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.

The boundary layer in a shock tube

1972 ◽  
Vol 56 (1) ◽  
pp. 19-47 ◽  
Author(s):  
J. D. A. Walker And ◽  
S. C. R. Dennis
Keyword(s):  
Boundary Layer ◽  
Thermal Properties ◽  
Shock Tube ◽  
Constant Temperature ◽  
Tube Wall ◽  
Initial Pressure ◽  
Compressible Boundary Layer ◽  
Boundary Layer Equations ◽  
Expansion Waves ◽  
Medium Strength

The boundary layer that forms on the walls of a shock tube, after the diaphragm which initially separates two gases at different pressures is burst, is investigated. Both the driver and driven gases are assumed to have the same thermal properties and the shock tube wall is maintained at constant temperature. Crocco variables are used and a method is presented for solving the compressible boundary-layer equations within the tube in similarity variables. Three cases, corresponding to different initial pressure ratios of the driver and driven gases, are calculated which are representative of weak and medium-strength shock and expansion waves.

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.

Second-order effects in free convection

1974 ◽  
Vol 62 (4) ◽  
pp. 793-809 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Equations Of State ◽  
Asymptotic Series ◽  
Inviscid Flow ◽  
Second Order ◽  
The Body ◽  
Order Effects ◽  
Boundary Layer Equations ◽  
Second Order Effects

The equations of conservation of momentum, energy and mass together with the equations of state are examined for free convection from a vertical paraboloid. A transformation due to Saville & Churchill is applied to the first- and second-order boundary-layer equations, which are then solved using series about the stagnation point, using asymptotic series far up the body and in between by a method due to Merk. The second-order outer inviscid flow is given in terms of infinite integrals as a solution of Laplace's equation in paraboloidal co-ordinates.Eight second-order effects are distinguished, depending on longitudinal and transverse curvatures, the displacement flow, heat flux into the boundary layer and the variation of density, viscosity, thermometric conductivity and the coefficient of expansion with temperature. Expressions for the skin friction, heat-transfer coefficient and various flux thicknesses are obtained and a comparison of the second-order effects is made.

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

1990 ◽  
Author(s):  
H. M. Jang ◽  
M. F. Platzer ◽  
J. A. Ekaterinaris ◽  
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 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 modelled properly.

On the laminar compressible boundary layer induced by the passage of a plane shock wave over a flat wall

1967 ◽  
Vol 63 (3) ◽  
pp. 889-907 ◽  
Author(s):  
J. A. D. Ackroyd
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Prandtl Number ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
Compressible Boundary Layer ◽  
Empirical Relationships ◽  
Flat Wall ◽  
Boundary Layer Equations ◽  
Semi Empirical

SummaryThe laminar compressible boundary layer induced by the passage of a plane shock wave over a flat wall is examined in detail. Use is made of the empirical viscosity-temperature relationship μ ∝ Tω. The boundary-layer equations are solved numerically for various values of the index ω, Prandtl number and shock strengths. The resulting solutions are then used to construct simple semi-empirical relationships for some of the more important boundary-layer parameters.

Computation of a Wall Boundary Layer With Discrete Jet Injections

1992 ◽  
Vol 114 (4) ◽  
pp. 756-764 ◽  
Author(s):  
P. Kulisa ◽  
F. Leboeuf ◽  
G. Perrin
Keyword(s):  
Boundary Layer ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Conservation Equations ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Jet Interactions

Cooling of turbine blades is often achieved with cold discrete jets introduced at the wall. In this paper, a new method for computation of a wall boundary layer with discrete jet interactions is presented. The jets are assumed to be arranged in rows and the flow is assumed locally periodic in the row direction. The conservation equations are spatially averaged between two jet orifices. The resulting equations look like two-dimensional boundary layer equations, but with three-dimensional jet source terms. The numerical method solves the boundary layer equations with a Keller box method. A strong interaction with inviscid flow is also introduced in order to avoid numerical difficulty in the jet region. Three-dimensional jet conservation equations are solved with an integral method, under the boundary layer influence. A coupling of the two methods is performed. Comparisons with low-speed experimental data are presented, particularly near the jet orifices. It is shown that the agreement between the results of computation and the experiments depends on the jet behavior very near the jet exit.

scholarly journals Finite-volume solution of the compressible boundary-layer equations

AIAA Journal ◽  
1987 ◽  
Vol 25 (4) ◽  
pp. 525-526
Author(s):  
Bernard Loyd ◽  
Earll M. Murman
Keyword(s):  
Boundary Layer ◽  
Finite Volume ◽  
Compressible Boundary Layer ◽  
Boundary Layer Equations
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