scholarly journals Buoyancy-driven algebraic (localised) boundary-layer disturbances

2021 ◽  
Vol 132 (1) ◽  
Author(s):  
S. M. Edwards ◽  
R. E. Hewitt
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Region ◽  
Dominant Mode ◽  
Spanwise Direction ◽  
Pressure Gradients ◽  
Cross Sectional ◽  
Gradient Parameter ◽  
Sectional Plane ◽  
Downstream Flow

AbstractWe show that a new class of steady linear eigenmodes exist in the Falkner–Skan boundary layer, associated with an algebraically developing, thermally coupled three-dimensional perturbation that remains localised in the spanwise direction. The dominant mode has a weak temperature difference that decays (algebraically) downstream, but remains sufficient (for favourable pressure gradients that are below a critical level) to drive an algebraically growing disturbance in the velocity field. We determine the critical Prandtl number and pressure gradient parameter required for downstream algebraic growth. We also march the nonlinear boundary-region equations downstream, to demonstrate that growth of these modes eventually gives rise to streak-like structures of order-one aspect ratio in the cross-sectional plane. Furthermore, this downstream flow can ultimately become unstable to a two-dimensional Rayleigh instability at finite amplitudes.

scholarly journals Global vorticity shedding for a vanishing wing

2012 ◽  
Vol 695 ◽  
pp. 112-134 ◽  
Author(s):  
M. S. Wibawa ◽  
S. C. Steele ◽  
J. M. Dahl ◽  
D. E. Rival ◽  
G. D. Weymouth ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Tip Vortex ◽  
Spanwise Direction ◽  
Streamwise Vorticity ◽  
Biologically Inspired ◽  
Cross Sectional ◽  
Image Velocimetry ◽  
Moving Body ◽  
Surrounding Fluid

AbstractIf a moving body were made to vanish within a fluid, its boundary-layer vorticity would be released into the fluid at all locations simultaneously, a phenomenon we call global vorticity shedding. We approximate this process by studying the related problem of rapid vorticity transfer from the boundary layer of a body undergoing a quick change of cross-sectional and surface area. A surface-piercing foil is first towed through water at constant speed, $U$, and constant angle of attack, then rapidly pulled out of the fluid in the spanwise direction. Viewed within a fixed plane perpendicular to the span, the cross-sectional area of the foil seemingly disappears. The rapid spanwise motion results in the nearly instantaneous shedding of the boundary layer into the surrounding fluid. Particle image velocimetry measurements show that the shed layers quickly transition from free shear layers to form two strong, unequal-strength vortices, formed within non-dimensional time ${t}^{\ensuremath{\ast} } = 0. 03$, based on the foil chord and forward velocity. These vortices are connected to, and interact with, the foil’s tip vortex through additional streamwise vorticity formed during the rapid pulling of the foil. Numerical simulations show that two strong spanwise vortices form from the shed vorticity of the boundary layer. The three-dimensional effects of the foil removal process are restricted to the tip of the foil. This method of vorticity transfer may be used for quickly introducing circulation to a fluid to provide forcing for biologically inspired flow control.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

scholarly journals An experiment on the adiabatic compressible turbulent boundary layer in adverse and favourable pressure gradients

1972 ◽  
Vol 51 (4) ◽  
pp. 657-672 ◽  
Author(s):  
J. E. Lewis ◽  
R. L. Gran ◽  
T. Kubota
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Adiabatic Wall ◽  
Flow Measurements ◽  
Low Speed ◽  
Velocity Transformation ◽  
Tunnel Model ◽  
Gradient Parameter

A wind-tunnel model was developed to study the two-dimensional turbulent boundary layer in adverse and favourable pressure gradients with out the effects of streamwise surface curvature. Experiments were performed at Mach 4 with an adiabatic wall, and mean flow measurements within the boundary layer were obtained. The data, when viewed in the velocity transformation suggested by Van Driest, show good general agreement with the composite boundary-layer profile developed for the low-speed turbulent boundary layer. Moreover, the pressure gradient parameter suggested by Alber & Coats was found to correlate the data with low-speed results.

Formation and decay of coherent structures in pipe flow

2010 ◽  
Vol 655 ◽  
pp. 258-279 ◽  
Author(s):  
JIMMY PHILIP ◽  
JACOB COHEN
Keyword(s):  
Coherent Structures ◽  
Pipe Flow ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Hairpin Vortices ◽  
Cross Sectional ◽  
Instability Waves ◽  
Sectional Plane ◽  
The Cross ◽  
Three Dimensional Coordinate

Experimental investigation of the generation and decay of coherent structures, namely, streaks (accompanied by a counter-rotating vortex pair) and hairpin vortices in pipe flow, is carried out by artificial injection of continuous disturbances. Flow visualization and velocity measurements show that for small amplitudes of disturbances (v0) streaks are produced, and increasing v0 produces instability waves on the streaks, which further break down into an array of hairpin vortices. However, the streaks and hairpins decay along the downstream direction (X). In fact, the critical value of v0 required for the initiation of hairpins at a given Re (Reynolds number) varies with the streamwise distance (in contrast to the previously found scaling of v0 ~ Re−1, valid only close to the location of injection, i.e. smaller X). This is a consequence of the decay of the coherent structures in the pipe. Moreover, the hairpins have been found to decay more slowly with increasing Re. Measurements of energy in the cross-sectional plane of the pipe, and maps of disturbance velocity at various X-locations show the transient growth and decay of energy for relatively low v0. For higher v0 and Re the energy has been seen to increase continuously along the length of the pipe under observation. Owing to the increase in the cross-sectional area occupied by the disturbance along the X-direction, it is observed that energy can transiently increase even when the total disturbance magnitude is decreasing. Observing the similarity of the present work and other investigations wherein decay of turbulence in pipe flow is found, a schematic illustration of the transition surface for pipe flow on a v0−Re−X, three-dimensional coordinate system is presented.

Turbulence structural changes for a three-dimensional turbulent boundary layer in a 30° bend

1994 ◽  
Vol 272 ◽  
pp. 183-210 ◽  
Author(s):  
Walter R. Schwarz ◽  
Peter Bradshaw
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Structural Changes ◽  
Three Dimensional ◽  
Energy Ratio ◽  
Pressure Gradients ◽  
Stress Energy ◽  
Cross Wire ◽  
Low Speed Wind Tunnel

A three-dimensional turbulent boundary layer (3DTBL) was generated on the floor of a low-speed wind tunnel by the imposition of a cross-stream pressure gradient using a 30° bend in the horizontal plane. The surface streamlines were deflected by as much as 22° relative to the local tunnel centreline. Downstream of the bend, the 3DTBL gradually relaxed towards a 2DTBL; this was an impulse-and-recovery experiment which focused on the outer layer. Mean velocities were measured with a three-hole yawmeter and turbulence quantities, which included the Reynolds-stress tensor and the triple products, were measured with a cross-wire hot-wire anemometer. The experiment isolated the effects of crossflow from those of adverse streamwise pressure gradients, which may have clouded interpretations of previous 3DTBL experiments. In particular, the detailed developments of the cross-stream shear stress and of the stress/energy ratio become clearer. The shear-stress vector lagged behind the velocity-gradient vector as crossflow developed; however, the two vectors became more closely aligned downstream of the bend. Reductions in the stress/energy ratio implied that crossflow made shear-stress production less efficient. Another effect of three-dimensionality was a change of sign in the vertical transport of turbulent kinetic energy by turbulence, in the inner part of the boundary layer.

scholarly journals Physiological non-Newtonian blood flow through single stenosed artery

2016 ◽  
Vol 43 (1) ◽  
pp. 99-115 ◽  
Author(s):  
Khairuzzaman Mamun ◽  
Most. Akhter ◽  
Mohammad Ali
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Three Dimensional ◽  
Cross Sectional ◽  
Number Range ◽  
Newtonian Model ◽  
Early Systole ◽  
Wall Shear ◽  
Downstream Flow

A numerical simulation to investigate the Non-Newtonian modeling effects on physiological flows in a three dimensional idealized artery with a single stenosis of 85% severity is given. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Determination of the physiological waveform is performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 96 to 800. Low Reynolds number k ? w model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has also been investigated to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of velocity, pressure, wall shear stress distributions and cross sectional velocities as well as the streamlines contour. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are minimum such as at early systole or diastole. In general, the velocities at throat regions are highest at all-time phase. However, at pick systole higher velocities are observed at post-stenotic region. Downstream flow of all models creates some recirculation regions at diastole.

Effect of Adverse Pressure Gradients on Turbulent Boundary Layers in Axisymmetric Conduits

1957 ◽  
Vol 24 (2) ◽  
pp. 191-196
Author(s):  
J. M. Robertson ◽  
J. W. Holl
Keyword(s):  
Boundary Layer ◽  
Flow Parameter ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Straight Pipe ◽  
Outer Flow ◽  
Dimensional Boundary

Abstract The development of the three-dimensional boundary layer in a diffuser with several discharge arrangements has been studied for air flow, in continuation of the work of Uram (1). The flow conditions in a diffuser when followed by a straight pipe, an additional length of the diffuser, or a jet, are compared. Extension of the method of analysis developed by Ross for two-dimensional layers is presented. In some cases the use of three-dimensionally defined parameters leads to different results. Ross’s (2) unique outer-flow parameter is found to be no longer satisfactory. Other outer parameters are presented as possible substitutes.

scholarly journals Injection into boundary layers: solutions beyond the classical form

2017 ◽  
Vol 822 ◽  
pp. 617-639 ◽  
Author(s):  
R. E. Hewitt ◽  
P. W. Duck ◽  
A. J. Williams
Keyword(s):  
Boundary Layer ◽  
Numerical Study ◽  
Flow Direction ◽  
Three Dimensional ◽  
Boundary Region ◽  
Navier Stokes ◽  
Injection Velocity ◽  
Finite Width ◽  
Viscous Effects ◽  
New States

This theoretical and numerical study presents three-dimensional boundary-layer solutions for laminar incompressible flow adjacent to a semi-infinite flat plate, subject to a uniform free-stream speed and injection through the plate surface. The novelty in this case arises from a fully three-dimensional formulation, which also allows for slot injection over a spanwise length scale comparable to the boundary-layer thickness. This approach retains viscous effects in both the spanwise and transverse directions, and effectively results in a parabolised Navier–Stokes system (sometimes referred to as the ‘boundary-region equations’). Any injection profile can be described in this approach, but we restrict attention to three-dimensional states driven by a finite-width slot aligned with the flow direction and self-similar in their downstream development. The classical two-dimensional states are known to only exist up to a critical (‘blow off’) injection amplitude, but the three-dimensional solutions here appear possible for any injection velocity. These new states take the form of low-speed streamwise-aligned streaks whose geometry depends on the amplitude of injection and the spanwise width of the injection slot; intriguingly, although very low wall shear is typically obtained, streamwise flow reversal is not observed, however hard the blowing. Asymptotic descriptions are provided in the limit of increasing slot width and fixed injection velocity, which allow for classification of the solutions according to two bounding injection rates.

scholarly journals Optimal wave packets in a boundary layer and initial phases of a turbulent spot

2010 ◽  
Vol 656 ◽  
pp. 231-259 ◽  
Author(s):  
S. CHERUBINI ◽  
J.-C. ROBINET ◽  
A. BOTTARO ◽  
P. DE PALMA
Keyword(s):  
Boundary Layer ◽  
Wave Packet ◽  
Scaling Law ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Optimal Time ◽  
Spanwise Direction ◽  
Turbulent Spot ◽  
Hairpin Vortices

The three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.

Paper 1: Centrifugal Compressors for Gas Turbines

1968 ◽  
Vol 183 (14) ◽  
pp. 1-10 ◽  
Author(s):  
T. B. Ferguson
Keyword(s):  
Boundary Layer ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Boundary Layer Theory ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Centrifugal Compressors ◽  
Blade Loading ◽  
Actual Flow ◽  
High Mach

The trends in fluid mechanical development of centrifugal compressors are discussed. The main developments in the impeller are the application of quasi-three-dimensional isentropic methods together with some separation criteria based on two-dimensional turbulent boundary layer theory. Diffusers are sometimes designed on a simplified two-dimensional basis but channel diffusers still appear to be preferred especially at high Mach numbers. Recent visualization studies have shown how far the actual flow in impellers may depart from the actual model and there is a lack of systematic quantitative experimental work on limiting blade loading and pressure gradients both in impellers and diffusers. A summary of gas turbine centrifugal compressors is also made.

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