The Interaction of Thermal Radiation in Optically Thick Boundary Layers

1967 ◽  
Vol 89 (4) ◽  
pp. 309-312 ◽  
Author(s):  
J. L. Novotny ◽  
Kwang-Tzu Yang
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Optical Thickness ◽  
Asymptotic Expansions ◽  
Energy Equation ◽  
Two Dimensional ◽  
Small Temperature ◽  
Dimensional Boundary

An analysis is presented to examine the role of the Rosseland or optically thick approximation in convection-radiation interaction situations. The analysis is formulated for the flow of a gray gas in a laminar two-dimensional boundary layer under the restriction of small temperature differences within the flow field. The boundary-layer energy equation is treated using the method of matched asymptotic expansions based on a parameter which characterizes the optical thickness of the gas. Two illustrative examples of the resulting equations are presented.

scholarly journals The equilibria of vesicles adhered to substrates by short-ranged potentials

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120729 ◽  
Author(s):  
Maurice J. Blount ◽  
Michael J. Miksis ◽  
Stephen H. Davis
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Layer Structure ◽  
Two Dimensional ◽  
Adhesive Interaction ◽  
Contact Potential ◽  
Layer Structures ◽  
Bending Stresses ◽  
Dimensional Boundary ◽  
Horizontal Substrate

In equilibrium, a vesicle that is adhered to a horizontal substrate by a long-range attractive, short-range repulsive force traps a thin layer of fluid beneath it. In the asymptotic limit that this layer is very thin, there are quasi-two-dimensional boundary-layer structures near the edges of the vesicle, where the membrane's shape is governed by a balance between bending and adhesive stresses. These boundary layers are analysed to obtain corrections to simpler models that instead represent the adhesive interaction by a contact potential, thereby resolving apparent discontinuities that arise when such models are used. Composite expansions of the shapes of two-dimensional vesicles are derived. When, in addition, the adhesive interaction is very strong, there is a nested boundary-layer structure for which the adhesive boundary layers match towards sharp corners where bending stresses remain important but adhesive stresses are negligible. Outside these corners, bending stresses are negligible and the vesicle's shape is given approximately by the arc of a circle. Simple composite expansions of the vesicle's shape are derived that account for the shape of the membrane inside these corners.

Triple-deck solutions for supersonic flows past flared cylinders

1987 ◽  
Vol 179 ◽  
pp. 469-487 ◽  
Author(s):  
Ph. Gittler ◽  
A. Kluwick
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Asymptotic Expansions ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Hysteresis Phenomenon ◽  
Two Dimensional ◽  
Planar Flow ◽  
Laminar Boundary Layers ◽  
External Flows

Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and supersonic external flows is investigated in the limit of large Reynolds numbers. Numerical solutions to the interaction equations are presented for flare angles α that are moderately large. If α > 0 the boundary layer separates upstream of the corner and the formation of a plateau structure similar to the two-dimensional case is observed. In contrast to the case of planar flow, however, separation can occur also if α < 0, owing to the axisymmetric effect of overexpansion and recompression. The separation point then is located downstream of the corner and, most remarkable, a hysteresis phenomenon is observed.

The spanwise perturbation of two-dimensional boundary layers

1966 ◽  
Vol 24 (1) ◽  
pp. 153-164 ◽  
Author(s):  
S. C. Crow
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Wind Tunnels ◽  
Two Dimensional ◽  
Surface Shear ◽  
Flow Reynolds Number ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Small Periodic

Large spanwise variations of boundary-layer thickness and surface shear have been found recently in wind tunnels designed to maintain two-dimensional flow. Bradshaw (1965) argues that these variations are caused by minute deflexions in the free-stream flow rather than by any intrinsic instability of the boundary layers. This paper is a study of the effect of a small, periodic transverse flow on a flat-plate boundary layer. The perturbation flow Reynolds number is assumed to be O(1) as it is in the experiments.

Effect of longitudinal surface curvature on boundary layers

1967 ◽  
Vol 29 (1) ◽  
pp. 187-199 ◽  
Author(s):  
Roddam Narasimha ◽  
S. K. Ojha
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Asymptotic Expansions ◽  
Order Effect ◽  
Similarity Solutions ◽  
Surface Curvature ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Boundary Layers ◽  
Critical Comparison

We consider here the higher order effect of moderate longitudinal surface curvature on steady, two-dimensional, incompressible laminar boundary layers. The basic partial differential equations for the problem, derived by the method of matched asymptotic expansions, are found to possess similarity solutions for a family of surface curvatures and pressure gradients. The similarity equations obtained by this anaylsis have been solved numerically on a computer, and show a definite decrease in skin friction when the surface has convex curvature in all cases including zero pressure gradient. Typical velocity profiles and some relevant boundary-layer characteristics are tabulated, and a critical comparison with previous work is given.

Equilibrium turbulent boundary layers with lateral streamline convergence or divergence

2009 ◽  
Vol 623 ◽  
pp. 273-282 ◽  
Author(s):  
T. B. NICKELS
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Convergence And Divergence ◽  
Necessary Constraints

The constraints necessary for equilibrium solutions of the boundary layer equations are explored for turbulent boundary layers subject to lateral convergence and divergence and with longitudinal pressure gradients. It is shown that in addition to the well-known equilibrium solutions for two-dimensional boundary layers there are additionalpossibleequilibrium states for boundary layers with these extra rates-of-strain acting. The necessary constraints for equilibrium are derived and discussed.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

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.

Review: Laminar-to-Turbulent Transition of Three-Dimensional Boundary Layers on Rotating Bodies

1994 ◽  
Vol 116 (2) ◽  
pp. 200-211 ◽  
Author(s):  
Ryoji Kobayashi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Turbulent Transition ◽  
Centrifugal Instability ◽  
Crossflow Instability ◽  
Dimensional Boundary ◽  
Axisymmetric Bodies

The laminar-turbulent transition of three-dimensional boundary layers is critically reviewed for some typical axisymmetric bodies rotating in still fluid or in axial flow. The flow structures of the transition regions are visualized. The transition phenomena are driven by the compound of the Tollmien-Schlichting instability, the crossflow instability, and the centrifugal instability. Experimental evidence is provided relating the critical and transition Reynolds numbers, defined in terms of the local velocity and the boundary layer momentum thickness, to the local rotational speed ratio, defined as the ratio of the circumferential speed to the free-stream velocity at the outer edge of the boundary layer, for the rotating disk, the rotating cone, the rotating sphere and other rotating axisymmetric bodies. It is shown that the cross-sectional structure of spiral vortices appearing in the transition regions and the flow pattern of the following secondary instability in the case of the crossflow instability are clearly different than those in the case of the centrifugal instability.

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