Development of a Vibration-Free Sorption-based J-T Cryochain for the Gravitational Wave Detectors of ETpathfinder
Arvi Xhahi is a PhD student in the department Energy, Materials and Systems. (Co)Promotors are prof.dr.ir. H.J.M. ter Brake and dr.ir. M.A.J. van Limbeek from the faculty Science & Technology (TNW) University of Twente.
Ultra-low-vibration cooling has long been a niche technology, primarily reserved for space applications where high-resolution detectors and optical instruments require such cooling systems. The rapid growth of gravitational-wave astronomy over the past decade has pushed measurement instruments (in ground-based laboratories) to unprecedented levels of sensitivity. Third generation gravitational wave detectors, including the Einstein Telescope, require operation temperatures in the cryogenic range of 10-20 K to access the needed resolution and broaden the repertoire of measurable phenomena. As a result, cryogenic cooling with ultra-low vibration emission has become important for large-scale ground-based applications. Only a handful of cryocooler technologies, outlined in Chapter 1, could satisfy the vibration and cooling demands of future GW detectors, and even those usually need a sizable active or passive vibration attenuation system to achieve truly vibration-free operation. Among those ultra-low-vibration cryocooler options, Joule-Thomson (JT) coolers driven by sorption compressors stand out because they are inherently vibration free. Therefore, the ETpathfinder project, a pilot in the development of the the Einstein Telescope, has adopted this technology as its baseline cooling system.
Chapter 2 presents the conceptual sorption-based JT cryochain that satisfies the cooling requirements of the ETpathfinder cryostat. The cryochain comprises three parallel cascade stages delivering cooling at 40 K with neon, 15 K with hydrogen, and 8 K with helium. Size and performance are estimated through thermodynamic optimization of each stage’s operating conditions, aiming to maximize the coefficient of performance (COP). A simple 1D finite-volume model captures the dynamics of the considered legacy cylindrical central-heater sorption cell design. The baseline configuration demands ∼ 364 W of input power and employs 26 sorption cells.
After conceptualizing the sorption-based JT cryochain, the attention shifted to the sorption compressor unit. A broader modeling framework was required to support the upcoming developments by enabling extensive design exploration and better capturing the complex physics of adsorption compressors. Chapter 3 describes the detailed development of a multi-physics FEM-based thermo-adsorption framework. This methodology integrates the modified Dubinin-Astakhov adsorption model, a Brinkman-based porous-flow formulation, and the conservation laws of mass and energy. Three distinct spatial representations of a sorption cell legacy central-heater design (a 1D-axisymmetric , a 2D-profile, and a 2D-axisymmetric) were implemented to illustrate this modeling approach. In all cases, the physics-based sorption cell model predictions show satisfactory agreement with available experimental data.
The general modeling framework enabled the study of novel multi-heater configurations, providing a foundation for exploring performance improvements in sorption cells, as detailed in Chapter 4. The study begins with a cylindrical sorption cell that includes a central heater zone and a peripheral heater array placed at a defined pitch radius. To accommodate the exploration and operating patterns of the multi-heater concept, a multidimensional Optimization-Driven Global Sensitivity Analysis framework is developed. The optimization procedure consists of a Genetic-Algorithm (GA) and a Machine-Learning (ML) computational unit. The Genetic Algorithm navigates the multi-parameter space by repeatedly evaluating a physics-based sorption FEM dynamic model. The ensemble of evaluations builds a comprehensive database of promising solutions. This database is then used to train the Machine Learning model, implemented as a Random Forest regressor, so that further predictions can be performed at a fraction of the original (physics-based model evaluation) computational cost. By combining kriging-based predictions with physics-based informed modeling, this innovative approach uncovers new design trends for sorption-based technology. In the second part of Chapter 4, a neon multi-heater sorption cell is designed and built following the proposed optimization process. A tailored experimental setup is built to characterize the cell at ∼ 70 K in order to verify the model predictions. Experimental results and model predictions are compared and again demonstrate good agreement, which further strengthens the model validation effort. The performance of the multi-heater baseline cell is then compared with that of the legacy single-heater cell under the neon-stage operating conditions of ETpathfinder and shows superior performance across several operating variants. In addition, flatter sorption-cell geometries (elliptical, rectangular, and obround) are explored. A comparative study between an obround multi-heater cell and the baseline cylindrical cell clearly indicates performance and size benefits of up to 40%.
Chapter 5 investigates the fluid induced vibration aspects of JT sorption based coolers. There is a pressing need to identify, via quantitative means, the upper-bounds of the sorption-based JT coolers to be employed in the ETpathfinder. Based on seismic measurements at the ETpathfinder site, the operational cooling system must not introduce vibration amplitudes greater than < 4 nm⁄√Hz in the 2 to 20 Hz frequency band. To assess whether the proposed JT cooler (especially its supercritical-helium stage) can meet the required refrigeration while staying within the specified disturbance limits, we first need to define appropriate experimental and numerical methods for quantifying those disturbances and then test them. Fluid-structure-interaction (FSI) simulations in conjunction with atomic-force-microcopy (AFM) measurements were the two selected pathways. Both quantification pathways were applied on a U-shaped tube geometry, with the final displacement spectra having a good agreement with each other. Furthermore, two J-T valves (a porous-plug and an orifice-plate) were experimentally characterized with AFM probing for a variety of flow conditions. Their vibration signatures were compared, revealing different relative behaviors. The study proved the feasibility and practicality of using room-temperature AFM as a high-precision vibration characterization apparatus for fluid devices and assemblies. It also shows that FSI or CFD simulations can provide the necessary prediction tools for cryogenic operation of critical JT cooler components.
