Casting for a turbine wheel

A nozzleless centered vortex fixed geometry turbine housing surrounding the periphery of a turbine wheel having an axis of rotation, said housing including at least one elongated substantially spiral compressible fluid passageway having an external inlet and an internal outlet for encompassing said wheel periphery, the said passageway being defined by a pair of opposed axisymmetrical side walls extending circumferentially around at least 360 arc degrees of said axis and having inner diameters proximate the periphery of said turbine wheel, said axisymmetry resulting in a predetermined constant distance between said opposing side walls at a given radius from said turbine wheel axis, said distance measured parallel to said turbine wheel axis and varying only as a function of radial distance and not as a function of arc degrees, and a peripheral wall extending between said side walls in a direction parallel to the axis of said turbine wheel, said peripheral wall coextensive with said axisymmetrical side walls around at least 360 arc degrees of said axis, the radial distance of said peripheral wall from said turbine wheel axis being defined by the path prescribed by the direction of said fluid flow in a free vortex concentric with said turbine wheel axis and constrained by said axisymmetrical side walls, the angle between a tangent to said peripheral wall at a given location and a radial line from the wheel axis to said location, measured in a plane perpendicular to the wheel axis of rotation, varying as a function of the radial and tangential components of the fluid velocity at that location, whereby there are no resolved wall pressure components, except for the effects of friction, which interact with the fluid tangential velocity as said fluid moves inwards from said inlet to said outlet.