Abstract
A detailed and systematic experimental analysis of the separation phenomena in a plane and uniform supersonic flow, clearly emphasizing the influence of the laminar, turbulent or transitional nature of the boundary layer, has been presented first by Chapman, Kuehn, and Larson [1]. It has led these authors to point out a theoretical approach based on the existence of similarity properties in the development of the boundary layer around the separation point. This very simple method, applicable to laminar as well as turbulent flow, leads to a rather complete description of separation. It is particularly well adapted to practical applications, and has been used in that way by Erdos and Pallone [2]. More recently Lewis, Kubota, and Lees [3] have considered an extension of Chapman’s work to the case of uniform and nonadiabatic hypersonic flows.
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Abbreviations
- C f :
-
Wall friction coefficient
- D :
-
Nozzle-throat diameter
- D z :
-
Nozzle-out diameter
- f 1 :
-
Similitude function; Eqs. (3) and (15)
- f 2 :
-
Similitude function; Eqs. (6) and (15)
- F :
-
Pressure correlation function; Eqs. (7) and (16)
- g :
-
\( = F/\tilde F\)
- h :
-
\( = K/\tilde K\)
- k :
-
=(l/δ *0 )/[F R /(θ R — θ R )]; Eq. (8)
- K :
-
=k · F R ; Eq.(8)
- l :
-
Reference length; l = x — x 0
- M :
-
Mach number
- p :
-
Pressure
- p i :
-
Stagnation pressure
- p′:
-
Non-dimensional pressure gradient = \(\frac{{\delta _0^*}}{{{q_0}}}\cdot\frac{{\partial p}}{{\partial x}}\)
- P :
-
Büsemann pressure number P(M) = \(\int { - \frac{1}{M}\cdot\frac{{\sqrt {{M^2} - 1} }}{{1 + \frac{{\gamma - 1}}{2}{M^2}}}} \)
- q :
-
Dynamic pressure = \(\frac{1}{2}P\gamma {M^2}\)
- R :
-
Nozzle longitudinal radius
- Re:
-
Reynolds number
- s :
-
Reduced abcissa = \(\frac{{x - {x_0}}}{l}\)
- T :
-
Temperature
- u :
-
0x velocity component
- v :
-
0y velocity eomponent
- 0x :
-
Reference axis (see section 3.1)
- X :
-
Nozzle axis
- 0y :
-
Axis normal to X
- Y :
-
Radial distance of a point in the flow
- α :
-
Mach angle
- γ :
-
Specific-heat ratio
- δ*:
-
Displacement thickness of the boundary layer
- η, ξ :
-
Characteristic coordinates
- θ :
-
Velocity inclination
- \(\bar \omega \)(M):
-
Function p/P i (M) (isentropic flow)
- 03F1; :
-
Specific mass
- τ :
-
Shear stress
- 0:
-
at origin of interaction
- R :
-
at selected value of the F function
- S :
-
at separation point
- W :
-
at wall
- ~:
-
Case of uniform adiabatic flow
- —:
-
Case of non-separated flow
References
Chapman, D. R., D. M. Kuehn and H. K. Larson: Investigation of separated flows in supersonic and subsonic streams with emphazis on the effect of transition. NACA-TR 1356 (1968).
Erdos, J., and A. Pallone: Shock boundary layer interaction and flow separation. R.A.D. — TR 61–23, AVCO Corp., Aug. 15 (1961).
Lewis, J. E., T. Kubota and L. Lees: Experimental investigation of supersonic laminar, two- dimensional boundary layer separation in a compression corner with and without cooling. AIAA J. 6, 7–14 (1968).
Carriere, P.: Recherches sur les décoUements dans les tuyères propulsives. Rev. roumaine des Sciences Techniques — Mécanique appliquée. Tome 13, No. 3 (1968) p. 339–415.
Michel, R.: Cours del’ Ecole Nationale Supérieure de l’Aéronautique. Paris 1967.
Curle, N.: The effect of heat transfer on laminar boundary layer separation in supersonic flow. Aero. Quart. 12, 309–336 (1961).
Herbert, M. V., and R.J. Herdt: Boundary layer separation in supersonic propelling nozzles, in the presence of external flow. NGTE, Report 260, Aug. 1964.
Carriere, P.: Exhaust nozzles. In AGARD Lecture Series on supersonic Turbomachinery. Varenne (Italy), May 1967 (to be published).
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© 1969 Springer-Verlag Berlin Heidelberg
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Carrière, P., Sirieix, M., Solignac, JL. (1969). Similarity properties of the laminar or turbulent separation phenomena in a non-uniform supersonic flow. In: Hetényi, M., Vincenti, W.G. (eds) Applied Mechanics. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85640-2_11
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DOI: https://doi.org/10.1007/978-3-642-85640-2_11
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