scholarly journals Viscoplastic boundary layers

2017 ◽  
Vol 813 ◽  
pp. 929-954 ◽  
Author(s):  
N. J. Balmforth ◽  
R. V. Craster ◽  
D. R. Hewitt ◽  
S. Hormozi ◽  
A. Maleki
Keyword(s):  
Boundary Layer ◽  
Yield Stress ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Boundary Layer Theory ◽  
Classical Solutions ◽  
Bingham Number ◽  
Boundary Layer Equations ◽  
Two Dimensional Flow

In the limit of a large yield stress, or equivalently at the initiation of motion, viscoplastic flows can develop narrow boundary layers that provide either surfaces of failure between rigid plugs, the lubrication between a plugged flow and a wall or buffers for regions of predominantly plastic deformation. Oldroyd (Proc. Camb. Phil. Soc., vol. 43, 1947, pp. 383–395) presented the first theoretical discussion of these viscoplastic boundary layers, offering an asymptotic reduction of the governing equations and a discussion of some model flow problems. However, the complicated nonlinear form of Oldroyd’s boundary-layer equations has evidently precluded further discussion of them. In the current paper, we revisit Oldroyd’s viscoplastic boundary-layer analysis and his canonical examples of a jet-like intrusion and flow past a thin plate. We also consider flow down channels with either sudden expansions or wavy walls. In all these examples, we verify that viscoplastic boundary layers form as envisioned by Oldroyd. For each example, we extract the dependence of the boundary-layer thickness and flow profiles on the dimensionless yield-stress parameter (Bingham number). We find that, while Oldroyd’s boundary-layer theory applies to free viscoplastic shear layers, it does not apply when the boundary layer is adjacent to a wall, as has been observed previously for two-dimensional flow around circular obstructions. Instead, the boundary-layer thickness scales in a different fashion with the Bingham number, as suggested by classical solutions for plane-parallel flows, lubrication theory and, for flow around a plate, by Piau (J. Non-Newtonian Fluid Mech., vol. 102, 2002, pp. 193–218); we rationalize this second scaling and provide an alternative boundary-layer theory.

Annulus Wall Boundary-Layer Measurements in a Four-Stage Compressor

1986 ◽  
Vol 108 (1) ◽  
pp. 2-6 ◽  
Author(s):  
N. A. Cumpsty
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Tip Clearance ◽  
The Other ◽  
Wall Boundary Layer ◽  
Multistage Compressors ◽  
Full Design

There are few available measurements of the boundary layers in multistage compressors when the repeating-stage condition is reached. These tests were performed in a small four-stage compressor; the flow was essentially incompressible and the Reynolds number based on blade chord was about 5 • 104. Two series of tests were performed; in one series the full design number of blades were installed, in the other series half the blades were removed to reduce the solidity and double the staggered spacing. Initially it was wished to examine the hypothesis proposed by Smith [1] that staggered spacing is a particularly important scaling parameter for boundary layer thickness; the results of these tests and those of Hunter and Cumpsty [2] tend to suggest that it is tip clearance which is most potent in determining boundary-layer integral thicknesses. The integral thicknesses agree quite well with those published by Smith.

A Review of Cascade Data on Secondary Losses in Turbines

1970 ◽  
Vol 12 (1) ◽  
pp. 48-59 ◽  
Author(s):  
J. Dunham
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Blade Loading ◽  
Axial Turbine ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Turbine Cascades

Theories and experiments on secondary losses in axial turbine cascades without end clearance are reviewed. A formula is given which correlates the effect of blade loading on secondary losses more successfully than hitherto. However, it is also shown that secondary losses increase with upstream wall boundary layer thickness. Only a tentative expression for that effect can be suggested. In order to predict secondary losses reliably more must be known about these wall boundary layers.

Some Characteristics of the Vortical Motions in the Outer Region of Turbulent Boundary Layers (Data Bank Contribution)

1992 ◽  
Vol 114 (4) ◽  
pp. 530-536 ◽  
Author(s):  
J. C. Klewicki ◽  
R. E. Falco ◽  
J. F. Foss
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Outer Region ◽  
Signal Amplitude ◽  
Threshold Level ◽  
Data Bank ◽  
Turbulent Boundary Layers ◽  
Spanwise Vorticity

Time-resolved measurements of the spanwise vorticity component, ωz, are used to investigate the motions in the outer region of turbulent boundary layers. The measurements were taken in very thick zero pressure gradient boundary layers (Rθ = 1010, 2870, 4850) using a four wire probe. As a result of the large boundary layer thickness, at the outer region locations where the measurements were taken the wall-normal and spanwise dimensions of the probe ranged between 0.7 < Δy/η < 1.2 and 2.1 < Δz/η < 3.9, respectively, where η is the local Kolmogorov length. An analysis of vorticity based intermittency is presented near y/δ = 0.6 and 0.85 at each of the Reynolds numbers. The average intermittency is presented as a function of detector threshold level and position in the boundary layer. The spanwise vorticity signals were found to yield average intermittency values at least as large as previous intermittency studies using “surrogate” signals. The average intermittency results do not indicate a region of threshold independence. An analysis of ωz event durations conditioned on the signal amplitude was also performed. The results of this analysis indicate that for decreasing Rθ, regions of single-signed ωz increase in size relative to the boundary layer thickness, but decrease in size when normalized by inner variables.

Wind-Tunnel Screens: Flow Instability and its Effect on Aerofoil Boundary Layers

1964 ◽  
Vol 68 (639) ◽  
pp. 198-198 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Flow Instability ◽  
Flow Direction ◽  
Flat Plates ◽  
Mixing Processes ◽  
Flow Through

Morgan has described a spatial instability in the flow through screens or grids of small open-area ratio. Head and Rechenberg and others have observed large span-wise variations in the thickness and shear stress of nominally two-dimensional boundary layers on flat plates and aerofoils in wind tunnels. It now appears that these spanwise variations are caused by the instability of flow through the screens. The jets of air issuing from the pores of the screen attempt to entrain more air by the usual mixing processes, but can only entrain it from each other, so that groups of jets coalesce in rather random (steady) patterns determined by small irregularities in the weave. The resulting variations in axial velocity are virtually eliminated by the wind tunnel contraction, but variations in flow direction are not so greatly reduced: a theoretical analysis shows that the observed variations of boundary-layer thickness, which often reach ± 10 per cent of the mean, can be produced by directional variations in the working section of the order of ± 1/20 deg, with a spanwise wavelength of the same order as the boundary-layer thickness.

scholarly journals Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers

2015 ◽  
Vol 774 ◽  
Author(s):  
Christina Vanderwel ◽  
Bharathram Ganapathisubramani
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Surface Flow ◽  
Secondary Flows ◽  
Flow Conditions ◽  
Roughness Elements

Large-scale secondary flows can sometimes appear in turbulent boundary layers formed over rough surfaces, creating low- and high-momentum pathways along the surface (Barros & Christensen, J. Fluid Mech., vol. 748, 2014, R1). We investigate experimentally the dependence of these secondary flows on surface/flow conditions by measuring the flows over streamwise strips of roughness with systematically varied spanwise spacing. We find that the large-scale secondary flows are accentuated when the spacing of the roughness elements is roughly proportional to the boundary layer thickness ${\it\delta}$, and do not appear for cases with finer spacing. Cases with coarser spacing also generate ${\it\delta}$-scale secondary flows with tertiary flows in the spaces in between. These results show that the ratio of the spanwise length scale of roughness heterogeneity to the boundary layer thickness is a critical parameter for the occurrence of these secondary motions in turbulent boundary layers over rough walls.

Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer

2014 ◽  
Vol 763 ◽  
pp. 136-165 ◽  
Author(s):  
Nicola De Tullio ◽  
Neil D. Sandham
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
High Speed ◽  
Stokes Equations ◽  
Roughness Element ◽  
Transition To Turbulence ◽  
Local Boundary ◽  
Wake Modes

AbstractThe excitation of instability modes in the wake generated behind a discrete roughness element in a boundary layer at Mach 6 is analysed through numerical simulations of the compressible Navier–Stokes equations. Recent experimental observations show that transition to turbulence in high-speed boundary layers during re-entry flight is dominated by wall roughness effects. Therefore, understanding the roughness-induced transition to turbulence in this flow regime is of primary importance. Our results show that a discrete roughness element with a height of about half the local boundary-layer thickness generates an unstable wake able to sustain the growth of a number of modes. The most unstable of these modes are a sinuous mode (mode SL) and two varicose modes (modes VL and VC). The varicose modes grow approximately 17 % faster than the most unstable Mack mode and their growth persists over a longer streamwise distance, thereby leading to a notable acceleration of the laminar–turbulent transition process. Two main mechanisms are identified for the excitation of wake modes: the first is based on the interaction between the external disturbances and the reverse flow regions induced by the roughness element and the second is due to the interaction between the boundary-layer modes (first modes and Mack modes) and the non-parallel roughness wake. An important finding of the present study is that, while being less unstable, mode SL is the preferred instability for the first of the above excitation mechanisms, which drives the wake modes excitation in the absence of boundary-layer modes. Modes VL and VC are excited through the second mechanism and, hence, become important when first modes and Mack modes come into interaction with the roughness wake. The new mode VC presents similarities with the Mack mode instability, including the tuning between its most unstable wavelength and the local boundary-layer thickness, and it is believed to play a fundamental role in the roughness-induced transition of high-speed boundary layers. In contrast to the smooth-wall case, wall cooling is stabilising for all the roughness-wake modes.

Self-consistent unstirred layers in osmotically driven flows

2010 ◽  
Vol 662 ◽  
pp. 197-208 ◽  
Author(s):  
K. H. JENSEN ◽  
T. BOHR ◽  
H. BRUUS
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Concentration Boundary ◽  
Concentration Boundary Layers ◽  
Unstirred Layers ◽  
Mathematical Relation ◽  
Wide Range ◽  
Self Consistent

It has long been recognized that the osmotic transport characteristics of membranes may be strongly influenced by the presence of unstirred concentration boundary layers adjacent to the membrane. Previous experimental as well as theoretical works have mainly focused on the case where the solutions on both sides of the membrane remain well mixed due to an external stirring mechanism. We investigate the effects of concentration boundary layers on the efficiency of osmotic pumping processes in the absence of external stirring, i.e. when all advection is provided by the osmosis itself. This case is relevant in the study of intracellular flows, e.g. in plants. For such systems, we show that no well-defined boundary-layer thickness exists and that the reduction in concentration can be estimated by a surprisingly simple mathematical relation across a wide range of geometries and Péclet numbers.

Penetration and Mixing Characteristics of Inclined Jets in Crossflow at Low Momentum Flux Ratios

2020 ◽  
Author(s):  
Rahul B. Vishwanath ◽  
Timothy M. Wabel ◽  
Adam M. Steinberg
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Momentum Flux ◽  
Flux Ratio ◽  
Leading Edge ◽  
Concentration Profiles ◽  
Injection Point ◽  
Fluid Concentration

Abstract This study investigates the factors affecting low momentum jets that are injected at an angle relative to a crossflow stream, which is relevant to film-cooling technologies. Quantitative measurements of the jet fluid concentration were obtained based on planar laser induced fluorescence (PLIF) from acetone vapor that was seeded into the jet. The jets were injected at four different axial locations downstream of the leading edge of a flat plate, resulting in different boundary layer thicknesses at the injection location. At each location, the jet-to-crossflow momentum flux ratio was varied from 0.5–5. The jet centerline trajectories were affected not only by the momentum flux ratios, but also by the approaching crossflow boundary layer thickness, with the jets penetrating the least for the thickest boundary layers. Measurements of the jet fluid concentration along the jet centerline showed an exponential decay rate of −1.3 across all cases. However, the behavior in the immediate vicinity of the jet depended on the boundary layer thickness, with thicker boundary layers resulting in a slower decay. Hence, the concentration profiles were shifted relative to the injection point depending on the injector position on the plate. The concentration profiles perpendicular to the jet axis were self-similar when scaled with the profile half-width.

Singularities encountered in three-dimensional boundary layers under an adverse or favourable pressure gradient

1995 ◽  
Vol 352 (1698) ◽  
pp. 45-87 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Plane Flow ◽  
Boundary Layer Equations ◽  
Dimensional Boundary

Singularities in solutions of the classical boundary-layer equations are considered, numerically and analytically, in an example of steady hypersonic flow along a flat plate with three-dimensional surface roughness. First, a wide parametric study of the breakdown of symmetry-plane flow is performed for two particular cases of the surface geometry. Emphasis is put on the structural stability of the singularities’ development to local/global variation of the pressure distribution. It is found that, as usual, the solution behaviour under an adverse pressure gradient involves the Goldstein- or marginal-type singularity at a point of zero streamwise skin friction. As the main alternative, typical of configurations with favourable or zero pressure forcing, an inviscid breakdown in the middle of the flow is identified. Similarly to unsteady flows, the main features of the novel singularity include infinitely growing boundary-layer thickness and finite limiting values of the skin-friction components. Subsequent analytical extensions of the singular symmetry-plane solution then suggest two different scenarios for the global boundary-layer behaviour: one implies inviscid breakdown of the flow at some singular line, the other describes the development of a boundary-layer collision at a downstream portion of the symmetry plane. In contrast with previous studies of the collision phenomenon in steady flows, the present theory suggests logarithmic growth of boundary-layer thickness on both sides of the discontinuity. Finally, an example of numerical solution of the full three dimensional boundary layer equations is given. The flow régime chosen corresponds to inviscid breakdown of a centreplane flow under a favourable pressure gradient and development of the discontinuity/collision downstream. The numerical results near the origin of the discontinuity are found to be supportive, producing quantitative agreement with the local analytical description.

Modeling Dilute Gas-Solid Turbulent Boundary Layers Using Moment Methods

2014 ◽  
Author(s):  
D. M. Dunn ◽  
K. D. Squires
Keyword(s):  
Boundary Layer ◽  
Gas Phase ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Method Of Moments ◽  
Boundary Layer Thickness ◽  
Turbulent Boundary Layers ◽  
Dispersed Phase ◽  
Second Phase ◽  
Carrier Flow

The specific focus of the current effort is on modeling dilute particle-laden turbulent boundary layers in which the gas-phase carrier flow is populated with a second phase of small, dispersed solid particles possessing material densities much larger than that of the carrier flow. A novel approach known as the conditional quadrature method of moments (CQMOM) developed by Yuan and Fox [1], derived from the quadrature-based method of moments (QMOM) developed originally by McGraw [2], is being implemented to model the dispersed particles as an Eulerian phase. Both enabled and disabled inter-particle collision treatments are included in the model for a dispersed phase coupled to the fluid via a drag force acting on the particles. Simulations are conducted with a Reynolds number of 2800 based on the boundary layer thickness at the inlet to the domain. The full 3-D mesh contains 800×128×98 structured cells with overall dimensions in terms of the inlet boundary layer thickness of 80×6 ×4 in the streamwise, spanwise, and wall-normal directions, respectively. The gas-phase carrier flow is computed using Direct Numerical Simulation of the incompressible Navier-Stokes equations. The boundary layer develops spatially from a turbulent inflow condition and drives the particulate phase via drag and collisions. Comparisons are made against simulations performed using Lagrangian-based discrete particle simulation (DPS) of the dispersed phase and demonstrate the utility of the Eulerian moment method approach. Both instantaneous and time-averaged quantities are presented.

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