Engineering task and calculation objective
The K6 module calculates the heat loss through superinsulation (multilayer insulation, MLI) according to the VDI Heat Atlas (VDI-Wärmeatlas), 12th edition 2019 — the standard German reference for heat transfer engineering. Superinsulation consists of many thin foils that are reflective on both sides — for example aluminized plastic films or aluminum foils — separated by poorly conducting spacers of glass-fiber paper or glass-silk fabric and arranged in a vacuum. Each foil acts as a radiation shield, so the radiative heat flow drops drastically with the number of foils.
Superinsulation is used above all in cryogenic engineering: in storage and transport vessels for liquefied gases (LIN, LOX, LH2, LHe, LNG), vacuum-insulated piping and cryostats. Anyone who designs such vessels or wants to estimate the boil-off rate of a tank must calculate the heat leak through the insulation — it directly determines holding time and product loss.
The module covers the governing contributions to heat transport: the residual radiation between the foils as a function of layer density (foils per unit insulation thickness) and foil type, the solid conduction through the spacer materials including the influence of the compressive load, and additional thermal bridges via supports, for which number, diameter and thermal conductivity are entered. The result is the heat leak of the insulated surface.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the superinsulation build-up: The foil type (e.g. aluminum foil with glass-fiber paper or aluminized plastic film with glass-silk fabric), the spacer material and the number of foils per unit insulation thickness — the central layer-density parameter — are selected.
- Set the boundary temperatures: The warm-side and cold-side temperatures of the insulation are specified, typically ambient temperature outside and the boiling temperature of the cryogen inside. Because of the T-to-the-fourth-power dependence of radiation, the warm side dominates the radiative contribution.
- Determine the radiation and conduction share of the insulation blanket: From the number of foils, the emission behavior of the foils and the spacer properties, the effective thermal conductivity of the blanket is determined. The compressive load enters significantly: if the insulation is compressed, solid conduction through the contact points of the spacers rises sharply.
- Account for thermal bridges via supports: For mechanical supports, number, diameter and solid thermal conductivity are entered; their conduction contribution is added to the heat flow through the blanket. In well-executed superinsulation, such thermal bridges can dominate the total loss.
- Evaluate the heat leak: As a result, the calculation delivers the heat leak through the insulation. From it, the effective thermal conductivity, the area-specific loss and — via the enthalpy of vaporization of the stored product — the boil-off rate of the vessel can be derived.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature hot wall | T1 | K |
| Temperature cold wall | T2 | K |
| Temperature difference | ΔT | K (diff) |
| Insulation surface | F | m² |
| Wall spacing | D | m |
| Gas number Selected gas | _Gasname | – |
| Thermal conductivity gas atmosph. pressure | λ0 | W/(m·K) |
| Pressure of residual gas | pG | Pa |
| Gas temperature | TG | °C |
| Constant at pG | C1 | µm |
| Constant | C2 | K (diff) |
| Mean free path of the gas molecules | lGas [1] | m |
| Cp/Cv of the gas | κ | - |
| Correction factor | k | - |
| Accomodation coefficient | α | - |
| Weighting factor | β [3] | - |
| Mean pore diameter | δ [16] | m |
| Knudsen number | Kn [4] | - |
| Thermal conductivity of residual gas | λG [2] | W/(m·K) |
| Heat flow losses | [5] | W |
| Number of foils per unit thickness insulation | N/D | 1/cm |
| (Alum. foils with fibreglass paper -curve 2-) | λ' | mW/(m·K) |
| (Vacuum-aluminized Dracon film with woven glass fabric) | λ' | mW/(m·K) |
| Compressive load | p | MPa(p) |
Calculation options
Bauform
Superinsulations of discontinuous structures · Superinsulations of discontinuous structures - free selection of gas · Superinsulation of continuous structures (spherical particles) · Superinsulation of continuous structures (spherical particles) - free selection of gas · Superinsulation of continuous structure (regular network) · Superinsulation of continuous structure (regular network) - free selection of gas
Frequently asked questions
Why is superinsulation so much more effective than conventional insulation?
In high vacuum, gas conduction and convection are almost completely eliminated; radiation and solid conduction remain. N radiation shields in series ideally reduce the radiative exchange by roughly a factor of N+1, and the spacers minimize contact conduction. Superinsulation thus achieves effective thermal conductivities on the order of 10⁻⁴ to 10⁻⁵ W/(m·K) — orders of magnitude better than foamed or fibrous insulation materials.
Is there an optimum number of foils per unit insulation thickness?
Yes. More foils per thickness lower the radiative share but, through denser packing, increase the contact pressure and hence solid conduction through the spacers. The minimum of the effective thermal conductivity therefore lies at a medium layer density; both too loose and too strongly compressed wrappings degrade the insulating performance.
How critical is the vacuum quality?
Very critical. If the residual gas pressure rises above roughly 10⁻³ to 10⁻² mbar, gas conduction between the foils sets in progressively and the heat leak can increase severalfold. That is why getters are used and the insulation space is designed to be monitorable; a creeping vacuum loss shows up in operation as a rising boil-off rate.
Why do supports and penetrations often dominate the heat loss in practice?
The blanket itself insulates extremely well, so even a few solid connections between warm and cold side — supports, neck tubes, pipe penetrations, suspensions — deliver a disproportionate conduction contribution. In the design, these thermal bridges must be captured explicitly with number, cross-section and material thermal conductivity and minimized constructively (long paths, thin-walled materials such as stainless steel or GRP).