Other one-equation models
An extensive list of one-equation models can be found in the literature. Most of them are more accurate, and also more complex than the basic Prandtl-Emmons-Glushko model. For example, the Baldwin-Barth model (1990) solves an equation for the turbulent Reynolds number instead of the turbulent kinetic energy
[1]. The approach is interesting, but includes nothing less than seven closure coefficients and three empirical damping functions. Spalart and Allmaras (1992) also developed a well-known turbulence model, that includes an equation for the turbulent eddy viscosity
[6]. Its eight coefficients and three damping functions have been calibrated especially for aerospace applications. In addition, a transition correction can be incorporated, which introduces four additional constants and two semi-empirical functions.
Applicability
The Baldwin-Barth and Spalart-Allmaras are complete models. This does not guarantee the accuracy of the results, but the interaction with the user is reduced. For simple flows, one-equation models generally do not perform better than algebraic models such as the Baldwin-Lomax model. However, they have been shown a greater potential for predicting separated flows
[5].
References
[1] B.S. Baldwin and T.J. Barth. A one-equation turbulence transport model for high reynolds number wall-bounded flows. NASA STI/Recon Technical Report N, 91:10252, 1990.
[2] H.W. Emmons. Shear flow turbulence. In Proceedings of the 2nd US Congress of Applied Mechanics, ASME, 1954.
[3] G.S. Glushko. Turbulent boundary layer on a flat plate in an incompressible fluid. Technical report, DTIC Document, 1966.
[4] N.N. Mansour, J. Kim, and P. Moin. Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. Journal of Fluid Mechanics, 194(1):15--44, 1988.
[5] M.J. Smith, M. Potsdam, T. Wong, J.D. Baeder, and S. Phanse. Evaluation of computational fluid dynamics to determine two-dimensional airfoil characteristics for rotorcraft applications. Journal of the American Helicopter Society, 51(1):70--79, 2006.
[6] P.R. Spalart and S.R. Allmaras. A one-equation turbulence model for aerodynamic flows. In AIAA, Aerospace Sciences Meeting and Exhibit, 30 th, Reno, NV, 1992.
