A generalized similarity method with a universal equation in differential form in the theory of a nonstationary boundary layer

Supersonic laminar boundary-layer equations near the plane of symmetry of a cone at incidence are treated by the similarity method. Numerical integration of differential equations governing such a flow is performed, taking into consideration the temperature dependence of the Prandtl numberPrand viscosity μ throughout the boundary layer. On the leeward side, a detailed consideration of the solutions shows the existence of two solutions up to a critical incidence beyond which it appears that no solution may be found. Calculations carried out for a set of values of the external flow Mach number show up a significant effect of this parameter on the behaviour of the boundary layer.

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On the ionized gas boundary layer adjacent to the bodies of revolution in the case of variable electroconductivity

Thermal Science ◽

10.2298/tsci111205223o ◽

2013 ◽

Vol 17 (2) ◽

pp. 555-566

Author(s):

Branko Obrovic ◽

Slobodan Savic ◽

Vanja Sustersic

Keyword(s):

Boundary Layer ◽

The Body ◽

Gas Flows ◽

Generalized Equations ◽

Ionized Gas ◽

Bodies Of Revolution ◽

Concrete Form ◽

General Similarity ◽

Transformation Of Variables ◽

Similarity Method

This paper studies the ionized gas i.e. air flow in an axisymmetrical boundary layer adjacent to the bodies of revolution. The contour of the body within the fluid is nonporous. The ionized gas flows under the conditions of equilibrium ionization. A concrete form of the electroconductivity variation law has been assumed and studied here. Through transformation of variables and introduction of sets of parameters, V. N. Saljnikov's version of the general similarity method has been successfully applied. Generalized equations of axisymmetrical ionized gas boundary layer have been obtained and then numerically solved in a three-parametric localized approximation.

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Nonstationary Boundary Layer

Mathematical Models in Boundary Layer Theory ◽

10.1201/9780203749364-4 ◽

2018 ◽

pp. 153-264

Author(s):

O. A. Oleinik ◽

V. N. Samokhin

Keyword(s):

Boundary Layer ◽

Nonstationary Boundary

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Compressible Boundary-Layer Swirling Flow in a Nozzle and a Diffuser With Highly Cooled Wall

Journal of Applied Mechanics ◽

10.1115/1.3424541 ◽

1979 ◽

Vol 46 (2) ◽

pp. 275-280 ◽

Cited By ~ 2

Author(s):

M. Kumari ◽

G. Nath

Keyword(s):

Boundary Layer ◽

Mass Transfer ◽

Swirling Flow ◽

Local Similarity ◽

Compressible Boundary Layer ◽

Implicit Finite Difference Scheme ◽

Infinite Region ◽

Implicit Finite Difference ◽

Similarity Method ◽

Good Agreement

The steady laminar compressible boundary-layer swirling flow with variable gas properties and mass transfer through a conical nozzle, and a diffuser with a highly cooled wall has been studied. The partial differential equations governing the nonsimilar flow have been transformed to a system of coordinates using modified Lees transformation. The resulting equations are transformed into coordinates having finite ranges by means of a transformation which maps an infinite region into a finite region. The ensuing equations are then solved numerically using an implicit finite-difference scheme. The results indicate that the variation of the density-viscosity product across the boundary layer and mass transfer have strong effect on the skin friction and heat transfer. Separationless flow along the entire length of the diffuser can be obtained by applying suction. The results are found to be in good agreement with those of the local nonsimilarity method but they differ appreciably from those of the local similarity method.

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