Numerical studies of the hypersonic strong interaction boundary-layer equations

AIAA Journal ◽  
1971 ◽  
Vol 9 (10) ◽  
pp. 2058-2060 ◽  
Author(s):  
M. J. WERLE ◽  
S. F. WORNOM
Keyword(s):  
Boundary Layer ◽  
Strong Interaction ◽  
Boundary Layer Equations ◽  
Numerical Studies

Viscous flow past a flat plate with uniform injection

1965 ◽  
Vol 284 (1398) ◽  
pp. 370-396 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Central Zone ◽  
Outer Zone ◽  
Analytic Study ◽  
Boundary Layer Equations ◽  
Numerical Studies ◽  
High Degree ◽  
Uniform Injection

The boundary-layer equations for an incompressible fluid in motion past a flat plate are examined, numerically and analytically, in the special case when the pressure gradient vanishes and there is a uniform injection of fluid from the plate. In the numerical study the principal properties of the boundary layer are computed as far as separation ( x ═ x δ ≑ 0.7456) with a high degree of accuracy. In the analytic study the structure of the singularity at separation is determined. It is of a new kind in boundary layer theory and its elucidation requires the division of the boundary layer into three zones—an outer zone in which the non-dimensional velocity u is much larger than x * (the non-dimensional distance from separation), a central zone in which u ~ x * and an inner zone in which u ≪ x *. A match is effected between solutions in the central and inner zones from which it is inferred that the skin friction τ 0 ~ ( x * / In (1/ x *) 2 as x * → 0. A completely satisfactory agreement between the numerical and analytic studies was not possible. The reason is that the analytic study is only valid when ln ( 1 / x *) ≫ 1 which means that for the analytic and numerical studies to have a common region of validity, the numerical integration must be extended to much smaller values of x * than is possible at present. It was also not possible to effect a match between the central and outer zones in the analytic solution due to the difficulty of finding the properties of the stress τ in the central zone as u / x * →∞.

Numerical studies of the laminar boundary layer for Mach numbers up to 15

1969 ◽  
Vol 36 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Henry A. Fitzhugh
Keyword(s):  
Boundary Layer ◽  
Skin Friction Coefficient ◽  
Order Effects ◽  
Approximate Methods ◽  
First Order ◽  
Boundary Layer Equations ◽  
Numerical Studies ◽  
Thickness Skin ◽  
Displacement Thickness ◽  
Exact Computer

A comprehensive set of exact solutions to the first-order boundary-layer equations has been computed using the finite difference computer programme of Sells, with and without wall cooling. The effects of Prandtl number, wall cooling and Mach number on separation point location were studied. Values of displacement thickness, skin friction coefficient and Stanton number are displayed graphically for the supersonic flow over a circular concave arc, for a subsonic cooled cylinder and for the case of a linearly retarded velocity distribution. The influence of pressure gradient on recovery factor was studied. Velocity and temperature profiles are shown for four cold wall cases. The exact computer results show the errors in many of the more approximate methods available for the case whereUe=U∞(1 -X/L). The importance of second-order effects and the applicability of a first-order solution are discussed briefly.

scholarly journals Boundary layer flow of air over water on a flat plate

1995 ◽  
Vol 284 ◽  
pp. 159-169 ◽  
Author(s):  
John J. Nelson ◽  
Amy E. Alving ◽  
Daniel D. Joseph
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Initial Conditions ◽  
Leading Edge ◽  
Water Layer ◽  
Large Reynolds Number ◽  
Boundary Layer Equations ◽  
Numerical Studies ◽  
Air Blowing ◽  
Layer Flow

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. We derive a simple non-similar analytic solution of the problem for which the interface height is proportional to x1/4 and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggest that this asymptotic non-similar air–water boundary layer solution is a global attractor for all initial conditions.

Numerical Studies on Behavior of Lorentz-Force-Applied Boundary Layer in Supersonic Flow

2009 ◽  
Vol 129 (6) ◽  
pp. 831-839
Author(s):  
Keisuke Udagawa ◽  
Sadatake Tomioka ◽  
Hiroyuki Yamasaki
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Lorentz Force ◽  
Numerical Studies

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

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