Non-Dimensionalization for Aero Troll CFD
Opening StatementThe non-dimensional values were obtained from reference (1).
Values with tildes (~) are dimensional while non accented values are non-dimensional.
Within CFD literature, it seems the variable used to represent total (stagnation) energy in the Q vector differs. Sometimes one sees , sometimes or sometimes . To clarify what refers to in Aero Troll CFD, I'll show some equations below. Some equations have been adapted from reference (2). At the moment, Aero Troll CFD neglects gravity, therefore: Assuming the perfect-gas law and constant specific heats: Therefore: Next, the pressure equation will be derived using the perfect gas law and constant specific heats. For a perfect gas, the following is true:
Starting with the perfect gas law:
Non-Dimensionalized EquationsPerfect-gas law: Speed of sound: Pressure: Total Enthalpy: Entropy:
1) Krist, S. L., Biedron, R. T., and Rumsey, C. L., "CFL3D User's Manual (Version 5.0)," NASA TM 1998-208444, June 1998.
2) White, F. R., "Fluid Mechanics, 2nd Edition," McGraw Hill, 1986.