Boundary-layer theory for blast waves

1975 ◽  
Vol 71 (1) ◽  
pp. 65-88 ◽  
Author(s):  
K. B. Kim ◽  
S. A. Berger ◽  
M. M. Kamel ◽  
V. P. Korobeinikov ◽  
A. K. Oppenheim
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flow Field ◽  
Classical Problem ◽  
Outer Region ◽  
Inviscid Flow ◽  
Boundary Layer Theory ◽  
Blast Waves ◽  
Matched Asymptotic Expansion ◽  
Flow Equations

The necessity for developing a boundary-layer theory in the case of blast waves stems from the fact that inviscid flow solutions often yield physically unrealistic results. For example, in the classical problem of the so-called non-zero counterpressure explosion, one obtains infinite temperature and zero density in the centre at all times even after the shock front deteriorates into a sound wave. In reality, this does not occur, as a consequence, primarily, of heat transfer that modifies the structure of the flow field around the centre without drastically affecting the outer region. It is profitable, therefore, to consider the blast wave as a flow field consisting of two regions: the outer, which retains the properties of the inviscid solution, and the inner, which is governed by flow equations including terms expressing the effects of heat transfer and, concomitantly, viscosity. The latter region thus plays the role of a boundary layer. Reported here is an analytical method developed for the study of such layers, based on the matched asymptotic expansion technique combined with patched solutions.

A theory of circulation control by slot-blowing, applied to a circular cylinder

1968 ◽  
Vol 33 (3) ◽  
pp. 495-514 ◽  
Author(s):  
J. Dunham
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Flow Field ◽  
Lift Force ◽  
Air Flow ◽  
Inviscid Flow ◽  
Boundary Layer Theory ◽  
Experimental Results ◽  
Circulation Control ◽  
Narrow Slot

Lift can be generated on a circular cylinder with its axis normal to an air flow by blowing a sheet of air tangentially round the upper surface from a narrow slot or slots. This lift force may be estimated by matching the external inviscid flow field with separation points calculated by Spalding's unified boundary-layer theory. The theory reproduces experimental results reasonably well, except in certain special conditions fully discussed.

Supersonic viscous flow over cones at large angles of attack

1976 ◽  
Vol 74 (3) ◽  
pp. 561-591 ◽  
Author(s):  
Clive A. J. Fletcher ◽  
Maurice Holt
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Wall Temperature ◽  
Numerical Solutions ◽  
Cone Angle ◽  
Inviscid Flow ◽  
The Body ◽  
Thickness Effect ◽  
Flow Equations ◽  
Displacement Thickness

Numerical solutions for the flow field about cones with nose angles of up to 30° at angles of attack up to 50° for a range of Reynolds numbers and wall temperature ratios are presented. The solutions obtained permit interaction between the inviscid region and the boundary layer on the body through the displacement-thickness effect. The solutions are valid throughout the flow field except in the region adjacent to the leeward line of symmetry. Comparisons are made with experimental results and other numerical solutions. Detailed flow structure and the variation of surface conditions with cone angle, incidence, Reynolds number and wall temperature are indicated. The numerical methods used for the inviscid flow equations are Telenin's method and the method of characteristics, while a modified form of the method of integral relations is applied to the boundary-layer equations.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

Compressible Boundary Layer-Inviscid Flow Interactions in Entrance Region of Internal Flows

1967 ◽  
Vol 89 (4) ◽  
pp. 281-288 ◽  
Author(s):  
V. D. Blankenship ◽  
P. M. Chung
Keyword(s):  
Boundary Layer ◽  
Shock Tube ◽  
Inviscid Flow ◽  
Perturbation Parameter ◽  
Entrance Region ◽  
Compressible Boundary Layer ◽  
Internal Flows ◽  
Flow Equations ◽  
Boundary Layer Equations ◽  
Interaction Problem

The coupling between the inviscid flow and the compressible boundary layer in the developing entrance region for internal flows is analyzed by solving the particular inviscid flow-boundary layer interaction problem. The interaction problem is solved by postulating certain series forms of solutions for the inviscid region and the boundary layer. The boundary-layer equations and inviscid-flow equations are perturbed to third order and each generated equation is solved numerically. In order to preserve the universality of each of the perturbed boundary-layer equations, the perturbation parameter is described by an integral equation which is also solved in series form. The final results describing the interaction problem are then constructed for any given conditions by forming the three series to a consistent order of magnitude. This technique of coordinate perturbation is generalized to show how it may be applied to the entrance regions of pipe flows, including mass injection or suction, and also to the laminar boundary layers in shock tube flows. It demonstrates analytically the manner in which the boundary layer and inviscid flow interact and create a streamwise pressure gradient. In particular, the interaction problem which occurs in shock tube flows is solved in detail by the use of this generalized method, as an example.

A numerical investigation of the Stokes boundary layer in the turbulent regime

2007 ◽  
Vol 570 ◽  
pp. 253-296 ◽  
Author(s):  
S. SALON ◽  
V. ARMENIO ◽  
A. CRISE
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Time Scale ◽  
Mixed Model ◽  
Experimental Studies ◽  
Outer Region ◽  
Transition To Turbulence ◽  
Turbulent Regime ◽  
Turbulent Statistics ◽  
Acceleration And Deceleration

The Stokes boundary layer in the turbulent regime is investigated by using large-eddy simulations (LES). The Reynolds number, based on the thickness of the Stokes boundary layer, is set equal to Reδ = 1790, which corresponds to test 8 of the experimental study of Jensen et al. (J. Fluid Mech. vol. 206, 1989, p. 265).Our results corroborate and extend the findings of relevant experimental studies: the alternating phases of acceleration and deceleration are correctly reproduced, as is the sharp transition to turbulence, observable at a phase angle between 30° and 45°, and its maximum between 90° and 105°. Overall, a very good agreement was found between our LES first- and second-order turbulent statistics and those of Jensen et al. (1989). Some discrepancies were observed when comparing turbulent intensities in the phases of the cycle characterized by a low level of turbulent activity.In the central part of the cycle, namely from the mid acceleration to the late deceleration phases, fully developed equilibrium turbulence is present in the flow field, and the boundary layer resembles that of a canonical, steady, wall-bounded flow. In those phases characterized by low turbulent activity, two separate regions can be detected in the flow field: a near-wall one, where the vertical turbulent kinetic energy varies much more rapidly than the other two components, thus giving rise to the formation of horizontal, pancake-like turbulence; and an outer region where both vertical and spanwise velocity fluctuations vary much faster than the streamwise ones, hence producing cigar-like turbulence.As a side result, the range of application of the plane-averaged dynamic mixed model was assessed based on the qualitative behaviour over the cycle of a significant parameter representing the ratio between a turbulent time scale and a free-stream time scale associated with the oscillatory motion.

Spreadsheets Solutions of the Boundary Layer Equations

2004 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Mechanics ◽  
Undergraduate Students ◽  
Classical Problem ◽  
Boundary Layer Equations ◽  
Specialized Software ◽  
Layer Flow ◽  
Basic Course ◽  
The Impact

A classical problem in fluid mechanics and heat transfer is boundary layer flow over a flat plate. This problem is used to demonstrate a number of important concepts in fluid mechanics and heat transfer. Typically, in a basic course, the equations are derived and the solutions are presented in tabular or chart from. Obtaining the actual solutions is mathematically and numerically too involved to be covered in basic courses. In this paper, it is shown that the similarity solution and the solution to boundary layer equations in the primitive variables can easily be obtained using spreadsheets. Without needing much programming skills, or needing to learn specialized software, undergraduate students can use this approach and obtain the solution and study the impact of different parameters.

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