Vane arc segment with thermal insulation element

A gas turbine engine comprising:

• a compressor section;
• a combustor in fluid communication with the compressor section;
• and
• a turbine section in fluid communication with the combustor, the turbine section having vanes disposed about a central axis of the gas turbine engine, each of the vanes includes:
• an airfoil piece defining first and second platforms and an airfoil section having an internal cavity and extending between the first and second platforms, the first platform defining a gaspath side, a non-gaspath side, and a first platform radial flange projecting from the non-gaspath side,
• support hardware supporting the airfoil piece via the first platform radial flange,
• a thermal insulation element adjacent the first platform radial flange and through which the support hardware supports the airfoil piece, the thermal insulation element isolating the airfoil piece from the support hardware such that there is no direct contact interface between the first platform and the support hardware, and
• an additional thermal insulation element, wherein the second platform further comprises a second platform radial flange that projects from a non-gaspath side of the second platform, the second platform radial flange defines a radial flange face, an inner flange face facing toward the internal cavity, and an outer flange face opposed from the inner flange face, the additional thermal insulation element defines an inner element face facing toward the internal cavity and an outer element face opposed from the inner element face, and the outer flange face contacts the inner element face, the second platform radial flange converges such that the internal cavity narrows between the second platform radial flange, and relative to a radial direction of the airfoil piece the outer flange face and the inner element face are sloped.