Recent experimental results within the NASA community have shown apparent degradation in the performance of multilayer insulation (MLI) when used in low-temperature applications, e.g., in liquid hydrogen tanks. There was speculation that this degradation was due to the appearance of radiative transmission of energy at these low temperatures since the black-body emission curve at low temperatures corresponds to long wavelengths that might be able to partially pass through the MLI sheets. The standard models for MLI could not be extended to include transmission effects, so a new mathematical system was developed that generalizes the description of the performance of this insulation material.

The mathematical approach allows the modeling of multilayer insulation (MLI) over a very broad range of performance characteristics. Multilayer insulation, commonly used in cryogenics, is composed of many layers of thin polymer, each coated with a very thin film of highly reflecting metal. The primary purpose of this insulation is to block radiative energy transfer. Previous work provides expressions for the steady-state performance of this insulation when the layers are treated as wavelength-independent absorbers/reflectors. The new mathematical approach goes well beyond this, and allows MLI to be modeled when the absorption/reflection is wavelength-dependent, when the layers exhibit wavelength-dependent transmission, when the reflectivity or transmission is dependent on angle, and when there is heat flow due to conduction.

The key to the new model is the definition of a square matrix that describes one time step in the evolution of the radiative energy, e.g., one set of reflections, absorptions, and transmissions. This matrix preserves energy, tracking where all the energy goes during each time step, and it can be applied multiple times to track the radiative energy over long time periods. Consequently, raising this matrix to a large power, easily done for a well-behaved square matrix, describes the final state of the system quickly, determining where all of the radiative energy is deposited. If the performance of the MLI sheets is wavelength-dependent, this matrix can be redefined to describe individual wavelength intervals, and then the final energy state can be found by summing over all wavelengths.

This mathematical model provides a means for modeling MLI performance over a much wider range of performance criteria than any other known model. Wavelength-dependent reflection, absorption, or transmission can be modeled. MLI was modeled with angular dependence on reflection and transmission. This model allows the inclusion of thermal conductivity and yields not only the final heat flux through the insulation, but the temperatures of each sheet of the MLI in the system.

This work was done by Robert Youngquist, Wesley Johnson, Mark Nurge, and Stanley Starr of Kennedy Space Center. KSC-13871

##### NASA Tech Briefs Magazine

This article first appeared in the February, 2015 issue of NASA Tech Briefs Magazine.

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