scholarly journals Flow phenomena in the very near wake of a flat plate with a circular trailing edge

2014 ◽  
Vol 756 ◽  
pp. 510-543 ◽  
Author(s):  
Man Mohan Rai

AbstractThe very near wake of a flat plate with a circular trailing edge, exhibiting pronounced shedding of wake vortices, is investigated with data from direct numerical simulations (DNSs). Computations were performed for two cases. In the first case the Reynolds numbers based on plate length and thickness were $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}1.255 \times 10^{6}$ and $1.0 \times 10^{4}$, respectively. In the second case the two Reynolds numbers were $3.025 \times 10^{5}$ and $5.0 \times 10^{3}$, respectively. The separating boundary layers are turbulent and statistically identical thus resulting in a wake that is symmetric in the mean. The focus here is on the instability of the detached shear layers and the evolution of rib-vortex-induced localized regions of reverse flow. These regions detach from the main body of reverse flow in the trailing edge region and are convected downstream. The detached shear layers intermittently exhibit unstable behaviour, sometimes resulting in the development of shear-layer vortices as seen in earlier cylinder flow investigations with laminar separating boundary layers. Only a small fraction of the separated turbulent boundary layer experiences this instability, and also rolls up into the initial shed vortices. The instability causes a broadband peak in pressure spectra computed within the shear layers. Phase-averaged intensity and shear stress distributions of the randomly fluctuating component of velocity in the very near wake are also provided here and compared with those obtained in the near wake. The distributions of the production terms in the transport equations for the turbulent stresses are also provided.

2015 ◽  
Vol 774 ◽  
pp. 5-36 ◽  
Author(s):  
Man Mohan Rai

The near and very near wake of a flat plate with a circular trailing edge, with vigorous vortex shedding, is investigated with data from direct numerical simulations (DNS). Computations were performed for four different combinations of the Reynolds numbers based on plate thickness ($D$) and momentum thickness near the trailing edge (${\it\theta}$). Unlike the case of the cylinder, these Reynolds numbers are independent parameters for the flat plate. The objectives of the study are twofold, to investigate the entrainment process when the separating boundary layers are turbulent and to better understand the instability of the detached shear layers (DSLs). A visualization of the entrainment process, the effect of changing the ratio ${\it\theta}/D$ on entrainment and wake-velocity statistics, and a way of understanding entrainment in a phase-averaged sense via distributions of the turbulent transport rate are provided here. The discussion on shear-layer instability focuses on the role of log-layer eddies in the destabilization process, the effect of high-speed streaks in the turbulent boundary layer in the vicinity of the trailing edge on shear-layer vortex generation rates, and a relationship between the prevalence of shear-layer vortex generation and shedding phase that is a result of an interaction between the shedding process and the shear-layer instability mechanism. A power-law relationship between the ratio of shear-layer and shedding frequencies and the Reynolds numbers mentioned above is obtained. A discussion of the relative magnitudes of the exponents is provided. A second power-law relationship between shed-vortex strength and these two Reynolds numbers is also proposed.


2021 ◽  
pp. 1475472X2110238
Author(s):  
Gyuzel Yakhina ◽  
Bastien Dignou ◽  
Yann Pasco ◽  
Stéphane Moreau

Several liner-type treatments (three different rectangular grooves covered by three different low porosity wire-mesh screens) on the trailing edge of a flat plate have been investigated in the anechoic wind-tunnel of Université de Sherbrooke. Far-field acoustic directivity measurements have been achieved at Reynolds numbers based on the plate length from [Formula: see text] to [Formula: see text], yielding radiation maps of all possible liner combinations that are then compared to the reference solid flat plate and to the plate with inserts alone. Noise from the flat plate corresponds to dipolar trailing-edge scattering with an extra shallow hump attributed to the unsteady flow recirculation behind the thick plate. When grooves are added, the latter contribution is amplified and additional cavity noise is observed with several tones and humps. The tones are shown to be resonance between high order modified Rossiter modes and cavity depthwise modes. The hump is a combination of drag dipoles and cavity monopoles from the groove row. The addition of screens always reduces the amplification of the dipolar edge scattering but exhibits very different non-linear responses for the cavity noise. The combination screen with the smallest cells and the insert with the shallowest cavities (corresponding to the same type of treatment applied previously on the Controlled-Diffusion airfoil) yields the lowest levels overall, while the screen with intermediate cell size almost always triggers noise amplification and the screen with a coarse mesh has an intermediate behavior. At high frequencies, the previously reported roughness noise is also observed.


1978 ◽  
Vol 84 (4) ◽  
pp. 705-715 ◽  
Author(s):  
Michio Nishioka ◽  
Tosio Miyagi

The two-dimensional wake of a thin flat plate parallel to the stream was maintained laminar and steady at Reynolds numbers up to 3000 in a low-turbulence wind tunnel. Velocity distributions in the wake were measured in detail for Reynolds numbers from 20 to 3000. One of the interesting results is the appearance of a velocity overshoot, namely that the velocity in the outer part of the shear layer exceeds that of the uniform flow in the vicinity of the trailing edge. Comparisons between the experimental results and Goldstein's theoretical predictions show good agreement in the far wake irrespective of the Reynolds number, but not in the near wake even at higher Reynolds numbers, in particular immediately behind the trailing edge.


1988 ◽  
Vol 189 ◽  
pp. 135-163 ◽  
Author(s):  
A. Haji-Haidari ◽  
C. R. Smith

The velocity field and turbulence structure in the near wake of a thick flat plate with a tapered trailing-edge geometry are examined using both hydrogen-bubble flow visualization and hot-film anemometry measurements. Tests were conducted for Re1 = 8.5 × 105 in the region 0 < x+ < 6400 behind the trailing edge. The probe and visualization results indicate a similarity between both (i) velocity and turbulence structure variations wih x+ in the near wake, and (ii) the corresponding changes in similar flow characteristics with y+ within a turbulent boundary layer. In particular, visualization data in the vicinity of the wake centreline reveal the existence of strong streamwise flow structures in the region close (x+ < 270) to the trailing edge. The streamwise orientation of the observed structures diminishes as x+ increases. From hot-film measurements, two separate regions along the wake centreline can be distinguished: (i) a linear growth region which extends over 0 < x+ < 100, wherein the centreline velocity varies linearly with x+; and (ii) a logarithmic growth region for x+ > 270, wherein the centreline velocity varies as log x+. The similarity in behaviour between these regions and the comparable wall region of a turbulent boundary layer suggests the existence of a common functionality. This similarity is demonstrated by a simple linear relationship of the form y+ = Kx+, which is shown to approximately collapse the velocity behaviour both across a turbulent boundary layer and along the wake centreline to a unified set of empirical relationships.


1960 ◽  
Vol 64 (599) ◽  
pp. 668-672 ◽  
Author(s):  
T. W. F. Moore

Summary:The results of experiments on the reattachment of a laminar boundary layer, separating from a rearward facing step in a flat plate aerofoil, are correlated with the properties of the short leading edge bubble which forms on thin aerofoils near the stall.The experiments, comprising pressure measurements, Pitot explorations, liquid film and smoke studies, indicate that for all Reynolds numbers above the value given by the Owen-KIanfer criterion the reattachment is turbulent behind a stationary air reverse flow vortex bubble. It is also found that the reattachment is laminar for Reynolds numbers below the critical, which further supports Crabtree's interpretation of the Owen-KIanfer criterion in terms of the condition for the growth of turbulent bursts.


2001 ◽  
Vol 123 (2) ◽  
pp. 394-400 ◽  
Author(s):  
Ram Balachandar ◽  
D. Blakely ◽  
M. Tachie ◽  
G. Putz

An experimental study was undertaken to investigate the characteristics of turbulent boundary layers developing on smooth flat plate in an open channel flow at moderately high Froude numbers (0.25<Fr<1.1) and low momentum thickness Reynolds numbers 800<Reθ<2900. The low range of Reynolds numbers and the high Froude number range make the study important, as most other studies of this type have been conducted at high Reynolds numbers and lower Froude numbers (∼0.1). Velocity measurements were carried out using a laser-Doppler anemometer equipped with a beam expansion device to enable measurements close to the wall region. The shear velocities were computed using the near-wall measurements in the viscous subregion. The variables of interest include the longitudinal mean velocity, the turbulence intensity, and the velocity skewness and flatness distributions across the boundary layer. The applicability of a constant Coles’ wake parameter (Π=0.55) to open channel flows has been discounted. The effect of the Froude number on the above parameters was also examined.


1969 ◽  
Vol 36 (4) ◽  
pp. 673-681 ◽  
Author(s):  
S. J. Shamroth

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.


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