Thermodynamic properties of equilibrium air by an exact two-equation model for Euler and Navier–Stokes CFD algorithms
✍ Scribed by Joe Iannelli
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 349 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0271-2091
No coin nor oath required. For personal study only.
✦ Synopsis
This paper details an exact two-equation procedure to generate pressure, temperature and mass and mole fractions as well as their thermodynamic and Jacobian partial derivatives for ®ve-species neutral equilibrium air. Applicable for arbitrary forms of equilibrium constants and especially designed for explicit and implicit CFD algorithms, the procedure algebraically reduces to two equations the six-equation thermodynamic system comprising the equations for internal energy, law of mass action and conservation of species mass and ratio of oxygen and nitrogen nuclei. This exact algebraic reduction explicitly expresses four mass fractions in terms of nitric oxide mass fraction and temperature, which are then determined through a rapidly converging numerical solution of the internal energy and nitric oxide mass action equations. The procedure then exactly determines the partial derivatives of pressure, temperature and mass fractions analytically. The mathematical formulation also introduces a convenient system non-dimensionalization that makes the procedure uniformly applicable to ¯ows ranging from shock tube ¯ows with zero initial velocity to aerothermodynamic ¯ows with supersonicahypersonic freestream Mach numbers. Over a wide range of density and internal energy the predicted distributions of mole fractions for the model ®ve species agree with independent published results, while pressure and temperature as well as their partial derivatives remain continuous, smooth and physically meaningful.