The Law of the Wake and Plane of Symmetry Flows in Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Vol 88 (1) ◽  
pp. 101-108 ◽  
Author(s):  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Three Dimensional Model ◽  
Law Of The Wall ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
The Law

Coles’ model incorporating the law of the wall and the law of the wake, proposed for two and three-dimensional turbulent boundary-layer flows, is examined for the special case of plane of symmetry flows in collateral and skewed three-dimensional boundary layers. Contrary to other published results, it is shown that the model is appropriate for adverse pressure gradient plane of symmetry flows in collateral environments away from separation. Additional, it appears that the departure from Coles’ law of the wake for recently reported three-dimensional flows is of the same basic form as that observed for plane of symmetry flows in transient development or two-dimensional flow with imminent separation. Since the Coles’ model, as most velocity profile models, is proposed only in an asymptotic sense for a well-developed flow, the fact that most of the three-dimensional flows heretofore reported are in transient or undeveloped states, suggests that the three-dimensional model be examined in well-developed three-dimensional boundary-layer flows before the question of the model’s validity can be properly answered.

Inviscid vortex motions in weakly three-dimensional boundary layers and their relation with instabilities in stratified shear flows

1993 ◽  
Vol 440 (1910) ◽  
pp. 701-710 ◽  
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Richardson Number ◽  
Shear Flows ◽  
Three Dimensional ◽  
Governing Equations ◽  
Boundary Layer Flows ◽  
Dimensional Boundary ◽  
Definition Of ◽  
Inviscid Instability

In this paper we consider the inviscid instability of three-dimensional boundary-layer flows with a small crossflow over locally concave or convex walls, along with the inviscid instability of stratified shear flows. We show how these two problems are closely related through the forms of their governing equations. A proposed definition of a generalized Richardson number for the neutrally stable inviscid vortex motions is given. Implications of the similarity between the two problems are discussed.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

Review: Laminar-to-Turbulent Transition of Three-Dimensional Boundary Layers on Rotating Bodies

1994 ◽  
Vol 116 (2) ◽  
pp. 200-211 ◽  
Author(s):  
Ryoji Kobayashi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Turbulent Transition ◽  
Centrifugal Instability ◽  
Crossflow Instability ◽  
Dimensional Boundary ◽  
Axisymmetric Bodies

The laminar-turbulent transition of three-dimensional boundary layers is critically reviewed for some typical axisymmetric bodies rotating in still fluid or in axial flow. The flow structures of the transition regions are visualized. The transition phenomena are driven by the compound of the Tollmien-Schlichting instability, the crossflow instability, and the centrifugal instability. Experimental evidence is provided relating the critical and transition Reynolds numbers, defined in terms of the local velocity and the boundary layer momentum thickness, to the local rotational speed ratio, defined as the ratio of the circumferential speed to the free-stream velocity at the outer edge of the boundary layer, for the rotating disk, the rotating cone, the rotating sphere and other rotating axisymmetric bodies. It is shown that the cross-sectional structure of spiral vortices appearing in the transition regions and the flow pattern of the following secondary instability in the case of the crossflow instability are clearly different than those in the case of the centrifugal instability.

Experimental Investigation of a Turbulent Boundary Layer Subjected to an Adverse Pressure Gradient

2011 ◽  
Author(s):  
Takanori Nakamura ◽  
Takatsugu Kameda ◽  
Shinsuke Mochizuki
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Friction Velocity ◽  
Adverse Pressure Gradient ◽  
Turbulent Intensity ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Velocity Scale ◽  
The Mean ◽  
The Law

Experiments were performed to investigate the effect of an adverse pressure gradient on the mean velocity and turbulent intensity profiles for an equilibrium boundary layer. The equilibrium boundary layer, which makes self-similar profiles, was constructed using a power law distribution of free stream velocity. The exponent of the law was adjusted to −0.188. The wall shear stress was measured with a drag balance by a floating element. The investigation of the law of the wall and the similarity of the streamwise turbulent intensity profile was made using both a friction velocity and new proposed velocity scale. The velocity scale is derived from the boundary layer equation. The mean velocity gradient profile normalized with the height and the new velocity scale exists the region where the value is almost constant. The turbulent intensity profiles normalized with the friction velocity strongly depend on the nondimensional pressure gradient near the wall. However, by mean of the local velocity scale, the profiles might be achieved to be similar with that of a zero pressure gradient.

scholarly journals Numerical Investigation of Boundary Layers in Wet Steam Nozzles

2016 ◽  
Author(s):  
Jörg Starzmann ◽  
Fiona R. Hughes ◽  
Alexander J. White ◽  
Marius Grübel ◽  
Damian M. Vogt
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Side Wall ◽  
Turbulence Models ◽  
Test Case ◽  
Wet Steam ◽  
Compression Waves ◽  
Wall Boundary Layer ◽  
Two Dimensional Flow

Condensing nozzle flows have been used extensively to validate wet steam models. Many test cases are available in the literature and in the past a range of numerical studies have dealt with this challenging task. It is usually assumed that the nozzles provide a one- or two-dimensional flow with a fully turbulent boundary layer. The present paper reviews these assumptions and investigates numerically the influence of boundary layers on dry and wet steam nozzle expansions. For the narrow nozzle of Moses and Stein it is shown that the pressure distribution is significantly affected by the additional blockage due to the side wall boundary layer. Comparison of laminar and turbulent flow predictions for this nozzles suggests that laminar-turbulent transition only occurs after the throat. Other examples are the Binnie nozzle and the Moore nozzles for which it is known that sudden changes in wall curvature produce expansion and compression waves that interact with the boundary layers. The differences between two- and three-dimensional calculations for these cases and the influence of laminar and turbulent boundary layers are discussed. The present results reveal that boundary layer effects can have a considerable impact on the mean nozzle flow and thus on the validation process of condensation models. In order to verify the accuracy of turbulence modelling a test case that is not widely known internationally is included within the present study. This experimental work is remarkable because it includes boundary layer data as well as the usual pressure measurements along the nozzle centreline. Predicted and measured boundary layer profiles are compared and the effect of different turbulence models is discussed. Most of the numerical results are obtained with the in-house wet steam RANS-solver, Steamblock, but for the purpose of comparison the commercial program ANSYS CFX is also used, providing a wider range of standard RANS-based turbulence models.

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