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Applicability

Because of their inability to account for flow history effects, algebraic models are unable to predict separated flow reliably. Johnson and King (1985) introduced an additional ordinary differential equation to capture boundary layer separation with an increased accuracy [5]. For this reason, it is often called 1/2 - equation model. While the model performs better that the Cebeci-Smith and Baldwin-Lomax models, the complexity and elegance of the formulation dropped dramatically. All in all, algebraic models provide reasonable results for free shear flows and attached boundary layers. However, it is important to remember that algebraic models are incomplete. They can only be used when experimental data are available to calibrate their coefficients.

References

[1] B.S. Baldwin and H. Lomax. Thin layer approximation and algebraic model for separated turbulent flows, volume 257. American Institute of Aeronautics and Astronautics, 1978.

[2] L.J.S. Bradbury. The structure of a self-preserving turbulent plane jet. Journal of Fluid Mechanics, 23(01):31--64, 1965.

[3] T. Cebeci and A.M.O. Smith. Analysis of turbulent boundary layers. NASA STI/Recon Technical Report A, 75:46513, 1974.

[4] F.H. Clauser. The turbulent boundary layer. Advances in applied mechanics, 4:1--51, 1956.

[5] D.A. Johnson and L.S. King. A mathematically simple turbulence closure model for attached and separated turbulent boundary layers. AIAA journal, 23(11):1684--1692, 1985.

[6] P. Klebanoff. Characteristics of turbulence in a boundary layer with zero pressure gradient. National Advisory Committee for Aeronautics, 1955.

[7] S.J. Kline, W.C. Reynolds, F.A. Schraub, and P.W. Runstadler. The structure of turbulent boundary layers. Journal of Fluid Mechanics, 30(04):741--773, 1967.

[8] H.W. Liepmann and J. Laufer. Investigations of free turbulent mixing. 1947.

[9] E.R. Van Driest. On turbulent flow near a wall. J. Aero. Sci, 23(11):1007--1011, 1956.

[10] I. Wygnanski, F. Champagne, and B. Marasli. On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. Journal of Fluid Mechanics, 168(1):31--71, 1986.

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