Scaling of square-prism shear layers

2018 ◽  
Vol 849 ◽  
pp. 1096-1119 ◽  
Author(s):  
D. C. Lander ◽  
D. M. Moore ◽  
C. W. Letchford ◽  
M. Amitay
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Power Law ◽  
Frequency Ratio ◽  
Shear Layers ◽  
Nonlinear Dependence ◽  
Front Face ◽  
Length Scale ◽  
Square Prism ◽  
Ratio Scaling

Scaling characteristics, essential to the mechanisms of transition in square-prism shear layers, were explored experimentally. In particular, the evolution of the dominant instability modes as a function of Reynolds number were reported in the range $1.5\times 10^{4}\lesssim Re_{D}\lesssim 7.5\times 10^{4}$. It was found that the ratio between the shear layer frequency and the shedding frequency obeys a power-law scaling relation. Adherence to the power-law relationship, which was derived from hot-wire measurements, has been supported by two additional and independent scaling considerations, namely, by particle image velocimetry measurements to observe the evolution of length and velocity scales in the shear layer during transition, and by comparison to direct numerical simulations to illuminate the properties of the front-face boundary layer. The nonlinear dependence of the shear layer instability frequency is sustained by the influence of $Re_{D}$ on the thickness of the laminar front-face boundary layer. In corroboration with the original scaling argument for the circular cylinder, the length scale of the shear layer was the only source of nonlinearity in the frequency ratio scaling, within the range of Reynolds numbers reported. The frequency ratio scaling may therefore be understood by the influence of $Re_{D}$ on the appropriate length scale of the shear layer. This length scale was observed to be the momentum thickness evaluated at a transition point, defined where the Kelvin–Helmholtz instability saturates.

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.

scholarly journals New Theories on Boundary Layer Transition and Turbulence Formation

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Chaoqun Liu ◽  
Ping Lu ◽  
Lin Chen ◽  
Yonghua Yan
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Shear Layer ◽  
Boundary Layer Transition ◽  
Length Scale ◽  
Multiple Level ◽  
Shear Layer Instability ◽  
Small Length ◽  
Layer Transition ◽  
Turbulence Generation

This paper is a short review of our recent DNS work on physics of late boundary layer transition and turbulence. Based on our DNS observation, we propose a new theory on boundary layer transition, which has five steps, that is, receptivity, linear instability, large vortex structure formation, small length scale generation, loss of symmetry and randomization to turbulence. For turbulence generation and sustenance, the classical theory, described with Richardson's energy cascade and Kolmogorov length scale, is not observed by our DNS. We proposed a new theory on turbulence generation that all small length scales are generated by “shear layer instability” through multiple level ejections and sweeps and consequent multiple level positive and negative spikes, but not by “vortex breakdown.” We believe “shear layer instability” is the “mother of turbulence.” The energy transferring from large vortices to small vortices is carried out by multiple level sweeps, but does not follow Kolmogorov's theory that large vortices pass energy to small ones through vortex stretch and breakdown. The loss of symmetry starts from the second level ring cycle in the middle of the flow field and spreads to the bottom of the boundary layer and then the whole flow field.

Non-Newtonian Natural Convection Along a Vertical Heated Wavy Surface Using a Modified Power-Law Viscosity Model

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
M. M. Molla ◽  
L. S. Yao
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Shear Rate ◽  
Power Law ◽  
Leading Edge ◽  
Numerical Results ◽  
Wavy Surface ◽  
Viscosity Model ◽  
Length Scale ◽  
Modified Power Law

Natural convection of non-Newtonian fluids along a vertical wavy surface with uniform surface temperature has been investigated using a modified power-law viscosity model. An important parameter of the problem is the ratio of the length scale introduced by the power-law and the wavelength of the wavy surface. In this model there are no physically unrealistic limits in the boundary-layer formulation for power-law, non-Newtonian fluids. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge removed; hence, the boundary-layer equations can be solved straightforwardly by marching downstream from the leading edge. Numerical results are presented for the case of shear-thinning as well as shear-thickening fluid in terms of the viscosity, velocity, and temperature distribution, and for important physical properties, namely, the wall shear stress and heat transfer rates in terms of the local skin-friction coefficient and the local Nusselt number, respectively. Also results are presented for the variation in surface amplitude and the ratio of length scale to surface wavelength. The numerical results demonstrate that a Newtonian-like solution for natural convection exists near the leading edge where the shear-rate is not large enough to trigger non-Newtonian effects. After the shear-rate increases beyond a threshold value, non-Newtonian effects start to develop.

On the effect of heat release in turbulence spectra of non-premixed reacting shear layers

2009 ◽  
Vol 626 ◽  
pp. 67-109 ◽  
Author(s):  
R. KNAUS ◽  
C. PANTANO
Keyword(s):  
Heat Release ◽  
Shear Layer ◽  
Mixture Fraction ◽  
Shear Layers ◽  
Scaling Analysis ◽  
Length Scale ◽  
Strong Nonlinearity ◽  
Temperature Spectrum ◽  
Moderate Reynolds Number ◽  
Temperature Spectra

Velocity, mixture fraction and temperature spectra obtained from five direct numerical simulations of non-reacting and reacting shear layers, using the infinitely fast chemistry approximation, are analysed. Two different global chemical reactions corresponding to methane and hydrogen combustion with air, respectively, are considered. The effect of heat release, i.e. density variation, on the inertial and dissipation turbulence subrange of the spectra is investigated. Analysis of the database supports the experimentally available measurements of spectra in turbulent reacting flows showing that heat release effects can be scaled out by utilizing Favre-averaged (density-weighted) large-scale turbulence quantities. This is supported by the simulation results for velocity and mixture fraction in our moderate-Reynolds-number flows but it appears to be less supported in the dissipation subrange of the temperature spectra. The departure from universal scaling using Favre-averaged quantities in the temperature spectrum, which is evident in the dissipation subrange, appears to be caused by the strong nonlinearity of the state relationship relating the mixture fraction to the temperature, as has been suggested previously. These effects are less pronounced at intermediate wavenumbers. Analysis suggests that the nonlinear state relationship and the spectra of mixture fraction moments can be used to reconstruct the temperature spectrum across the flow. Moreover, the governing equation for the temperature variance is analysed to identify a possible surrogate for the overall rate of dissipation of temperature fluctuations and their corresponding dissipation length scale. This scaling analysis is then used to separate planes across the shear layer where the temperature dissipation length scale is alike that of the mixture fraction from regions where smaller length scales are present, and are evidenced in the dissipation subrange using Kolmogorov scaling. In our simulations, these regions correspond to the centre of the shear layer and the mean flame location. The new estimate for the temperature dissipation length scale is able to collapse the compensated spectra profiles at all planes across the shear layer for all simulations.

The reattachment and relaxation of a turbulent shear layer

1972 ◽  
Vol 52 (1) ◽  
pp. 113-135 ◽  
Author(s):  
P. Bradshaw ◽  
F. Y. F. Wong
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Flow Region ◽  
Turbulent Shear ◽  
Length Scale ◽  
Low Speed ◽  
Turbulent Shear Layer ◽  
Recirculating Flow ◽  
Speed Flow ◽  
Complicated Nature

Existing experiments on the low-speed flow downstream of steps and fences, and some new measurements downstream of a backward-facing step, are used to demonstrate the complicated nature of the flow in the reattachment region and its effect on the slow non-monotonic return of the shear layer to the ordinary boundary-layer state. A key feature of the flow is found to be the splitting of the shear layer at reattachment, where part of the flow is deflected upstream into the recirculating flow region to supply the entrainment; the part of the flow that continues downstream suffers a pronounced decrease in eddy length scale, evidently because the larger eddies are torn in two. This phenomenon will occur in all cases where a shear layer reattaches after a prolonged region of separation, either at low speed or in supersonic flow. For simplicity, the discussion in the present paper is confined to low-speed flows.

The Effect of Free-Stream Turbulence on Turbulent Boundary Layers

1983 ◽  
Vol 105 (3) ◽  
pp. 284-289 ◽  
Author(s):  
P. E. Hancock ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Normal Component ◽  
Skin Friction Coefficient ◽  
Nonlinear Dependence ◽  
Length Scale ◽  
Mean Flow ◽  
Stream Length ◽  
Flow Measurements ◽  
Free Stream Turbulence

Mean flow measurements, and some turbulence measurements, have been made in a two-dimensional incompressible constant-pressure (“flat plate”) turbulent boundary layer beneath a nearly homogeneous nearly-isotropic (grid-generated) turbulent free stream. An appreciably nonlinear dependence of the skin-friction coefficient and other boundary layer parameters on rms free-stream turbulence intensity has been confirmed. A much wider range of free-stream length scales has been studied than in previous work, and the results (which agree well with previous data where they overlap) clearly indicate the large effect of free-stream length scale on the response of the boundary layer. The decrease of free-stream turbulence effect with increasing length scale is at least partly attributable to simple reduction of normal-component velocity fluctuations by the solid surface; this would not be the case in free shear layers.

Numerical study of the motions within a slowly precessing sphere at low Ekman number

2001 ◽  
Vol 437 ◽  
pp. 283-299 ◽  
Author(s):  
JÉRÔME NOIR ◽  
D. JAULT ◽  
P. CARDIN
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Numerical Study ◽  
Ekman Layer ◽  
Shear Layers ◽  
Nonlinear Interactions ◽  
Geostrophic Velocity ◽  
Ekman Number ◽  
Geostrophic Shear ◽  
Good Agreement

A geostrophic circulation and a pair of oblique oscillating shear layers arise in a spherical uid cavity contained in a slowly precessing rigid body. Both are caused by the breakdown of the Ekman boundary layer at two critical circles. We rely on numerical modelling to characterize these motions for very small Ekman numbers. Both the O(E1/5) amplitude of the velocity in the oscillating shear layer and the width (also O(E1/5)) of these oblique layers are the result of in ux into the interior from the regions where the Ekman layer breaks down. The oscillating motions are confined to narrow shear layers and their amplitude decays exponentially away from the characteristic surfaces. Nonlinear interactions inside the boundary layer drive the geostrophic shear layer attached to the critical circles. This steady layer, again of O(E1/5) thickness, contains O(E−3/10) velocities. Our results are in good agreement with the experimental measurement by Malkus of the geostrophic velocity arising in a slowly precessing spheroid.

Turbulent structure of high-amplitude pressure peaks within the turbulent boundary layer

2013 ◽  
Vol 735 ◽  
pp. 381-426 ◽  
Author(s):  
S. Ghaemi ◽  
F. Scarano
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Shear Layer ◽  
Pressure Field ◽  
Three Dimensional ◽  
High Amplitude ◽  
Shear Layers ◽  
Turbulent Structure ◽  
Streamwise Vortices ◽  
Ejection Event

AbstractThe positive and negative high-amplitude pressure peaks (HAPP) are investigated in a turbulent boundary layer at $R{e}_{\theta } = $ 1900 in order to identify their turbulent structure. The three-dimensional velocity field is measured within the inner layer of the turbulent boundary layer using tomographic particle image velocimetry (tomo-PIV). The measurements are performed at an acquisition frequency of 10 000 Hz and over a volume of $418\times 149\times 621$ wall units in the streamwise, wall-normal and spanwise directions, respectively. The time-resolved velocity fields are applied to obtain the material derivative using the Lagrangian method followed by integration of the Poisson pressure equation to obtain the three-dimensional unsteady pressure field. The simultaneous volumetric velocity, acceleration, and pressure data are conditionally sampled based on local maxima and minima of wall pressure to analyse the three-dimensional turbulent structure of the HAPPs. Analysis has associated the positive HAPPs to the shear layer structures formed by an upstream sweep of high-speed flow opposing a downstream ejection event. The sweep event is initiated in the outer layer while the ejection of near-wall fluid is formed by the hairpin category of vortices. The shear layers were observed to be asymmetric in the instantaneous visualizations of the velocity and acceleration fields. The asymmetric pattern originates from the spanwise component of temporal acceleration of the ejection event downstream of the shear layer. The analysis also demonstrated a significant contribution of the pressure transport term to the budget of the turbulent kinetic energy in the shear layers. Investigation of the conditional averages and the orientation of the vortices showed that the negative HAPPs are linked to both the spanwise and quasi-streamwise vortices of the turbulent boundary layer. The quasi-streamwise vortices can be associated with the hairpin category of vortices or the isolated quasi-streamwise vortices of the inner layer. A bi-directional analysis of the link between the HAPPs and the hairpin paradigm is also conducted by conditionally averaging the pressure field based on the detection of hairpin vortices using strong ejection events. The results demonstrated positive pressure in the shear layer region of the hairpin model and negative pressure overlapping with the vortex core.

Subharmonic transition to turbulence in a flat-plate boundary layer at Mach number 4.5

1996 ◽  
Vol 317 ◽  
pp. 301-335 ◽  
Author(s):  
N. A. Adams ◽  
L. Kleiser
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Shear Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Shear Layers ◽  
High Shear ◽  
Break Up ◽  
Flat Plate Boundary Layer

The subharmonic transition process of a flat-plate boundary layer at a free-stream Mach number of M∞ = 4.5 and a Reynolds number of 10000 based on free-stream velocity and initial displacement thickness is investigated by direct numerical simulation up to the beginning of turbulence. A second-mode instability superimposed with random noise of low amplitude is forced initially. The secondary subharmonic instability evolves from the noise in accordance with theory and leads to a staggered Λ-vortex pattern. Finite-amplitude Λ-vortices initiate the build-up of detached high-shear layers below and above the critical layer. The detached shear-layer generation and break-up are confined to the relative-subsonic part of the boundary layer. The breakdown to turbulence can be separated into two phases, the first being the break-up of the lower shear layer and the second being the break-up of the upper shear layer. Four levels of subsequent roll-up of the lower, Y-shaped shear layer have been observed, leading to new vortical structures which are unknown from transition at low Mach numbers. The upper shear layer behaviour is similar to that of the well-known high-shear layer in incompressible boundary-layer transition. It is concluded that, as in incompressible flow, turbulence is generated via a cascade of vortices and detached shear layers with successively smaller scales. The different phases of shear-layer break-up are also reflected in the evolution of averaged quantities. A strong decrease of the shape factor, as well as an increase of the skin friction coefficient, and a gradual loss of spanwise symmetry indicate the final breakdown to turbulence, where the mean velocity and temperature profiles approach those measured in fully turbulent flow.

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