skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Coherent motions in a turbulent wake of an axisymmetric bluff body
The wake flow past an axisymmetric body of revolution at a diameter-based Reynolds number$$Re=u_{\infty }D/\nu =5000$$is investigated via a direct numerical simulation. The study is focused on identification of coherent vortical motions and the dominant frequencies in this flow. Three dominant coherent motions are identified in the wake: the vortex shedding motion with the frequency of$$St=fD/u_{\infty }=0.27$$, the bubble pumping motion with$$St=0.02$$, and the very-low-frequency (VLF) motion originated in the very near wake of the body with the frequency$$St=0.002$$–$$0.005$$. The vortex shedding pattern is demonstrated to follow a reflectional symmetry breaking mode, whereas the vortex loops are shed alternatingly from each side of the vortex shedding plane, but are subsequently twisted and tangled, giving the resulting wake structure a helical spiraling pattern. The bubble pumping motion is confined to the recirculation region and is a result of a Görtler instability. The VLF motion is related to a stochastic destabilisation of a steady symmetric mode in the near wake and manifests itself as a slow, precessional motion of the wake barycentre. The VLF mode with$$St=0.005$$is also detectable in the intermediate wake and may be associated with a low-frequency radial flapping of the shear layer.  more » « less
Award ID(s):
1944568 1707075
PAR ID:
10483348
Author(s) / Creator(s):
;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
962
ISSN:
0022-1120
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Journal of Fluid Mechanics)
    Dynamic stall at low Reynolds numbers,$$Re \sim O(10^4)$$, exhibits complex flow physics with co-existing laminar, transitional and turbulent flow regions. Current state-of-the-art stall onset criteria use parameters that rely on flow properties integrated around the leading edge. These include the leading edge suction parameter or$$LESP$$(Rameshet al.,J. Fluid Mech., vol. 751, 2014, pp. 500–538) and boundary enstrophy flux or$$BEF$$(Sudharsanet al.,J. Fluid Mech., vol. 935, 2022, A10), which have been found to be effective for predicting stall onset at moderate to high$$Re$$. However, low-$$Re$$flows feature strong vortex-shedding events occurring across the entire airfoil surface, including regions away from the leading edge, altering the flow field and influencing the onset of stall. In the present work, the ability of these stall criteria to effectively capture and localize these vortex-shedding events in space and time is investigated. High-resolution large-eddy simulations for an SD7003 airfoil undergoing a constant-rate, pitch-up motion at two$$Re$$(10 000 and 60 000) and two pitch rates reveal a rich variety of unsteady flow phenomena, including instabilities, transition, vortex formation, merging and shedding, which are described in detail. While stall onset is reflected in both$$LESP$$and$$BEF$$, local vortex-shedding events are identified only by the$$BEF$$. Therefore,$$BEF$$can be used to identify both dynamic stall onset and local vortex-shedding events in space and time. 
    more » « less
  2. ; ; (, Journal of Fluid Mechanics)
    We investigate the effects of fluid elasticity on the flow forces and the wake structure when a rigid cylinder is placed in a viscoelastic flow and is forced to oscillate sinusoidally in the transverse direction. We consider a two-dimensional, uniform, incompressible flow of viscoelastic fluid at$$Re=100$$, and use the FENE-P model to represent the viscoelastic fluid. We study how the flow forces and the wake patterns change as the amplitude of oscillations,$$A^*$$, the frequency of oscillations (inversely proportional to a reduced velocity,$$U^*$$), the Weissenberg number,$$Wi$$, the square of maximum polymer extensibility,$$L^2$$, and the viscosity ratio,$$\beta$$, change individually. We calculate the lift coefficient in phase with cylinder velocity to determine the range of different system parameters where self-excited oscillations might occur if the cylinder is allowed to oscillate freely. We also study the effect of fluid elasticity on the added mass coefficient as these parameters change. The maximum elastic stress of the fluid occurs in between the vortices that are observed in the wake. We observe a new mode of shedding in the wake of the cylinder: in addition to the primary vortices that are also observed in the Newtonian flows, secondary vortices that are caused entirely by the viscoelasticity of the fluid are observed in between the primary vortices. We also show that, for a constant$$Wi$$, the strength of the polymeric stresses increases with increasing reduced velocity or with decreasing amplitude of oscillations. 
    more » « less
  3. ; (, Journal of the Institute of Mathematics of Jussieu)
    Abstract What proportion of integers$$n \leq N$$may be expressed as$$x^2 + dy^2$$for some$$d \leq \Delta $$, with$$x,y$$integers? Writing$$\Delta = (\log N)^{\log 2} 2^{\alpha \sqrt {\log \log N}}$$for some$$\alpha \in (-\infty , \infty )$$, we show that the answer is$$\Phi (\alpha ) + o(1)$$, where$$\Phi $$is the Gaussian distribution function$$\Phi (\alpha ) = \frac {1}{\sqrt {2\pi }} \int ^{\alpha }_{-\infty } e^{-x^2/2} dx$$. A consequence of this is a phase transition: Almost none of the integers$$n \leq N$$can be represented by$$x^2 + dy^2$$with$$d \leq (\log N)^{\log 2 - \varepsilon }$$, but almost all of them can be represented by$$x^2 + dy^2$$with$$d \leq (\log N)^{\log 2 + \varepsilon}\kern-1.5pt$$. 
    more » « less
  4. ; (, Forum of Mathematics, Sigma)
    Abstract Given a permutation statistic$$\operatorname {\mathrm {st}}$$, define its inverse statistic$$\operatorname {\mathrm {ist}}$$by. We give a general approach, based on the theory of symmetric functions, for finding the joint distribution of$$\operatorname {\mathrm {st}}_{1}$$and$$\operatorname {\mathrm {ist}}_{2}$$whenever$$\operatorname {\mathrm {st}}_{1}$$and$$\operatorname {\mathrm {st}}_{2}$$are descent statistics: permutation statistics that depend only on the descent composition. We apply this method to a number of descent statistics, including the descent number, the peak number, the left peak number, the number of up-down runs and the major index. Perhaps surprisingly, in many cases the polynomial giving the joint distribution of$$\operatorname {\mathrm {st}}_{1}$$and$$\operatorname {\mathrm {ist}}_{2}$$can be expressed as a simple sum involving products of the polynomials giving the (individual) distributions of$$\operatorname {\mathrm {st}}_{1}$$and$$\operatorname {\mathrm {st}}_{2}$$. Our work leads to a rederivation of Stanley’s generating function for doubly alternating permutations, as well as several conjectures concerning real-rootedness and$$\gamma $$-positivity. 
    more » « less
  5. ; (, Flow)
    We present high-fidelity numerical simulations of the interaction of an oblique shock impinging on the turbulent boundary layer developed over a rectangular flexible panel, replicating wind tunnel experiments by Daubet al.(AIAA Journal, vol. 54, 2016, pp. 670–678). The incoming free-stream Mach and unit Reynolds numbers are$$M_{\infty } = 3$$and$$Re_{\infty }=49.4\times 10^6 {\rm m}^{-1}$$, respectively. The reference boundary layer thickness upstream of the interaction with the shock is$$\delta _0 = 4$$mm. The oblique shock is generated with a rotating wedge initially parallel to the flow that increases the deflection angle up to$$\theta _{{max}} = 17.5^{\circ }$$within approximately$$15$$ms. A loosely coupled partitioned flow–structure interaction simulation methodology is used, combining a finite-volume flow solver of the compressible wall-modelled large-eddy simulation equations, an isoparametric finite-element solid mechanics solver and a spring-system-based mesh deformation solver. Simulations are conducted with rigid and flexible panels, and the results compared to elucidate the effects of panel flexibility on the interaction. Three-dimensional effects are evaluated by conducting simulations with both full ($$50 \delta _0$$) and reduced ($$5\delta _0$$) spanwise panel width, the latter enforcing spanwise periodicity. Panel flexibility is found to increase the separation bubble size and modify its spectral dynamics. Time- and spanwise-averaged streamwise profiles of the wall pressure exhibit a drop over the flexible panel prior to the interaction and a reduced peak pressure in comparison with the rigid case. Spectral analyses of wall pressure data indicate that the low-frequency motions have a similar spectral distribution for the rigid and flexible cases, but the flexible case shows a wider region dominated by low-frequency motions and traces of the panel vibration on the wall pressure signal. The sensitivity of the interaction to small variations in the wedge extent and incoming boundary layer thickness is evaluated. Predictions obtained from lower-fidelity modelling simplifications are also assessed. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email