Method for designing a flow device

A method for designing a flow device, comprising the steps of:

• defining the physical properties of said flow device;
• and
• deriving from said physical properties the corresponding geometry of said flow device via inverse flow equations;
• and
• forming the flow device based on the derived geometry;
• wherein said step of deriving the geometry comprising deriving geometry using inverse flow equations of the form:
• ∂ x _ ∂ σ = h 2 J ⁢ ⁢ ∂ x _ ∂ ψ ⁢ x ⁢ ∂ x _ ∂ χ ( 1 )
• with the stream functions ψ and χ, the natural (streamline) coordinate σ, the position vector x, wherein J denotes the Jacobi determinant;
• J = ∂ x _ ∂ σ ⁢ ⌊ ∂ x _ ∂ ψ ⁢ x ⁢ ∂ x _ ∂ χ ⌋ ≡ { ∂ x _ ∂ σ ⁢ ⁢ ∂ x _ ∂ ψ ⁢ ⁢ ∂ x _ ∂ χ } , ( 2 )
• and wherein h is the stretching factor of the natural coordinate defined by h 2 ≡ ∂ x _ ∂ σ · ∂ x _ ∂ σ , ( 3 )
• with the auxiliary equations ∂ H ∂ ψ - T ⁢ ⁢ ∂ s ∂ ψ - 1 ρ ⁢ ⁢ J ⁢ ⁢ ∂ ∂ ψ ⁢ ( h 2 ρ ⁢ ⁢ J ) + 2 ρ ⁢ ⁢ J ⁢ { ∂ x _ ∂ σ ⁢ ⁢ ∂ x _ ∂ ψ ⁢ ⁢ Ω _ } = 0 , ⁢ and ( 4 ) ∂ H ∂ χ - T ⁢ ⁢ ∂ s ∂ χ - 1 ρ ⁢ ⁢ J ⁢ ⁢ ∂ ∂ χ ⁢ ( h 2 ρ ⁢ ⁢ J ) - 2 ρ ⁢ ⁢ J ⁢ { ∂ x _ ∂ σ ⁢ ⁢ Ω _ ⁢ ⁢ ∂ x _ ∂ ψ } = 0 , ( 5 )
• wherein H=H(ψ,χ) is the total enthalpy, s=s(ψ,χ), is the entropy, T is the temperature, ρ is the density, and Ω is the angular velocity of the frame of reference.