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Advanced Virgo : cryostat designs Some thermal aspects

Advanced Virgo : cryostat designs Some thermal aspects. Eric Hennes, University of Amsterdam. Contents geometrical overview questions to be answered thermal properties modeling method results for several design parameters conclusion. Gravitational Waves group Amsterdam Nikhef-VU-UvA

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Advanced Virgo : cryostat designs Some thermal aspects

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  1. Advanced Virgo : cryostat designsSome thermal aspects Eric Hennes, University of Amsterdam Contents • geometrical overview • questions to be answered • thermal properties • modeling method • results for several design parameters • conclusion Gravitational Waves group Amsterdam Nikhef-VU-UvA Cascina, Februari 3, 2009 Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  2. transparant areaviewed by mirror cold area viewed by mirror Baffle ring at Ta Simplified geometry Ambient temperature Ta=300K cylinder Tc=80 K fixed mirror Dc tm Dm ` Lcm Lc Mirror: Dm = 0.4 m tm = 0.1 m Am = p(Dmtm+Dm2/2) Rm = Dm/2 Distance: Lcm = 2.5 m Cylinder: Dc = 0.65 or 1.0 m Lvc = 2.5 m Ac = pDcLc Exterior: isolated Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  3. To be estimated • Cryostat power consumption Pac due to radiation • Radiative heat flow Pmc =Pam from and to mirror (in equilibrium) • Mirror temperature distribution, without or with baffle(s) • Effect T-distribution on mirror optics (optical path) • (Design of baffle heating) ` Pmc Pam Pac ` Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  4. Thermal material properties involved Mirror: Thermal conductivity : k = 1.36 W/Km Thermo-optic coefficient :dn/dT = 0.98 10-5 K-1 Thermal Expansivity : a = 0.54 mm//Km Emissivity:: em = 0.89 Cryostate Emissivity: : ec = 0.1 (initial) = 0.2 (nominal, t< 2 years) = 0.9 (worst “icing” case) Baffle “ : eb = 0.12 Ambiance “ : eamb = 1.0 (“black”) Reflection of radiation : diffuse, i.e. non-specular Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  5. Modeling method / tools 1 Mirror temperature distribution : FEM (COMSOL) Domain : DT=0 Boundary : .n=J (outward conducted power flux) Radiation heat exchange general : FEM Isothermal mirror equilibrium : analytical approximation cooling power: ambiance to mirror: mirror to cryostat: solving Tm (equilibrium): Pmc= Pam Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  6. Modeling method / tools 2 View factor calculation general : FEM (COMSOL) 2 simple bodies (Am<<Ac) : analytical approximation: general: A1F12=A2F21 with Fcc: view factor between two circular faces 1 and 2 at distance d: Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  7. Modeling method / tools 3 Mirror geometrical properties change (mirror initially flat) mirror thickness change due to thermal expansion: mirror surface radii of curvature: FEM mechanical analysis Thermal lensing change in optical path: radius of curvature of equivalent isothermal lens (one side flat): Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  8. Dc=0.65m, no baffles, linear prism elements FEM models (thermal & thermo-mechanical) Dc=1m, 3 baffles, quadratic hex elements Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  9. 9 nm Results small cryostate (ec=0.2), no baffles Front Back Temperature profile (299.70 – 299.86 K) dz=13 nm Enlargement factor : 2E6 Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  10. mirror Dc b4 b3 b2 b1 Summary results for ec=0.2 Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  11. Cryostat power for several emissivities ec Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

  12. Final remarks & conclusion • All radii of curvature are larger than 100 km and exceed by far those predicted for beam power absorption (see van Putten et al.) Conclusion: no mirror optics problems expected for any proposed design • Lowest cryostat power is obtained using (only) 2 baffles on either side • Including the recoil mass into the models will result into a smaller radial temperature gradient, and consequently, into even larger radii of curvature Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA

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