A computer code that generates shock-free transonic compressor cascade shapes while taking into account viscosity effects is developed. The mathematical model for the inviscid flow field is the full potential equation. The Kutta-Joukowski condition is satisfied by varying the free stream angle at downstream infinity. A boundary fitted computational grid of C-type is generated using a sequence of conformal mapping and nonorthogonal coordinate stretching and shearing transformations. The inviscid calculation is performed sequentially on up to four consecutively refined grids thereby accelerating the convergence of the solution process. The full potential equation is solved using a finite area technique and rotated, type-dependent finite differencing. Artificial viscosity of the first order is added in a fully conservative form. Shock-free cascade airfoil shapes are obtained using the fictitious gas concept of Sobieczky and the method of characteristics in the rheograph plane. Viscosity effects are incorporated via a boundary layer displacement thickness. The integral boundary layer code is based on Rotta’s turbulence model and assumes transition region of zero length.
Design of Shock-Free Compressor Cascades Including Viscous Boundary Layer Effects
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Dulikravich, GS, & Sobieczky, H. "Design of Shock-Free Compressor Cascades Including Viscous Boundary Layer Effects." Proceedings of the ASME 1983 International Gas Turbine Conference and Exhibit. Volume 1: Turbomachinery. Phoenix, Arizona, USA. March 27–31, 1983. V001T01A050. ASME. https://doi.org/10.1115/83-GT-134
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