Contents
1.3 Basic concepts
1.3.3 Thermal modelling
Thermal models are usually built with dedicated software specially designed for solving the radiative and thermal problem that rises when the fluxes and temperatures are calculated. Some of the most used software are Systema Thermica, developed by Airbus Defense & Space, Thermal Desktop, developed by C&R Technologies, and ESATAN-TMS initially developed by ESA and supported by ITP Aero. All of them have the same structure which, for Space Systems modelling, is mainly divided in a geometrical definition module and a thermal and radiative calculation modules. The geometrical module allows the definition of the main parts of the system for the radiative heat transfer calculation. All of them uses a Monte-Carlo ray tracing algorithm to compute radiation exchange factors and view factors. Once created the node and conduction network, the thermal module solves the resultant differential equation system whose order varies depending on the used method (finite difference, finite element or lumped capacitance). In Europe, one of the conventionally used package for thermal analysis in the space industry is ESATAN-TMS, which is based on the lumped parameter method.
The lumped parameter method, which is used in this Doctoral Dissertation, is based on modelling a continuous medium as a discrete network of isothermal nodes. They represent the capacitance of the system and they are linked by linear or radiative conductors representing the conduction, convection or radiation heat transfer with other nodes in the model. The discrete approximation has several
advantages in numerical as well as experimental work. For transient solution calculation, the model results in a ordinary differential equation system which for a n-node system can be expressed as,
CidTi dt =
n
X
j
GLi,j(Tj−Ti) +σ
n
X
j
GRi,j(Tj4−Ti4) + ˙Qi, (1.5) where Ci corresponds to the i-node thermal capacity; Ti and Tj are the i-node and j-node temperatures respectivelly; GLi,j is the linear conductor between node i and j; GRi,j is the radiative conductor between node i and j and ˙Qi is the total heat flux accounting for albedo, planetary and solar radiation as well as for internal heat dissipated by system equipment such as electronics and heaters. This equation can be numerically solved by discretizing the time domain and using methods such as Crank-Nicholson.
For steady-state calculations, while a continuous system obeys a differential equation system, the network approach obeys a non-linear algebraic equation system given by,
0 =
n
X
j
GLi,j(Tj −Ti) +
n
X
j
GRi,j(Tj4−Ti4) + ˙Qi, (1.6) which can be numerically solved using methods such as Newton.
Thermal models are usually divided in two different parts. On one hand, the Geometrical Mathematical Model (GMM), which contains information about the geometry of the system, its thermo-optical properties and the thermal environment.
Radiative conductors as well as radiative fluxes are obtained by means of the calculation of the Radiative Exchange Factors (REFs) and the View Factors (VFs) using a Monte-Carlo Ray Tracing algorithm (MCRT). On the other hand, the Thermal Mathematical Model (TMM) contains all the required information to solve Equation (1.5) so materials, linear conductors, internal heat dissipation, boundaries, etc are defined here.
The process flow for the thermal modelling is summarized in Figure 1.7. It starts with the definition of the GMM selecting thermo-optical properties, defining the geometry and creating the mesh. Next, user-defined thermal conductors and thermo- physical properties such as materials and thermal capacities are included. The system’s modelling ends with the definition of the boundary conditions representing the equipment operation. The analysis starts with the selection of the orbit and the system orientation based on the mission requirements. Accounting for all of this and the system’s characteristics, the worst-case thermal environmental conditions are defined. This is the main step in which this investigation is focused. Once
1. Introduction 21
Figure 1.7: Thermal modelling process.
selected, the radiative calculations are performed in order to complete the TMM for solving the system of equations.
Thermal analysis must be performed with the objective of predicting extreme temperatures of the system during its whole operational life. To get so, the worst- case conditions are usually evaluated. They not only depend on the thermal environment but also on the operational mode of the system and its thermo- optical properties accounting for degradation effects. In space thermal design, it is very common to defined hot and cold worst-cases to evaluate the system response in steady state. Sometimes, in complex systems, more than a case for the hottest or coldest environmental conditions could be selected as the maximum or minimum temperatures respectively for different instruments do not appear under the same circumstances.
Steady-state analysis are suitable for low inertia space system in which the temperature response is more coupled to the environmental changes. In contrast, when a massive system is analysed under the steady-state conditions, differences between the real response and the analysis results could be considerable since the temperature response is slower. When analysing a stratospheric balloon-borne payload, a steady-state analysis could be quite representative. This is because they have a long residence time over a considered point in the Earth leading to a slow change in the thermal environmental conditions so the system has enough time to follow a quasi-steady state during the flight. However, the ascent phase cannot be analysed under this conditions because of the high variability of the environmental parameters with the altitude.
Following this approach for the thermal analysis the obtained temperatures would represent the calculated temperature range which in terms of the ECSS, is the temperature range "for the operating and non-operating mode and the minimum switch-on condition of a unit, based on worst case considerations (i.e. an appropriate combination of external fluxes, materials properties and unit dissipation profiles to describe hot and cold conditions) excluding failure cases". As shown in Figure 1.8, thepredicted temperature range should also consider the uncertainties that include inaccuracies in temperature calculations due to inaccurate physical, environmental and modelling parameter.
Figure 1.8: Temperature ranges for Thermal Control System.
1.3.3.1 System level analysis cases
Driving and coordinating a thermal design process add additional work to do related with different areas. The whole system is usually divided in several subsystems and the thermal design of each one is quite often carried out by different institutions.
From a technical point of view, it is necessary to coordinate that work in order to ease the integration of each instrument in the system thermal model. In addition, the thermal environment affecting each instrument has to be derived from a system level study. By doing so, the thermal engineer in charge of performing each unit model can run several simulations to design a thermal control that fulfils its requirements.
The thermal design process at a system level starts with the development of a preliminary thermal model. It would be based on the initial specifications of the system and it would not be necessarily too detailed. What is important to be
1. Introduction 23
defined in the model is the relative position between components, the envelopes of each part and the baseline for the thermo-optical properties. The main objective of this model is not obtaining information about temperatures but the quantification of the direct solar flux, the Earth infrared flux and the albedo flux. In this way, parametric analyses could be performed in order to obtain the environmental conditions during the flight that could lead the instruments to their maximum and minimum temperatures.
Once the thermal environment has been properly defined and the worst extreme cases of an instrument selected, the boundary conditions for analysing it separately should be obtained. As has been said, the thermal design of a space or stratospheric mission is usually performed by several institutions and the conditions for the analyses at a unit level should be defined at a system level. The way these boundary conditions are obtained consists in the analysis of the whole system with the extreme cases conditions of every subsystem. However, not only the environmental conditions drive the temperature of a unit. The conductive interface and the radiative environment also affect it. For that reason, defining the dissipated power of the nearby instruments, its thermo-optical-properties and the expected envelopes, improves the real environment the unit is going to find.
The thermal design must evolve in parallel with the whole design and the thermal environmental conditions may change during this process. An iterative process must be followed in order to update the thermal model and obtain the boundaries for the unit model analysis. This process is summarized in Figure 1.9. By doing this, the uncertainties associated to the thermal modelling can be reduced.
1.3.3.2 Unit level analysis cases
Worst-cases particularized for each instrument should be provided by the system thermal engineer. Sometimes their conditions are not unique for the whole system so parametric analysis are usually convenient as it will be explained in Section 4.2.4. Boundary conditions for the unit-level analysis can be provided by different ways. Usually, the units are located in inner enclosures where the environmental conditions do not change so quickly so steady state analysis are appropriate.
In order to represent a real environment so the units could be separately analysed, radiative and conductive sink temperatures are provided. On the one hand, the radiative sink temperature, according to ECSS is a "virtual black body radiation temperature used to define the equivalent radiative thermal load on an item". It includes both the natural environment load (solar, planetary albedo and infrared fluxes) and the radiative exchanges with other items and can be obtained as,
Figure 1.9: Thermal environment characterization process for obtaining unit-lever boundary conditions.
TSink,R = 4
v u u tTi4+
Pn
j GRi,j(Tj4−Ti4)
εAi + Qa,i+QE,i+QS,i
σεAi . (1.7)
where Ti is the temperature of the item; Tj the temperature of the surrounding elements; GRi,j the radiative conductor between nodes i and j; ε the infrared emissivity; Ai the area of the item exposed to j and Qa,i, QE,i and QS,i are the albedo, Earth infrared and solar heat load.
On the other hand, the conductive sink temperature is the temperature which would provide an equivalent conductive flux to the unit through the defined thermal coupling with the conductive interface. It can be calculated as follows,
TSink,C =
Pn
j GLi,jTj
Pn
j GLi,j , (1.8)
where GLi,j is the linear conductor between nodes i and j.