A Method of Solving Supersonic Laminar Boundary-Layer Separation and Its Application to Wedges and Curved Surfaces

1965 ◽  
Vol 32 (4) ◽  
pp. 747-756
Author(s):  
Oscar Pinkus
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Boundary Layer Separation ◽  
Integral Solution ◽  
Separated Flows ◽  
Curved Surfaces ◽  
Laminar Boundary Layers ◽  
Compressible Boundary Layers ◽  
Supersonic Laminar

By use of a quartic velocity profile with one of its coefficients varying along the boundary layer, a technique is developed to calculate the general characteristics of adiabatic separated flows. The technique is based on the integral solution of the differential equations of laminar compressible boundary layers utilizing the energy-momentum concept and on expressions derived from the notion of a dividing streamline in the separated region. Detaching, central, and reattaching regions are defined which, by their combination, embrace most known forms of flow separation. The derived equations are here applied to the case of separated laminar boundary layers on compression corners and curved surfaces.

Influencing Factors on Submicron Particle Movement Patterns in Supersonic Laminar Boundary Layers

2014 ◽  
Author(s):  
Xing Li ◽  
Bofeng Bai
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Drag Force ◽  
Lift Force ◽  
Particle Movement ◽  
Submicron Particle ◽  
Laminar Boundary Layers ◽  
Saffman Lift Force ◽  
Supersonic Laminar

The process of submicron particle movement in laminar boundary layers is present in many practical applications such as the particles depositing on the turbine blade and mist droplets depositing on the surface of aircrafts. Although great progress has been made on this issue during the last decades, many underlying mechanisms still remain unclear. Here, we developed a theoretical model to understand how submicron particles will behave when they enter a supersonic laminar boundary layer above an adiabatic plate along with the main stream. In this model, we used the Lagrangian method to track the particles and calculate their trajectories, and the Eulerian method was used to calculate the flow field. Because of the large velocity and temperature gradient near the wall and the small size of the particle in this question, four forces (e.g., drag force, Saffman lift force, thermophoretic force and Brownian force) acting on the particle are considered. The effects of entering position, Mach number, the size and density of particles are investigated. We discovered that there are three particle movement patterns when they enter the supersonic boundary layer, and that the drag force and Saffman lift force play dominating roles on which pattern will happen in this process. Moreover, the results also reveal that the particle tends to move towards the wall as the diameter and the density of the particle and the Mach number of main flow increases. Finally, we suggested a dimensionless number to describe the three patterns of particle motion. This research provides a better understanding of the particle movement process in the supersonic laminar boundary layer, which can be a useful guidance for the industrial processes involving this phenomenon.

Laminar boundary layers behind detonation waves

1983 ◽  
Vol 387 (1793) ◽  
pp. 331-349 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Flow Analysis ◽  
Time Dependent ◽  
Detonation Waves ◽  
Planar Geometry ◽  
Laminar Boundary Layers ◽  
Spherical Detonation ◽  
Layer Flow

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer

1966 ◽  
Vol 33 (2) ◽  
pp. 429-437 ◽  
Author(s):  
J. C. Rotta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Calculation Methods ◽  
Recent Developments ◽  
Incompressible Boundary

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.

A Reference Temperature Method for Compressible Laminar Boundary Layers

1973 ◽  
Vol 2 (4) ◽  
pp. 201-204
Author(s):  
R. Camarero
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Reference Temperature ◽  
Integral Approach ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Boundary Layers ◽  
Temperature Method ◽  
Compressibility Effects

A calculation procedure for the solution of two-dimensional and axi-symmetric laminar boundary layers in compressible flow has been developed. The method is an extension of the integral approach of Tani to include compressibility effects by means of a reference temperature. Arbitrary pressure gradients and wall temperature can be specified. Comparisons with experiments obtained for supersonic flows over a flat plate indicate that the method yields adequate results. The method is then applied to the solution of the boundary layer on a Basemann inlet.

An Accurate Calculation Method for Two-dimensional Incompressible Laminar Boundary Layers, Including Cases with Regions of Sharp Pressure Gradient

1977 ◽  
Vol 28 (3) ◽  
pp. 149-162 ◽  
Author(s):  
N Curle
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Calculation Method ◽  
Boundary Layer Separation ◽  
Pressure Gradients ◽  
Accurate Calculation ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Type Boundary

SummaryThe paper develops and extends the calculation method of Stratford, for flows in which a Blasius type boundary layer reacts to a sharp unfavourable pressure gradient. Whereas even the more general of Stratford’s two formulae for predicting the position of boundary-layer separation is based primarily upon an interpolation between only three exact solutions of the boundary layer equations, the present proposals are based upon nine solutions covering a much wider range of conditions. Four of the solutions are for extremely sharp pressure gradients of the type studied by Stratford, and five are for more modest gradients. The method predicts the position of separation extremely accurately for each of these cases.The method may also be used to predict the detailed distributions of skin friction, displacement thickness and momentum thickness, and does so both simply and accurately.

A Fast Approximate Solution of the Laminar Boundary-Layer Equations

1986 ◽  
Vol 108 (2) ◽  
pp. 200-207 ◽  
Author(s):  
Sei-ichi Iida ◽  
Akira Fujimoto
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Computational Time ◽  
Computational Techniques ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Layer Characteristic ◽  
Comparison Of The Results ◽  
Steady Laminar

A new approximate method of calculating steady laminar boundary-layers is presented. This method is based on the mutual relationships between boundary-layer characteristic quantities. The governing equations are efficiently solved without assuming a specific velocity profile. Moreover, a method of estimating the velocity profile using the characteristic quantities is also proposed. Comparison of the results obtained for a wide variety of applications to boundary-layer flows with separations with exact solutions indicates that the present method enables one to obtain solutions with sufficient accuracy and shorter computational time when compared with existing computational techniques.

A Method for the Calculation of 3D Boundary Layers on Practical Wing Configurations

1981 ◽  
Vol 103 (1) ◽  
pp. 104-111 ◽  
Author(s):  
J. P. F. Lindhout ◽  
G. Moek ◽  
E. De Boer ◽  
B. Van Den Berg
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Eddy Viscosity ◽  
Separated Flow ◽  
Laminar Boundary Layers ◽  
Eddy Viscosity Model ◽  
Airplane Wing ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

This paper gives a description of a calculation method for 3D turbulent and laminar boundary layers on nondevelopable surfaces. A simple eddy viscosity model is incorporated in the method. Special attention is given to the organization of the computations to circumvent as much as possible stepsize limitations. The method is also able to proceed the computation around separated flow regions. The method has been applied to the laminar boundary layer flow over a flat plate with attached cylinder, and to a turbulent boundary layer flow over an airplane wing.

On the interaction between shock waves and boundary layers

1951 ◽  
Vol 47 (3) ◽  
pp. 545-553 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Reynolds Number ◽  
Shock Waves ◽  
Boundary Layers ◽  
Weak Shock ◽  
Boundary Layer Separation ◽  
Weak Shock Wave ◽  
Layer Separation ◽  
Boundary Layer Equations

AbstractThe effect on the boundary-layer equations of a weak shock wave of strength ∈ has been investigated, and it is shown that ifRis the Reynolds number of the boundary layer, separation occurs when ∈ =o(R−i). The boundary-layer assumptions are then investigated and shown to be consistent. It is inferred that separation will occur if a shock wave meets a boundary and the above condition is satisfied.

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