Thermal Conductivity of VIPs as a Function of Internal Pressure

Transcription

1 Thermal Conductivity of VIPs as a Function of Internal Pressure The insulation properties of a VIP panel are determined by its effective thermal conductivity, as described in Eq.1. The lower the thermal conductivity of the panel, the better the insulation properties. m K ( 1) λ λ + λ EFF COP TB, λ TB - The contribution to λ EFF due to the heat conducted by the envelope - known as the thermal bride effect. λ TB stays constant alon the VIP operation time and is dependent on the structure of the encapsulatin laminate (metallized film or Al foil based). λcop - The contribution to λ EFF due to heat transferred throuh the center of the panel (from the hot side to the cold side). The value of λ COP chanes over time because of permeation in of atmospheric ases. The rate of chane depends on the barrier properties of the film (permeation rates of water vapor and air). The increase of λ COP depends on the specific properties of the core material and the surroundin air pressure. Many oranic and inoranic insulation materials (such as the commonly used lass fiber and fumed silica) with a porous, open cell structure are available to use as a core for VIPs. In such porous materials, specific heat conductivity can be defined as a function of as pressure. In porous materials, heat is propaated by three processes [1]: thermal conductance throuh the solid core ( λ ), IR radiation ( λ ) and heat convection ( λ S presented in Eq., R CV ) throuh the pores by the as molecules, as Since S m K ( ) λ λ + λ + λ COP S R CV, λ and λ do not depend on pressure, Eq. can be written as follows, R m K ( 3) λ λ + λ( P COP ), λ λ S + λ R is the initial (immediately after evacuatin the panel) thermal conductivity of the core material. Thermal Conductivity as a Function of Pressure Ed A, July 15

2 λ(p) chanes over time as the pressure inside the VIP increases due to the short term outassin mechanism and lon term ases permeation. The amount of heat transferred by convection is determined by the density of as molecules, which in turn determines the inter-particle collision frequency and the internal pressure. The influence of air pressure on the thermal conductivity of porous materials can be expressed analytically by the followin formula []: ( 4) λ λ( P) 1+ βk n l mean Kn and δ l mean k B T π d P where Kn - the Knudsen number - is the ratio between the mean free path. l mean is the averae distance the molecule passes between two collisions with other air molecules. δ is the characteristic pore size, d is the diameter of the as molecules and β is a constant between 1.5 and., characterizin the efficiency of enery transfer when as molecules hit the solid structure of the porous material. k B and T are Boltzmann constant and temperature respectively. The constant β depends on the as type, the solid material and the temperature. If we rewrite the previous Eq. (4) as a formula which accentuates the three main parameters for aseous heat conduction in porous media as appears in Eq. (3) we et: ( 5) λ ( T ) λ ( P) 1+ C T ( / δ P ) 1+ ( P / P ) λ ( T ) λ is the thermal conductivity of the as in open space (λ5.5 /mk in the case of air) CT P1 /, is the pressure at which the as thermal conductivity reaches the value of one half of λ, δ β k B and C is a factor defined as. P 1 /, is the internal pressure at which the thermal conductivity π d of the panel increases by 1.5/mK over the value of λ.the value P 1/, is stronly dependent on δ (the averae pore size of the core material. The smaller the averae pore, the larer the 1/, P 1 /,. Thermal Conductivity as a Function of Pressure Ed A, July 15

3 For air molecules the relation between the averae pores diameter φ and P 1/ is iven by: (6) φ(in µ) 3/P 1/ (mbar) Summary: Summarizin all said above, the relationship between the thermal conductivity of VIPs and their internal pressure is iven by: λas (7) λ ( P) λ + P1 + 1 P λ is thermal conductivity at low pressure, such as λ as is the thermal conductivity of air in free space ( m K depends on the averae pore size of the core material. mbar for lassfiber cores, and P1 ). is the characteristic pressure that A proprietary method developed by Hanita for determinin the characteristic values of λ and P of an inspected core material 1 This simple technique is based on simultaneous measurement of the internal pressure and the center of the panel thermal conductivity (see Fiures (a) and (b) below). Inspected core material inside hih barrier laminate ( Vacuum aues (a) Sample for core material characterization (b) Sample inside thermal conductivity measurement device (LaserComp FOX314) Thermal Conductivity as a Function of Pressure Ed A, July 15

4 At first, measurement of initial thermal conductivity λ (hot plate at 35 C, cold plate at 1 C) is made after the whole system was evacuated by a turbo molecular vacuum pump. This ensures that the pressure inside the envelope is kept at a low level of mbar. Later on, controlled amounts of as are injected into the envelope throuh the leak tiht connector. The thermal conductivity is measured after each air injection toether with correspondin pressure measurement. The followin Fiure (c) shows the results of two tests on the same lass fiber core (not the same sample), Fiure (c): Thermal conductivity after as injection The blue and purple marks describe the test results, while the orane line is the best fitted plot of Eq.7. The characteristic parameters found for the tested FG core material are shown in Table 1. λ [ / mk] 3.7 [ mk] λ as / 5.5 P 1 [ mbar] There are wide varieties of core materials with different properties, and four of them are presented in Table below: Table 1: FG parameters 1.5 Thermal Conductivity as a Function of Pressure Ed A, July 15

5 Name Type λ [ / mk] P [ mbar] Type I Glass fiber Type II Glass fiber Type III Glass fiber Type IV Fumed silica Table : Core types Fiure (d) below shows the thermal conductivity of core materials as a function of pressure: Type I Type II Type III Type IV λ [mw/mk] P[mbar] Fiure (d): Thermal conductivity of the 4 types of core materials as a function of the internal pressure The difference between the cores at low pressure is more obvious when the curves are plotted usin linear pressure scale, as presented in Fiure (e). Thermal Conductivity as a Function of Pressure Ed A, July 15

6 Type I Type II Type III Type IV 5 λ [mw/mk] P[mbar] Fiure (e): Thermal conductivity of core materials as a function of pressure - linear The raph (f) below describes as an example how λcop of the panels with the 4 different cores increase alon 1 years of service life. For the calculation it was assumed that the same envelope was used for all 4 panels, and that the pressure increase rate at a steady state was.3 mbar per year for all. Type I Type II Type III Type IV 15 1 λ [mw/mk] years Fiure (f): Thermal conductivity of different core material over panel lifetime Thermal Conductivity as a Function of Pressure Ed A, July 15

7 Remarks: 1. In real life, the thermal conductivity of a fumed silica panel (Type IV) will increase faster than described in the raph below due permeation of water vapor durin the operation period. The permeated water molecules are absorbed by the FS powder particles causin λ S to increase in time. Theoretically, the thermal conductivity of fumed silica increases by.5 /mk per 1%wt of absorbed H O molecules. In the case of FG cores, desiccants are always used and they ensure no effect of the water vapor permeation on λ as lon as the desiccants have not been saturated.. The fiure above describes only the thermal conductivity of the center of panel. In real life applications, the thermal bride effect should be added to total thermal conductivity. A major part of the heat transferred may be due to thermal bride, which is dependent on the envelope type and panel size. References: [1] H. Schwab, Vakuumisolationspaneele - Gas- und Feuchteeintra sowie Feuchteun Wa rmetransport, PhD thesis, Bayerischen Julius-Maximilians-Universita t Wu rzbur, Wu rzbur, 4, 115 pp [] E.H. Kennard, Kinetic theory of Gases, with an Introduction to Statistical Mechanics, Mc-Graw-Hill, New York, 1938 [3] R. Caps, U. Heinemann, M. Ehrmanntraut, J. Fricke, Evacuated insulation panels with pyroenic silica powders: properties and applications, Hih Temperatures- Hih Pressures 33 (1) Eddie Shufer Materials Science and Enineerin, M.Sc. R&D Ultra Hih Barrier Laminates Hanita Coatins RCA Ltd Thermal Conductivity as a Function of Pressure Ed A, July 15