Conventional methodologies

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but they did not have enough information to implement it in a new criterion for selection of the extreme cases.

In 1994, the release of [105] meant a great change in the previously established criteria. New projects such as the Space Station Program [114] demanded a better definition of the thermal environment on Low Earth Orbits. Design difficulties with both "hot case" and "cold case" requirements on various subsystems caused a re-evaluation of the natural environment specification. Moreover, wider use of lightweight structures sensitive to rapid thermal fluctuations greatly increased the importance of this definition. Not only did designs become more and more complex, with harder requirements, but also the capabilities of the technology and the available data recovered from different Earth-observation satellite missions led to a new methodology for the worst-case thermal environment selection. ERBE is a multisatellite experiment consisting of the low-inclination ERBS and two NOAA Sun-synchronous satellites. They collected such Earth radiation budget parameters as incident and reflected sunlight and the OLR from November 1984 and July 1987.

Direct 16-s instrument measurements along the ERBS or NOAA satellite trajectory were selected for this study because they considered that the average times are much too long compared to the thermal time constant of most satellite systems.

Complexity in the selection criteria increased from 1994 leading NASA to release a dedicated handbook "Guidelines for the Selection of the Near-Earth Thermal Environment Parameters specially oriented to Spacecraft Analysis and Design" [14].

In order to support the guidelines and with the aim of facilitating the selection of the worst-case thermal environment, a software called Simple Thermal Environment Model (STEM) were developed and detailed in [17].

Regarding the albedo and OLR selection, the following considerations were taken into account:

• The meaning of the term probability was modified due to the lack of data.

The previous approach could not be derived from the limited data set available for this study. The required data set would cover a very long time period compared to the mission design life. For critical applications, an additional design margin is recommended based on the comparison of mission life to duration of database. In a non-critical application, percentiles would be set as the fraction of time the values are expected to be exceeded, rather than on the probability they would be exceeded over a mission lifetime.

• Data were adjusted to the Top of Atmosphere (TOA) (around 30 km) to eliminate the altitude dependence and albedo is referred to zero Solar Zenith Angle.

• The Lambertian consideration of albedo scattering (equal in all directions) was replaced for a Solar Zenith Angle dependence model. It is limited by the beta angle at local noon and 90º at ground sunrise/sunset, and a correction term was used depending on the average orbit SZA. However, the effect of applying this correction term to values higher than 65^◦ does not completely remove the angular dependence of the albedo. Using these values for the statistical analysis would lead to a non-representative distribution of albedo for the lowest SZAs, which provides the higher heat loads. In order to avoid this issue, only values corresponding to SZA < 60^◦ are considered for the analysis.

• Albedo and OLR values are considered to be partially correlated. Once an extreme value is selected, the corresponding pair is selected. Different worst cases values (hot and cold) are provided as a function of the orbit inclination and the averaging time. The shorter the average time is the more extreme the values of the albedo and OLR.

• In this new release, an additional parameter is considered in the worst-case selection. Three potential pairs of albedo and OLR values can be selected depending on the ratio solar absorptance to IR emissivity. By doing so, a major step is taken providing a new perspective where the extreme environmental parameters values, which led the system to reach the maximum and minimum temperatures, strongly depend on its surface characteristics.

The ISS program [40] demanded a more complex thermal analysis. Based on the same approach to select the albedo and OLR extreme values, a single or multiple pulse analysis can be performed. This methodology is suitable for systems that carry components with lower time constants. A base value for higher time constants is used for the entire orbit and pulses are applied before sunrise (or in the solar noon plus 180^◦ if there is no eclipse) or in the solar noon for the cold and hot cases, respectively.

The ISS approach is included in the last document released by NASA about natural environments definitions for design [115]. As they say, "this approach is useful for a situation like ISS where a single set of albedo/OLR conditions need to be specified for a variety of hardware elements. However, in simpler cases, a single hardware element and surface treatment, this approach can lead to unneeded analysis when the extreme hot and cold cases can be selected directly."

The thermal environment criteria for spacecraft design has evolved along with the technology over the years. The availability of Earth-observation data has provided

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valuable information that has allowed for a better characterization of the thermal environment to be available. The STEM [17] methodology, which has been explained in Chapter 2, has not progressed in a considerably way since 1994 when ERBE data was incorporated to the approach [105]. Other space organizations such as ESA through the European Cooperation for Space Standardization (ECSS) [28], also refers to [17] for the worst-case selection. However, they state that some assumptions made are not valid for some cases such as polar orbits around Earth where albedo reflectivity can increase around the polar ice caps and external equipment with low thermal inertia that can be sensitive to infrared fluxes and albedo variation.

As previously commented, the methodology developed in [14] has some limita- tions regarding the nature of data used. Moreover, this methodology was adapted to the characteristics of the thermal analysis tools of the epoch, such as Thermal Radiation Analysis System (TRASYS) and Thermal Synthesizer System (TSS).

Currently, software analysis tools, such as ESATAN TMS, Thermica or Thermal Desktop, provide much more utilities than the ones available in the nineties, allowing for more complex analysis, parametric sweeps, etc. to be performed.

In the last decade, the growth of the internet capacities together with an increasing interest in big data strategies have led the main organizations (NASA and ESA) to provide open access to huge satellite-based observations databases.

One of them is CERES, which provides information the Earth’s radiative fluxes on the Top of Atmosphere among other things. A review of the study performed by Anderson Smith [105] seems appropriate in order to achieve the following objectives:

• Providing enough independent data to account for a suitable risk probability definition in order to reduce uncertainties and margins.

• Accounting for all available data including those values with SZA > 65^◦ allowing us to consider diurnal variations.

• Adapting the criteria to low thermal constant systems such as CubeSats and nanosatellites that have a huge dependence on the thermal environment variations.

• Providing support not only for selecting the worst-case values of albedo and OLR but also for selecting the worst-case orbit through parametric analyses.

• Adapting the proposed methodology to be used by current analysis tools.

Here, time-dependant profiles are obtained to consider the hottest and coldest condition in a defined orbit. CERES data is analysed in order to understand the influence of different parameters. Once obtained the real albedo and OLR throughout an orbit, these time series are treated in order to obtain worst cases of albedo and OLR accounting for the system characteristics. The proposed methodology will deal with the previously mentioned objectives.

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