Approximate Calculations Using Integral Boundary Layer Equations

2010 ◽  
pp. 59-85
Keyword(s):  
Boundary Layer ◽  
Integral Boundary ◽  
Boundary Layer Equations

Development and assessment of computer methods for three-dimensional turbulent boundary layers

1999 ◽  
Vol 103 (1024) ◽  
pp. 287-297
Author(s):  
J. Wu ◽  
U. R. Müller
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Theoretical Data ◽  
Field Method ◽  
Curvilinear Coordinates ◽  
Integral Boundary ◽  
Boundary Layer Equations ◽  
Computer Methods

Abstract This paper describes the development of a finite difference method that solves the boundary-layer equations for three-dimensional compressible turbulent flows. The most prominent achievements are the employment of a Newton technique for the simultaneous solution of all governing equations, an option to choose an algebraic or a k-ε eddy-viscosity turbulence model, and the flexible use of curvilinear coordinates. The method is validated by comparisons with a number of experimental and theoretical data sets of three-dimensional, compressible and incompressible, steady and unsteady boundary layers. In parallel, the performance of a three-dimensional compressible industrial integral boundary-layer technique is evaluated by comparisons with experimental test cases and with the results of the field method.

Study of the Boundary Layer on Ship Forms

1970 ◽  
Vol 14 (03) ◽  
pp. 153-167
Author(s):  
W. C. Webster ◽  
T.T. Huang
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Three Dimensional ◽  
Momentum Thickness ◽  
Flow Conditions ◽  
Integral Boundary ◽  
Outer Flow ◽  
Boundary Layer Equations ◽  
Pressure Distributions ◽  
Layer Flow

This paper presents a theoretical investigation of the development of the boundary layer about a ship. The "outer flow" conditions, including the streamlines and pressure distributions, are found from linearized, thin-ship theory using the method of Guilloton. Linearized, integral boundary-layer equations appropriate for three-dimensional turbulent flow are integrated numerically along the streamlines to determine the momentum thickness, the shape factor, and the angle of the boundary-layer flow to the outer flow. The results of computations for Series 60, block 0.60 and 0.80 are presented for various Froude numbers and ship lengths.

Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 1—Description of the Method

1993 ◽  
Vol 115 (1) ◽  
pp. 94-100 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Boundary Layer ◽  
Numerical Test ◽  
Unsteady Flows ◽  
Boundary Layer Separation ◽  
Displacement Effect ◽  
Integral Boundary ◽  
Time Resolved ◽  
Boundary Layer Equations ◽  
Momentum Integral ◽  
Viscous Solutions

An efficient coupled approach between inviscid Euler and integral boundary layer solutions has been developed for quasi-3-D unsteady flows induced by vibrating blades. For unsteady laminar and turbulent boundary layers, steady correlations are adopted in a quasi-steady way to close the integral boundary layer model. This quasi-steady adoption of the correlations is assessed by numerical test results using a direct solution of the unsteady momentum integral equation. To conduct the coupling between the inviscid and viscous solutions for strongly interactive flows, the unsteady Euler and integral boundary layer equations are simultaneously time-marched using a multistep Runge–Kutta scheme, and the boundary layer displacement effect is accounted for by a first order transpiration model. This time-resolved coupling method converges at conditions with considerable boundary layer separation.

An Analytical Study of Laminar Film Condensation: Part 1—Flat Plates

1961 ◽  
Vol 83 (1) ◽  
pp. 48-54 ◽  
Author(s):  
Michael Ming Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Velocity Gradient ◽  
Film Condensation ◽  
Transfer Coefficients ◽  
Flat Plates ◽  
Integral Boundary ◽  
Boundary Layer Equations ◽  
Laminar Film ◽  
Laminar Film Condensation

The boundary-layer equations of momentum and energy are written in a modified integral form and solved for the case of laminar film condensation along a vertical flat plate. The analysis differs from previous works by employing the more realistic boundary condition of stationary vapor at large distances instead of zero velocity gradient at the interface. Solutions for both the liquid film and vapor boundary layer are given for the case μvρv ≪ μρ. Velocity and temperature profiles are obtained using perturbation method and the modified integral boundary-layer equations. The results show a significant negative velocity gradient at the interface as a result of vapor drag except for small values of kΔt/μλ. Theoretical heat-transfer coefficients are computed and found to be lower than previous theories, especially for low Prandtl numbers. Comparison with experimental heat-transfer data is given. The heat-transfer results are also presented in the form of an approximate formula for ease of application.

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