Possible Similarity Solutions of Unsteady Boundary Layer Equations in Certain Three-Dimensional Orthogonal Curvilinear Coordinates

1964 ◽  
Vol 19 (7) ◽  
pp. 1226-1231 ◽  
Author(s):  
B. R. Luthra
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Similarity Solutions ◽  
Curvilinear Coordinates ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Equations ◽  
Orthogonal Curvilinear Coordinates

Singularities in solutions of the three-dimensional laminar-boundary-layer equations

1985 ◽  
Vol 160 ◽  
pp. 257-279 ◽  
Author(s):  
James C. Williams
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
New Type ◽  
Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

2012 ◽  
Author(s):  
Md. Abdus Sattar
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Length Scale ◽  
Local Similarity ◽  
Unsteady Boundary Layer ◽  
Similarity Equation ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

Development and assessment of computer methods for three-dimensional turbulent boundary layers

1999 ◽  
Vol 103 (1024) ◽  
pp. 287-297
Author(s):  
J. Wu ◽  
U. R. Müller
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Theoretical Data ◽  
Field Method ◽  
Curvilinear Coordinates ◽  
Integral Boundary ◽  
Boundary Layer Equations ◽  
Computer Methods

Abstract This paper describes the development of a finite difference method that solves the boundary-layer equations for three-dimensional compressible turbulent flows. The most prominent achievements are the employment of a Newton technique for the simultaneous solution of all governing equations, an option to choose an algebraic or a k-ε eddy-viscosity turbulence model, and the flexible use of curvilinear coordinates. The method is validated by comparisons with a number of experimental and theoretical data sets of three-dimensional, compressible and incompressible, steady and unsteady boundary layers. In parallel, the performance of a three-dimensional compressible industrial integral boundary-layer technique is evaluated by comparisons with experimental test cases and with the results of the field method.

The interacting boundary-layer flow due to a vortex approaching a cylinder

1997 ◽  
Vol 346 ◽  
pp. 319-343 ◽  
Author(s):  
Z. XIAO ◽  
O. R. BURGGRAF ◽  
A. T. CONLISK
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Two Dimensions ◽  
Unsteady Boundary Layer ◽  
Reynolds Number Flow ◽  
Boundary Layer Equations ◽  
Number Flow ◽  
Layer Flow ◽  
High Reynolds

In this paper the solution to the three-dimensional and unsteady interacting boundary-layer equations for a vortex approaching a cylinder is calculated. The flow is three-dimensional and unsteady. The purpose of this paper is to enhance the understanding of the structure in three-dimensional unsteady boundary-layer separation commonly observed in a high-Reynolds-number flow. The short length scales associated with the boundary-layer eruption process are resolved through an efficient and effective moving adaptive grid procedure. The results of this work suggest that like its two-dimensional counterpart, the three-dimensional unsteady interacting boundary layer also terminates in a singularity at a finite time. Furthermore, the numerical calculations confirm the theoretical analysis of the singular structure in two dimensions for the interacting boundary layer due to Smith (1988).

Sign in / Sign up

Export Citation Format

Share Document