On Integral Methods for Predicting Shear Layer Behavior

1969 ◽  
Vol 36 (4) ◽  
pp. 673-681 ◽  
Author(s):  
S. J. Shamroth
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Integral Equations ◽  
Boundary Layers ◽  
Specific Problem ◽  
Shear Layers ◽  
Near Wake ◽  
Integral Methods ◽  
Layer Behavior ◽  
Momentum Integral

The origin and consequences of a nonphysical constraint which may arise when boundary-layer momentum integral equations are used to predict the behavior of shear layers are examined. It is pointed out that should the constraint occur within the domain of integration of the momentum integral equations, the effect may either be catastrophic or significantly constrain the solution. Several methods of solution having the usual advantages associated with boundary-layer momentum integral equations, but free from this constraint, are proposed for the specific problem of the plane turbulent near wake. One method developed to avoid this constraint in the case of a plane turbulent near wake appears to be perfectly general, and therefore, it may be possible to apply this method to both boundary layers and wakes.

Calculation of Three-Dimensional Boundary Layers on Rotor Blades Using Integral Methods

1993 ◽  
Vol 115 (2) ◽  
pp. 342-353 ◽  
Author(s):  
M. T. Karimipanah ◽  
E. Olsson
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Rotor Blades ◽  
Rotating Flow ◽  
Momentum Thickness ◽  
Transonic Compressor ◽  
Integral Methods ◽  
Momentum Integral

The important effects of rotation and compressibility on rotor blade boundary layers are theoretically investigated. The calculations are based on the momentum integral method and results from calculations of a transonic compressor rotor are presented. Influence of rotation is shown by comparing the incompressible rotating flow with the stationary one. Influence of compressibility is shown by comparing the compressible rotating flow with the incompressible rotating one. Two computer codes for three-dimensional laminar and turbulent boundary layers, originally developed by SSPA Maritime Consulting AB, have been further developed by introducing rotation and compressibility terms into the boundary layer equations. The effect of rotation and compressibility on the transition have been studied. The Coriolis and centrifugal forces that contribute to the development of the boundary layers and influence its behavior generate crosswise flow inside the blade boundary layers, the magnitude of which depends upon the angular velocity of the rotor and the rotor geometry. The calculations show the influence of rotation and compressibility on the boundary layer parameters. Momentum thickness and shape factor increase with increasing rotation and decrease when compressible flow is taken into account. For skin friction such effects have inverse influences. The different boundary layer parameters behave similarly on the suction and pressure sides with the exception of the crossflow angle, the crosswise momentum thickness, and the skin friction factor. The codes use a nearly orthogonal streamline coordinate system, which is fixed to the blade surface and rotates with the blade.

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.

Wall Boundary Layers in Turbomachines

1972 ◽  
Vol 14 (6) ◽  
pp. 411-423 ◽  
Author(s):  
H. Marsh ◽  
J. H. Horlock
Keyword(s):  
Boundary Layer ◽  
Integral Equations ◽  
Cross Flow ◽  
Inlet Guide Vanes ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Alternative Approach ◽  
Flow Through ◽  
The Many ◽  
Momentum Integral

Equations for the passage-averaged flow in a cascade are used to derive the momentum integral equations governing the development of the wall boundary layer in turbomachines. Several existing methods of analysis are discussed and an alternative approach is given which is based on the passage-averaged momentum integral equations. The analysis leads to an anomaly in the prediction of the cross flow and to avoid this it is suggested that for the many-bladed cascade there should be a variation of the blade force through the boundary layer. This variation of the blade force can be included in the analysis as a force deficit integral. The growth of the wall boundary layer has been calculated by four methods and the predictions are compared with two sets of published experimental results for flow through inlet guide vanes.

The Isobars in Boundary Layers at Supersonic Speeds

1968 ◽  
Vol 19 (2) ◽  
pp. 105-126 ◽  
Author(s):  
D. F. Myring ◽  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Equations Of Motion ◽  
Normal Pressure ◽  
Simple Extension ◽  
Pressure Gradients ◽  
Boundary Layer Flows ◽  
Hyperbolic Flow ◽  
The Individual ◽  
Momentum Integral

SummaryFor boundary layer flows over curved surfaces at moderately high supersonic speeds the existence of normal pressure gradients within the boundary layer becomes important even for small curvatures and they cannot be ignored. The describing equations are basically parabolic in form so that the simplifications inherent in hyperbolic flows would not at first sight seem to be relevant. However, the equations of motion for a two-dimensional, supersonic, rotational, viscous flow are analysed along the lines of a hyperbolic flow and the individual effects of viscosity and vorticity are examined with regard to the isobar distributions. It is found that these two properties have compensating effects and the experimental evidence presented confirms the conclusion that inside the boundary layer the isobars follow much the same rules as those which determine the isobars in the external hyperbolic flow. Since for turbulent boundary layers the fullness of the Mach number profile produces almost linear Mach lines in the boundary layer, this provides a simple extension to the methods of analysis, and the momentum integral equation is reformulated using a swept element bounded by linear isobars. The final equation is similar in form to the conventional one except that the momentum and displacement thicknesses are now defined by integrals along the swept isobars, and all normal pressure gradients due to centrifugal effects are accounted for.

Smooth and Rough Turbulent Boundary Layers: A Look at Skin Friction, Pressure Gradient and Roughness

2006 ◽  
Author(s):  
Katherine A. Newhall ◽  
Raul Bayoan Cal ◽  
Brian Brzek ◽  
Gunnar Johansson ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Rough Surfaces ◽  
Boundary Layer Equation ◽  
Roughness Parameter ◽  
Surface Boundary ◽  
Favorable Pressure Gradient ◽  
Momentum Integral

The skin friction for a turbulent boundary layer can be measured and calculated in several ways with varying degrees of accuracy. In particular, the methods of the velocity gradient at the wall, the integrated boundary layer equation and the momentum integral equation are evaluated for both smooth and rough surface boundary layers. These methods are compared to the oil film interferometry technique measurements for the case of smooth surface flows. The integrated boundary layer equation is found to be relatively reliable, and the values computed with this technique are used to investigate the effect of increasing external favorable pressure gradient for both smooth and rough surfaces, and increasing roughness parameter for the rough surfaces.

Momentum integral methods for the laminar free shear layer

AIAA Journal ◽  
1964 ◽  
Vol 2 (4) ◽  
pp. 625-629 ◽  
Author(s):  
TOSHI KUBOTA ◽  
C. FORBES DEWEY
Keyword(s):  
Shear Layer ◽  
Free Shear Layer ◽  
Integral Methods ◽  
Momentum Integral

Turbulent Boundary Layer Flow on the End Wall of a Cylindrical Vortex Chamber

1975 ◽  
Vol 189 (1) ◽  
pp. 305-315 ◽  
Author(s):  
T. J. Kotas
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Vortex Chamber ◽  
Cylindrical Vortex ◽  
Layer Flow ◽  
Momentum Integral ◽  
End Wall

A presentation of some measurements of velocities in the turbulent boundary layer on the end wall of a vortex chamber. These show that the boundary layer flow is three-dimensional with large inward radial velocities. Consequently, most of the fluid entering the vortex chamber passes into the central region through the boundary layers on the end walls rather than the main space of the vortex chamber. A momentum integral solution is used to obtain an estimate of the radial flow through the end-wall boundary layers. A comparison of the theoretical curves with the experimental results gives support to the main assumptions used in the solutions.

Boundary Layers With Viscous Potential Outer Flows

Volume 1 ◽  
2004 ◽  
Author(s):  
Alireza Najafiyazdi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Additional Term ◽  
Reynolds Numbers ◽  
Momentum Equation ◽  
Outer Flow ◽  
Bernoulli’S Equation ◽  
Momentum Integral

In this paper we try to derive improved formulations for laminar boundary layers in incompressible flows by using the concept of viscous potential flows, presented in Joseph [1] and Joseph [2], as the outer flow. Bernoulli’s equation is used at the edge of boundary layer to make the basic assumption to deduce the presented formulas. The momentum equation is derived directly from the Navier-Stokes equations and then simplified using an order of magnitude analyze. However an additional term, μ∂2u∞∂x2, remains in the momentum equation to represent the contribution of the viscosity of the outer potential flow at the edge of the boundary layer. The viscosity of the outer viscous flow shows itself also in momentum-integral and energy-integral equations. Numerical results showed that at high Reynolds numbers and low angles of attack the results of the two formulas are almost the same, but for lower Reynolds numbers and higher angles of attack the difference between the results is remarkable.

Momentum Integral for Curved Shear Layers

1975 ◽  
Vol 97 (2) ◽  
pp. 253-256 ◽  
Author(s):  
Ronald M. C. So
Keyword(s):  
Boundary Layer ◽  
Shear Layers ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Displacement Effect ◽  
Curved Boundary ◽  
Curvature Effects ◽  
Von Karman ◽  
Momentum Integral ◽  
Von Kármán

If the exact metric influence of curvature is retained and the displacement effect neglected, it can be shown that the momentum integral for two-dimensional, curved boundary-layer flows is identical to the von Karman momentum integral. As a result, attempts by previous researchers to account for longitudinal curvature effects by adding more terms to the momentum integral are shown to be correct.

Sign in / Sign up

Export Citation Format

Share Document