# Asymptotic Analysis of Two—Dimensional Turbulent Separating Flows

Chapter
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 40)

## Summary

A universal law of the wall is developed by applying asymptotic theory for turbulent flows at high Reynolds numbers. This law is valid for attached as well as for separated flows and hence describes correctly the change of the law of the wall from attached to separated flows. This change is demonstrated for two examples: Couette—Poiseuille flows and equilibrium boundary layers.

The asymptotically correct flow resistance formulae for the Couette—Poiseuille flows are developed by applying an indirect turbulence model in addition to the universal law of the wall. The results for the equilibrium boundary layers are used to develop an integral method for calculating turbulent boundary layers including those with separation. The theoretical results are compared with experiments.

## References

1. [1]
Dengel, P.; Fernholz, H.H.: An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation, J. Fluid Mech., vol. 212, pp. 615–636, 1990
2. [2]
El Telbany, M.M.M; Reynolds, A.J.: Velocity distribution in plane turbulent channel flows, J. Fluid Mech., vol. 100, pp. 1–29, 1980
3. [3]
Gersten, K.: Asymptotische Theorie für turbulente Strömungen bei großen Reynolds—Zahlen, Ernst—Becker—Gedächtnis—Kolloqium, TH Darmstadt, Schriftenreihe Wissenschaft und Technik, Nr. 28, S. 67–94, 1985Google Scholar
4. [4]
Gersten, K.: Some contributions to asymptotic theory for turbulent flows, in: Proc. of 2nd Int. Symp. on Transport Phenomena in “Turbulent Flows”, Tokyo, pp. 201–214, 1987Google Scholar
5. [5]
Gersten, K.: Introduction to asymptotic theory for turbulent flows, ZAMM, Bd. 69, S. T 555—T 558, 1988Google Scholar
6. [6]
Gersten, K.: Die Bedeutung der Prandtlschen Grenzschichttheorie nach 85 Jahren, Z. Flugwiss. Weltraumforsch., Bd. 13, S. 209–218, 1989
7. [7]
Gersten, K.: Some open questions in turbulence modelling from viewpoint of asymptotic theory, Proc. of Tenth Australian Fluid Mechanics Conference, Melbourne, vol. II, pp. 12. 1–12. 4, 1989Google Scholar
8. [8]
Gersten, K.; Herwig, H.: Strömungsmechanik. Grundlagen der Impuls—, Wärme— und Stoffübertragung aus asymptotischer Sicht, Vieweg—Verlag, Braunschweig, 1992Google Scholar
9. [9]
Klauer, J.: Berechnung ebener turbulenter Scherschichten mit Ablösung und Rückströmung bei hohen Reynoldszahlen, VDI—Fortschrittbericht, Reihe 7: Strömungstechnik, Nr. 155, VDI—Verlag, Düsseldorf, 1989Google Scholar
10. [10]
Mellor, G.L.: The large Reynolds number asymptotic theory of turbulent boundary layers, Int. J. Engng. Sci., vol. 10, pp. 851–873, 1972
11. [11]
Melnik, R.E.: An asymptotic theory of turbulent separation, Computers & Fluids, vol. 17, no. 1, pp. 165–184, 1989
12. [12]
Simpson, R.L.; Chew, Y.T.; Shivaprasad, B.G.: The structure of a separating turbulent boundary layer, J. Fluid Mech., vol. 113, pp. 23–51, 1981
13. [13]
Stratford, B.S.: An experimental flow with zero skin friction throughout its region of pressure rise, J. Fluid Mech., vol. 5, pp. 17–35, 1959