Thermal Model

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Description

The Thermal Model class represents the thermal state of a physical spacecraft component. It can operate in two distinct modes:

• Lookup Mode – Uses precomputed temperature profiles from CSV datasets (empirical or ground-test data).
• Simulated Mode – Computes temperatures dynamically using heat exchange and power balance equations within the thermal network.

The thermal model provides:

• A per-component temperature state variable, Temperature [K].
• The rate of change of temperature (TemperatureDot [K/s]).
• Net heat flow (NetPower [W]) into or out of the component.
• Handling of thermal connections (radiative or conductive) to other models.
• Data lookup and initialization from CSV-based temperature tables for verification or testing.

This class is typically attached to a Physical Object and managed globally by the Thermal System.

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Module Implementation

Energy Balance

In simulated mode, the thermal energy balance follows the first law of thermodynamics:

$${\dot{Q}}_{\mathrm{net}}={\dot{Q}}_{\mathrm{in}}-{\dot{Q}}_{\mathrm{out}}+P_{\mathrm{gen}}$$

where:

• ${\dot{Q}}_{\mathrm{net}}$ ​: Net power input W
• $P_{\mathrm{gen}}$​: Internal power generation (e.g., electronics dissipation) W

The temperature change is derived from:

$$\frac{dT}{dt}=\frac{{\dot{Q}}_{\mathrm{net}}}{m\cdot c_p}$$

and numerically integrated as:

$$T_{t+\Delta t}=t_t+\frac{{\dot{Q}}_{\mathrm{net}}\Delta T}{m\cdot c_p}$$

where:

• $m$ : Component mass kg
• $c_p$ ​: Specific heat capacity J/kg·K

Lookup Mode

In lookup mode, the model retrieves temperature directly from the CSV data file based on simulation time $t$:

$$T(t)=f_{\mathrm{lookup}}(t)$$

and computes an approximate temperature derivative as:

$$\dot{T}=\frac{T_{t+\Delta T}-T_t}{\Delta t}$$

This mode is typically used for test data correlation or hardware-in-the-loop validation.

Model Initialization

When initialized with a CSV file:

1. The file must contain at least two columns, typically time [s] and temperature [K].
2. The system validates the dataset and sets:
   • AnalysisModel = Lookup
   • `IsInitialised = true
3. If invalid or missing data is detected, the model reverts to Simulated mode.

Thermal Connections

Each Thermal Model may connect to one or more others through Thermal Connection objects, which define the heat exchange mechanism:

• Conduction: Linear temperature-dependent heat transfer.
• Radiation: Non-linear $T^4$ radiative coupling using Stefan–Boltzmann law.

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Assumptions/Limitations

• Each model represents a lumped thermal mass, assuming uniform temperature throughout the component.
• Only conduction and radiation are modelled while convection is excluded (valid in space vacuum).
• CSV lookup assumes uniformly sampled time intervals or performs linear interpolation.
• Thermal coupling network topology must be static during simulation runtime.
• Nonlinear radiation behaviour is simplified via average emissivity between connected nodes.
• Lookup mode cannot extrapolate beyond the final time sample.
• Does not handle multi-phase transitions.
• No explicit solver for conductive heat diffusion across geometry, only node-to-node lumped conductance.

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References

[1] Bergman, Theodore et al. Fundamentals of Heat and Mass Transfer. 8th ed. Wiley, 2017. Web. 29 Oct. 2025.

[2] Howell, J.R., Mengüc, M.P., Daun, K., & Siegel, R. (2020). Thermal Radiation Heat Transfer (7th ed.). CRC Press. https://doi.org/10.1201/9780429327308