Patent ID: 6654710
Filing Date: 2003-11-25
Classification: G06F

Abstract:
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: &PartialD;x_&PartialD;Ïƒ=h2J&it;â€ƒ&it;&PartialD;x_&PartialD;Ïˆ&it;x&it;&PartialD;x_&PartialD;Ï‡(1)with the stream functions &psgr; and &khgr;, the natural (streamline) coordinate &sgr;, the position vector x, wherein J denotes the Jacobi determinant; J=&PartialD;x_&PartialD;Ïƒ&it;&LeftFloor;&PartialD;x_&PartialD;Ïˆ&it;x&it;&PartialD;x_&PartialD;Ï‡&RightFloor;&Congruent;{&PartialD;x_&PartialD;Ïƒ&it;â€ƒ&it;&PartialD;x_&PartialD;Ïˆ&it;â€ƒ&it;&PartialD;x_&PartialD;Ï‡},(2)and wherein h is the stretching factor of the natural coordinate defined by h2&Congruent;&PartialD;x_&PartialD;Ïƒ&CenterDot;&PartialD;x_&PartialD;Ïƒ,(3)with the auxiliary equations &PartialD;H&PartialD;Ïˆ-T&it;â€ƒ&it;&PartialD;s&PartialD;Ïˆ-1Ï &it;â€ƒ&it;J&it;â€ƒ&it;&PartialD;&PartialD;Ïˆ&it;(h2Ï &it;â€ƒ&it;J)+2Ï &it;â€ƒ&it;J&it;{&PartialD;x_&PartialD;Ïƒ&it;â€ƒ&it;&PartialD;x_&PartialD;Ïˆ&it;â€ƒ&it;Î©_}=0,â€ƒ&it;and(4)&PartialD;H&PartialD;Ï‡-T&it;â€ƒ&it;&PartialD;s&PartialD;Ï‡-1Ï &it;â€ƒ&it;J&it;â€ƒ&it;&PartialD;&PartialD;Ï‡&it;(h2Ï &it;â€ƒ&it;J)-2Ï &it;â€ƒ&it;J&it;{&PartialD;x_&PartialD;Ïƒ&it;â€ƒ&it;Î©_&it;â€ƒ&it;&PartialD;x_&PartialD;Ïˆ}=0,(5)wherein H=H(&psgr;,&khgr;) is the total enthalpy, s=s(&psgr;,&khgr;), is the entropy, T is the temperature, &rgr; is the density, and &OHgr; is the angular velocity of the frame of reference.