Three-dimensional boundary layers with short spanwise scales

2014 ◽  
Vol 756 ◽  
pp. 452-469 ◽  
Author(s):  
Richard E. Hewitt ◽  
Peter W. Duck
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Boundary Layers ◽  
Line Source ◽  
Flow Direction ◽  
Three Dimensional ◽  
Computational Procedure ◽  
External Flow ◽  
Short Scale ◽  
Source Sink

AbstractWe investigate three-dimensional (laminar) boundary layers that include a spanwise scale comparable to the boundary-layer thickness. A forcing of short spanwise scales requires viscous dissipation to be retained in the two-dimensional cross-section, perpendicular to the external flow direction, and in this respect the flows are related to previous work on corner boundary layers. We use two examples to highlight the main features of this category of boundary layer: (i) a flat plate of narrow (spanwise) width, and (ii) a narrow (spanwise) gap cut into an otherwise infinite flat plate; in both cases the plate is aligned with a uniform oncoming stream. We find that a novel feature arises in connection with the external flow; the presence of a narrow gap/plate (or indeed any comparable short-scale feature of long streamwise extent) necessarily modifies the streamwise mass flux in that vicinity, which in turn induces an associated boundary-layer transpiration on the same short spanwise length scale. This (short-scale) transpiration region leads to a half-line-source/sink correction to the outer inviscid, irrotational flow. Crucially, the volumetric flux associated with this line-source/sink must be explicitly included as part of the computational procedure for the leading-order boundary layer, and as such there is a weak interaction between the outer (inviscid) flow and the boundary layer. This is a generic feature of boundary layers that are forced through the presence of short-scale spanwise variations.

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.

scholarly journals Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances

1992 ◽  
Vol 242 ◽  
pp. 701-720 ◽  
Author(s):  
M. Tadjfar ◽  
R. J. Bodonyi
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Stokes Flow ◽  
Free Stream ◽  
Flow Direction ◽  
Roughness Element ◽  
Three Dimensional ◽  
Unsteady Motion ◽  
Time Harmonic ◽  
Tollmien Schlichting

Receptivity of a laminar boundary layer to the interaction of time-harmonic free-stream disturbances with a three-dimensional roughness element is studied. The three-dimensional nonlinear triple–deck equations are solved numerically to provide the basic steady-state motion. At high Reynolds numbers, the governing equations for the unsteady motion are the unsteady linearized three-dimensional triple-deck equations. These equations can only be solved numerically. In the absence of any roughness element, the free-stream disturbances, to the first order, produce the classical Stokes flow, in the thin Stokes layer near the wall (on the order of our lower deck). However, with the introduction of a small three-dimensional roughness element, the interaction between the hump and the Stokes flow introduces a spectrum of all spatial disturbances inside the boundary layer. For supercritical values of the scaled Strouhal number, S0 > 2, these Tollmien–Schlichting waves are amplified in a wedge-shaped region, 15° to 18° to the basic-flow direction, extending downstream of the hump. The amplification rate approaches a value slightly higher than that of two-dimensional Tollmien–Schlichting waves, as calculated by the linearized analysis, far downstream of the roughness element.

Boundary-Layer Flow Between the Attachment Lines on a Flat Plate Delta Wing at Incidence

1962 ◽  
Vol 13 (1) ◽  
pp. 1-16
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Delta Wing ◽  
Three Dimensional ◽  
External Flow ◽  
Two Dimensional ◽  
Conical Flow ◽  
Slender Body Theory ◽  
Layer Flow ◽  
Body Theory ◽  
Transition Fronts

SummaryA three-dimensional laminar-boundary-layer calculation is carried out over the area concerned. The external flow is simplified, being calculated by slender-body theory assuming conical flow, with two point vortices above the wing, their positions and strength being determined by experiment. Attempts are made to draw transition fronts both for two-dimensional and sweep instability from this calculation. The combination of these gives fronts similar to those observed in some experiments. Because there is little or no pressure gradient over the area in question it is suggested that it is a region where distributed suction might usefully be applied in order to maintain laminar flow and reduce drag.

An Approach to Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Author(s):  
A. D. Carmichael
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Basic Assumption ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Factor H ◽  
Simple Method ◽  
The Cross

A relatively simple method for predicting some of the characteristics of three-dimensional turbulent boundary layers is presented. The basic assumption of the method is that the cross-flow is small. An empirical correlation of a basic shape factor of the cross-flow boundary layer against the streamwise shape factor H is provided. This correlation, together with data for the streamwise boundary layer, is used to predict the cross flow. The solution is very sensitive to the accuracy of the streamwise boundary-layer data which is predicted by conventional two-dimensional methods.

Computation and Simulation of Wake-Generated Unsteady Pressure and Boundary Layers in Cascades: Part 1 — Description of the Approach and Validation

1994 ◽  
Author(s):  
S. Fan ◽  
B. Lakshminarayana
Keyword(s):  
Boundary Layer ◽  
Unsteady Flow ◽  
Flat Plate ◽  
Boundary Layers ◽  
Guide Vane ◽  
Numerical Procedure ◽  
Computational Domain ◽  
Unsteady Pressure ◽  
Blade Row ◽  
Euler Solver

The unsteady pressure and boundary layers on a turbomachinery blade row arising from periodic wakes due to upstream blade rows are investigated in this paper. A time accurate Euler solver has been developed using an explicit four-stage Runge-Kutta scheme. Two dimensional unsteady non-reflecting boundary conditions are used at the inlet and the outlet of the computational domain. The unsteady Euler solver captures the wake propagation and the resulting unsteady pressure field, which is then used as the input for a 2-D unsteady boundary layer procedure to predict the unsteady response of blade boundary layers. The boundary layer code includes an advanced k-ε model developed for unsteady turbulent boundary layers. The present computational procedure has been validated against analytic solutions and experimental measurements. The validation cases include unsteady inviscid flows in a flat plate cascade and a compressor exit guide vane (EGV) cascade, unsteady turbulent boundary layer on a flat plate subject to a traveling wave, unsteady transitional boundary layer due to wake passing and unsteady flow at the mid-span section of an axial compressor stator. The present numerical procedure is both efficient and accurate in predicting the unsteady flow physics resulting from wake/blade-row interaction, including wake induced unsteady transition of blade boundary layers.

Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

Instability in a viscous flow driven by streamwise vortices

2001 ◽  
Vol 432 ◽  
pp. 127-166 ◽  
Author(s):  
K. W. BRINCKMAN ◽  
J. D. A. WALKER
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Wall Layer ◽  
External Flow ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Wall Flow ◽  
Turbulent Wall ◽  
Near Wall

Unsteady separation processes at large finite, Reynolds number, Re, are considered, as well as the possible relation to existing descriptions of boundary-layer separation in the limit Re → ∞. The model problem is a fundamental vortex-driven three-dimensional flow, believed to be relevant to bursting near the wall in a turbulent boundary layer. Bursting is known to be associated with streamwise vortex motion, but the vortex/wall interactions that drive the near-wall flow toward breakdown have not yet been fully identified. Here, a simulation of symmetric counter-rotating vortices is used to assess the influence of sustained pumping action on the development of a viscous wall layer. The calculated solutions describe a three-dimensional flow at finite Re that is independent of the streamwise coordinate and consists of a crossflow plane motion, with a developing streamwise flow. The unsteady problem is constructed to mimic a typical cycle in turbulent wall layers and numerical solutions are obtained over a range of Re. Recirculating eddies develop rapidly in the near-wall flow, but these eddies are eventually bisected by alleyways which open up from the external flow region to the wall. At sufficiently high Re, an oscillation was found to develop in the streamwise vorticity field near the alleyways with a concurrent evolution of a local spiky behaviour in the wall shear. Above a critical value of Re, the oscillation grows rapidly in amplitude and eventually penetrates the external flow field, suggesting the onset of an unstable wall-layer breakdown. Local zones of severely retarded streamwise velocity are computed which are reminiscent of the low-speed streaks commonly observed in turbulent boundary layers. A number of other features also bear a resemblance to observed coherent structure in the turbulent wall layer.

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