The project “Technologiedemonstrator zur Messung von Verdampfungsgeschwindigkeiten von Metallen und Legierungen” aimed to quantify evaporation rates of metals in a Knudsen‑cell environment. By combining analytical theory, Direct Simulation Monte Carlo (DSMC) modelling, and commercial COMSOL Multiphysics simulations, the team produced a comprehensive dataset that serves as a benchmark for future experimental work and space‑flight applications.
Technical Results
Analytical calculations were based on the Hertz–Knudsen–Langmuir equation, implemented in a MATLAB routine that incorporates vapor‑pressure data from the SGPS database of SGTE. For zinc, the mass flow from a 1 mm diameter opening varied from 1.0 × 10⁻⁸ kg s⁻¹ at 690 K to 1.5 × 10⁻⁸ kg s⁻¹ at 750 K. The routine also evaluated the Clausing factor for cylindrical openings of different aspect ratios, revealing values ranging from 0.952 for a 0.1 mm radius to 0.191 for a 10 mm radius.
To validate the analytical approach, a 3‑D MATLAB DSMC model was constructed. Using a 0.75 mm opening and zinc vapor, the DSMC mass flow at 723 K was 1.26 × 10⁻⁸ kg s⁻¹, only 4 % lower than the analytical prediction of 1.31 × 10⁻⁸ kg s⁻¹. Clausing factors derived from DSMC matched literature values within 0.1 % across all tested geometries, confirming the model’s accuracy for non‑tabulated shapes.
COMSOL Multiphysics simulations of a realistic cell (height 18.5 mm, radius 4.5 mm, 1 mm opening) produced a mass flow of 1.247 × 10⁻⁷ kg s⁻¹ at 723 K, within 2 % of the DSMC result. This agreement demonstrates that the commercial solver can reliably capture Knudsen‑cell physics when the correct boundary conditions are applied.
For a modified cell incorporating a side opening and a nanowave sensor, simulations predicted mass flows of 11.56 ng s⁻¹ at 920 °C, 34.91 ng s⁻¹ at 975 °C, and 82.52 ng s⁻¹ at 924 °C. Experimental measurements during the 2018 parabolic‑flight campaign yielded 1.51–6.46 ng s⁻¹, indicating that the simulation overestimates the flux by a factor of 5–8. This discrepancy highlights the need for refined thermal modelling of the cell walls and sensor interface.
Collaboration
The project was coordinated by the Technical University of Clausthal, with key partners providing complementary expertise:
Hochschule Mannheim (HSM) – Developed the DSMC framework and performed extensive parameter studies on opening geometry and temperature gradients.
Deutsches Zentrum für Luft‑ und Raumfahrt (DLR), Institut für Materialphysik im Weltraum – Supplied the experimental platform for parabolic‑flight tests and supplied temperature data for boundary conditions.
Airbus Defence and Space GmbH – Contributed flight‑ready hardware and facilitated integration of the nanowave sensor into the cell design.
Through joint workshops and shared data repositories, the consortium achieved a unified modelling workflow that bridges analytical theory, numerical simulation, and experimental validation. The collaborative effort not only produced a robust dataset for zinc evaporation but also established a methodology applicable to other metals and alloys in space‑flight environments.