Role of slipstream instability in formation of counter-rotating vortex rings ahead of a compressible vortex ring

2014 ◽  
Vol 753 ◽  
pp. 29-48 ◽  
Author(s):  
C. L. Dora ◽  
T. Murugan ◽  
S. De ◽  
Debopam Das

AbstractCounter-rotating vortex rings (CRVRs) are observed to form ahead of a primary compressible vortex ring that is generated at the open end of a shock tube at sufficiently high Mach numbers. In most of the earlier studies, the embedded shock strength has been asserted as the cause for the formation of CRVRs. In the present study, particle image velocimetry (PIV) measurements and high-order numerical simulations show that CRVRs do not form in the absence of a Mach disk in the sonic under-expanded jet behind the primary vortex ring. Kelvin–Helmholtz-type shear flow instability of the slipstream originating from the triple point of the Mach disk and subsequent eddy pairing, as observed by Rikanati et al. (Phys. Rev. Lett., vol. 96, 2006, art. 174503) in shock-wave Mach reflection, is found to be responsible for CRVR formation. The growth rate of the slipstream in the present problem follows the model proposed by them. The parameters influencing the formation of CRVRs as well as their dynamics is investigated. It is found that the strength of the Mach disk and its duration of persistence results in an exit impulse that determines the number of CRVRs formed.

2018 ◽  
Vol 837 ◽  
pp. 729-764 ◽  
Author(s):  
Yang Xu ◽  
Jin-Jun Wang ◽  
Li-Hao Feng ◽  
Guo-Sheng He ◽  
Zhong-Yi Wang

For the first time, an experiment has been conducted to investigate synthetic jet laminar vortex rings impinging onto porous walls with different geometries by time-resolved particle image velocimetry. The geometry of the porous wall is changed by varying the hole diameter on the wall (from 1.0 mm to 3.0 mm) when surface porosity is kept constant ($\unicode[STIX]{x1D719}=75\,\%$). The finite-time Lyapunov exponent and phase-averaged vorticity field derived from particle image velocimetry data are presented to reveal the evolution of the vortical structures. A mechanism associated with vorticity cancellation is proposed to explain the formation of downstream transmitted vortex rings; and both the vortex ring trajectory and the time-mean flow feature are compared between different cases. It is found that the hole diameter significantly influences the evolution of the flow structures on both the upstream and downstream sides of the porous wall. In particular, for a porous wall with a small hole diameter ($d_{h}^{\ast }=0.067$, 0.10 and 0.133), the transmitted finger-type jets will reorganize into a well-formed transmitted vortex ring in the downstream flow. However, for the case of a large hole diameter of $d_{h}^{\ast }=0.20$, the transmitted vortex ring is not well formed because of insufficient vorticity cancellation. Additionally, the residual vorticity gradually evolves into discrete jet-like structures downstream, which further weaken the intensity of the transmitted vortex ring. Consequently, the transmitted flow structures for the $d_{h}^{\ast }=0.20$ case would lose coherence more easily (or probably even transition to turbulence), resulting in a faster decay of the axial velocity and stronger entrainment of the transmitted jet. For all porous wall cases, the velocity profile of the transmitted jet exhibits self-similar behaviour in the far field ($z/D_{0}\geqslant 6.03$), which agrees well with the velocity distribution of free synthetic jets. With the help of the control-volume approach, the time-mean drag of the porous wall is evaluated experimentally for the first time. It is shown that the porous wall drag increases with the decrease in the hole diameter. Moreover, for a porous wall with a small hole diameter ($d_{h}^{\ast }=0.067$, 0.10 and 0.133), it appears that the porous wall drag mainly derives from the viscous effect. However, as $d_{h}^{\ast }$ increases to 0.20, the form drag associated with the porous wall geometry becomes significant.


1998 ◽  
Vol 360 ◽  
pp. 121-140 ◽  
Author(s):  
MORTEZA GHARIB ◽  
EDMOND RAMBOD ◽  
KARIM SHARIFF

The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.


Author(s):  
Sun-Chul Kim

Point vortex motion on the surface of a spheroid is studied. Exact dynamical equations from the corresponding Hamiltonian are constructed by computing the conformal metric which induces a modified stereographic projection. As a concrete example, the motion of point vortices at the same latitude (called the point vortex ring ) is investigated as an extension of the sphere case. The role of eccentricity to the stability of the rotating motion is analysed. The influence of a pole vortex is also discussed.


2021 ◽  
Vol 28 (2) ◽  
pp. 022309
Author(s):  
A. E. Fraser ◽  
P. W. Terry ◽  
E. G. Zweibel ◽  
M. J. Pueschel ◽  
J. M. Schroeder

2013 ◽  
Vol 554-557 ◽  
pp. 1738-1750 ◽  
Author(s):  
Hua Gui Zhang ◽  
Khalid Lamnawar ◽  
Abderrahim Maazouz

This work aims to highlight the importance of interphase triggered from interdiffusion at neighboring layers on controlling the interfacial flow instability of multilayer coextrusion based on a compatible bilayer system consist of poly(methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF) melt streams. A fundamental rheological measurement on the bilayer structures provides a good strategy to probe the mutual diffusion process occurred at neighboring layers and to quantify the rheology and thickness of the interphase generated thereof. By implementing steady shear measurements on the multilayer’s, subtle interfacial slippage can be observed at a condition of short welding time and rather high shear rate due to the disentanglement of chains at the interphase. Pre-shear at an early stage on the multilayer was found to greatly promote the homogenizing process by inducing branched structures and hence increasing interfacial area. In coextrusion, some key classical decisive parameters concerning the interfacial instability phenomena such as viscosity ratio, thickness ratio and elasticity ratio, etc. were highlighted. These key factors that are significant in controlling the interfacial stability of coextrusion in an incompatible system seem not that important in a compatible system. In comparison to the severe flow instability observed in the coextrusion of PMMA/PE incompatible bilayer, the coextrusion of PMMA/PVDF compatible bilayer appears to be smooth without apparent interfacial flow instability due to the presence of the interphase. Interdiffusion can reduce (even eliminate) the interfacial flow instability of coextrusion despite of the very high viscosity ratio of PVDF versus PMMA at low temperatures. Indeed, in the coextrusion process, on one hand, the interdiffusion should be studied by taking into account of the effect of polymer chain orientation which was demonstrated to decelerate the diffusion coefficient. On the other hand, the interfacial shear stress was able to promote mixing and homogenizing process at the interface, which favours the development of the interphase and guarantees the stable interfacial flow. The degree of the interphase is related to a lot of parameters like contact time, processing temperature, interfacial shear stress and compatibility of the polymers, etc. Therefore, apart from the classical mechanical parameters, the interphase created from the interdiffusion should be taken into consideration as an important factor on determining the interfacial instability phenomena. References [1] H. Zhang, K. Lamnawar, A. Maazouz, Rheological modeling of the diffusion process and the interphase of symmetrical bilayers based on PVDF and PMMA with varying molecular weights. Rheol. Acta 51 (2012) 691-711 [2] H. Zhang, K. Lamnawar, A. Maazouz, Rheological modeling of the mutual diffusion and the interphase development for an asymmetrical bilayer based on PMMA and PVDF model compatible polymers, Macromolecules (2012), Doi: http://dx.doi.org/10.1021/ma301620a [3] H. Zhang, K. Lamnawar, A. Maazouz, Role of the interphase in the interfacial flow stability of multilayer coextrusion based on PMMA and PVDF compatible polymers, to be submitted. [4] K. Lamnawar, A. Maazouz, Role of the interphase in the flow stability of reactive coextruded multilayer polymers, Polymer Engineering & Science, 49, (2009), 727 - 739 [5] K. Lamnawar, H. Zhang, A. Maazouz, one chapter” State of the art in co-extrusion of multilayer polymers: experimental and fundamental approaches” in Encyclopedia of Polymer Science and Technology (wiley library) (feature article)


2011 ◽  
Vol 133 (1) ◽  
Author(s):  
F. Aloui ◽  
E. Berrich ◽  
D. Pierrat

In some industrial processes, and especially in agrofood industries, the cleaning in place mechanism used for hydraulic circuits plays an important role. This process needs a good knowledge of the hydrodynamic flows to determinate the appropriate parameters that assure a good cleaning of these circuits without disassembling them. Generally, different arrangements are present in these hydraulic circuits, such as expansions, diffusers, and elbows. The flow crossing these singularities strongly affects the process of cleaning in place. This work is then a contribution to complete recent studies of “aliments quality security” project to ameliorate the quality of the cleaning in place. It presents experimental and numerical investigations of a confined turbulent flow behavior across a conical diffuser (2α=16 deg). The role of a perturbation caused by the presence of an elbow in the test section, upstream of the progressive enlargement, was studied. The main measurements were the static pressure and the instantaneous velocity fields using the particle image velocimetry (PIV). Post-processing of these PIV measurements were adopted using the Γ2 criterion for the vortices detection and the proper orthogonal decomposition (POD) technique to extract the most energetic modes contained in the turbulent flow and to the turbulent flow filtering. A database has been also constituted and was used to test the validity of the most models of turbulence, and in particular, a variant of the shear stress transport (SST) model.


1986 ◽  
Vol 170 ◽  
pp. 21-51 ◽  
Author(s):  
J. M. Russell

The analog of Whitham's law of conservation of wave action density is derived in the case of Rayleigh instability waves. The analysis allows for wave propagation in two space dimensions, non-unidirectionality of the background flow velocity profiles and weak horizontal nonuniformity and unsteadiness of those profiles. The small disturbance equations of motion in the Eulerian flow description are subject to a change of dependent variable in which the new variable represents the pressure-driven part of a disturbance material coordinate function as a function of the Cartesian spatial coordinates and time. Several variational principles expressing the physics of the small disturbance equations of motion are presented in terms of this new variable. A law of conservation of ‘bilinear wave action density’ is derived by a method intermediate between those of Jimenez and Whitham (1976) and Hayes (1970a). The distinction between the observed square amplitude of an amplified wavetrain and the wave action density is discussed. Three types of algebraic focusing are discussed, the first being the far-field ‘caustics’, the second being near-field ‘movable singularities’, and the third being a focusing mechanism due to Landahl (1972) which we here derive under somewhat weaker hypotheses.


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