typical gas pressure p 1/2 Δλ/ΔX H20 climate T(t) climate T(t); r.h.(t) air pressure p air (t) silica density ρ vapour pressure p H2O (T, t) VIP thickness d water content X H20 (t) + + x

Comparison with Experimental Results from EMPA Increase of thermal conductivity after 10 years of storage is reproduced almost exactly Increase of gas pressure is calculated within 10 % error Comparison

Experimental 1.Method: Direct Measurement Make measurements of gas pressure and thermal conductivity increase of silica VIP at elevated temperature and dry conditions (several months, 80 °C, dry) and Make measurements of gas pressure, moisture and thermal conductivity increase of silica VIP at moderate temperature and humid conditions (several months, 50 °C / 70% r.h.) Questions: How to correlate thermal conductivity change to other temperature conditions? How to calculate temperature dependent thermal conductivity?

Experimental 2. Method: Indirect Measurement Make measurements of gas pressure and thermal conductivity increase of VIP with coarse (non-silica) core at one or more temperature(s) and dry condition (several days, 25 °C) => temperature dependent permeation of air P air (=> Arrhenius equation) and make measurements of moisture increase by weight of thin VIP at one or more temperature(s) and humid condition(s) (several weeks, 40 °C / 90% r.h.)  temperature and rel. humidity dependent permeation of moisture P H2O Calculate mean thermal conductivity as function of climate according to eq.(1)

Conclusions Make life time calculation of VIPs as simple as possible and as general as possible Annex 65 should evaluate the different methods Characterization of envelope should be as fast as possible (days instead of months)

Thank you for your attention