Laminar to Turbulent Buoyant Vortex Ring Regime in Terms of Reynolds Number, Bond Number, and Weber Number

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Xueying Yan ◽  
Rupp Carriveau ◽  
David S. K. Ting
Keyword(s):  
Reynolds Number ◽  
Vortex Ring ◽  
Weber Number ◽  
High Speed ◽  
Reynolds Numbers ◽  
Bond Number ◽  
Vortex Rings ◽  
Transition Regime ◽  
Turbulent Vortex ◽  
Buoyant Vortex Rings

When buoyant vortex rings form, azimuthal disturbances occur on their surface. When the magnitude of the disturbance is sufficiently high, the ring will become turbulent. This paper establishes conditions for categorization of a buoyant vortex ring as laminar, transitional, or turbulent. The transition regime of enclosed-air buoyant vortex rings rising in still water was examined experimentally via two high-speed cameras. Sequences of the recorded pictures were analyzed using matlab. Key observations were summarized as follows: for Reynolds number lower than 14,000, Bond number below 30, and Weber number below 50, the vortex ring could not be produced. A transition regime was observed for Reynolds numbers between 40,000 and 70,000, Bond numbers between 120 and 280, and Weber number between 400 and 800. Below this range, only laminar vortex rings were observed, and above, only turbulent vortex rings.

Initial motion of a viscous vortex ring

1994 ◽  
Vol 446 (1928) ◽  
pp. 589-599 ◽  
Keyword(s):  
Reynolds Number ◽  
Asymptotic Analysis ◽  
Vortex Ring ◽  
Kinematic Viscosity ◽  
Reynolds Numbers ◽  
Initial Radius ◽  
Dimensionless Form ◽  
Ring Radius ◽  
Initial Motion ◽  
Matched Asymptotic Analysis

The behaviour of a viscous vortex ring is examined by a matched asymptotic analysis up to three orders. This study aims at investigating how much the location of maximum vorticity deviates from the centroid of the vortex ring, defined by P. G. Saffman (1970). All the results are presented in dimensionless form, as indicated in the following context. Let Γ be the initial circulation of the vortex ring, and R denote the ring radius normalized by its initial radius R i . For the asymptotic analysis, a small parameter ∊ = ( t / Re ) ½ is introduced, where t denotes time normalized by R 2 i / Γ , and Re = Γ/v is the Reynolds number defined with Γ and the kinematic viscosity v . Our analysis shows that the trajectory of maximum vorticity moves with the velocity (normalized by Γ/R i ) U m = – 1/4π R {ln 4 R /∊ + H m } + O (∊ ln ∊), where H m = H m ( Re, t ) depends on the Reynolds number Re and may change slightly with time t for the initial motion. For the centroid of the vortex ring, we obtain the velocity U c by merely replacing H m by H c , which is a constant –0.558 for all values of the Reynolds number. Only in the limit of Re → ∞, the values of H m and H c are found to coincide with each other, while the deviation of H m from the constant H c is getting significant with decreasing the Reynolds number. Also of interest is that the radial motion is shown to exist for the trajectory of maximum vorticity at finite Reynolds numbers. Furthermore, the present analysis clarifies the earlier discrepancy between Saffman’s result and that obtained by C. Tung and L. Ting (1967).

Investigations Of Pressure Pulsations In A Model Of Draft Tube Of Hydraulic Turbine Caused By Vortex Rings

2016 ◽  
Vol 11 (4) ◽  
pp. 25-32
Author(s):  
Sergey Skripkin ◽  
Mikhail Tsoy ◽  
Sergey Shtork ◽  
Pavel Kuibin
Keyword(s):  
Vortex Ring ◽  
High Speed ◽  
Draft Tube ◽  
Hydraulic Turbine ◽  
Vortex Rings ◽  
Experimental Investigations ◽  
Visualization Technique ◽  
Vortex Rope ◽  
Hydro Turbine ◽  
Hydraulic Turbines

Current work is devoted to experimental investigations of behavior of precessing vortex rope in a draft tube model of hydraulic turbine. We used combination of stationary and freely rotating swirlers as a hydro turbine model. Such construction provides velocity distribution on the draft tube inlet close to distribution in natural hydraulic turbines operated at non-optimal conditions. The phenomenon of precessing vortex rope reconnection with further formation of vortex ring was founded in this experimental research using high-speed visualization technique. Synchronization of highspeed visualization and pressure measurements allowed us to relate pressure shock on the draft tube wall with vortex ring moving along wall.

scholarly journals Blockage Correction and Reynolds Number Dependency of an Alpine Skier: A Comparison Between Two Closed-Section Wind Tunnels

Proceedings ◽  
2020 ◽  
Vol 49 (1) ◽  
pp. 19
Author(s):  
Ola Elfmark ◽  
Robert Reid ◽  
Lars Morten Bardal
Keyword(s):  
Reynolds Number ◽  
High Speed ◽  
Absolute Error ◽  
Reynolds Numbers ◽  
Correction Method ◽  
Wind Tunnels ◽  
Alpine Skier ◽  
Blockage Correction ◽  
Reynolds Number Dependency ◽  
The Impact

The purpose of this study was to investigate the impact of blockage effect and Reynolds Number dependency by comparing measurements of an alpine skier in standardized positions between two wind tunnels with varying blockage ratios and speed ranges. The results indicated significant blockage effects which need to be corrected for accurate comparison between tunnels, or for generalization to performance in the field. Using an optimized blockage constant, Maskell’s blockage correction method improved the mean absolute error between the two wind tunnels from 7.7% to 2.2%. At lower Reynolds Numbers (<8 × 105, or approximately 25 m/s in this case), skier drag changed significantly with Reynolds Number, indicating the importance of testing at competition specific wind speeds. However, at Reynolds Numbers above 8 × 105, skier drag remained relatively constant for the tested positions. This may be advantageous when testing athletes from high speed sports since testing at slightly lower speeds may not only be safer, but may also allow the athlete to reliably maintain difficult positions during measurements.

Secondary instability and subcritical transition of the leading-edge boundary layer

2016 ◽  
Vol 792 ◽  
pp. 682-711 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Instability ◽  
Bypass Transition ◽  
Wall Suction ◽  
Transition Mechanism

The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as$Re\approx 175$, i.e. far below the linear critical Reynolds number$Re_{crit}\approx 583$of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above$Re_{tr}\approx 250$. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number$Re_{tr}\approx 250$at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

Turbulent Annular Pipe Flow in Subcritical Transition Regime: Direct Numerical Simulation of a Large Domain

2015 ◽  
Author(s):  
Takahiro Ishida ◽  
Takahiro Tsukahara
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Numbers ◽  
Radius Ratio ◽  
Transition Regime ◽  
Transitional Regime ◽  
Large Domain ◽  
High Reynolds ◽  
Annular Pipe ◽  
Transition Scenario

We performed direct numerical simulations of annular Poiseuille flow (APF) with a radius ratio of η (= rin/rout) = 0.8, in order to investigate the subcritical transition scenario from the developed turbulent state to the laminar state. In previous studies on annular Poiseuille flow, the flows at high Reynolds numbers were well examined and various turbulence statistics were obtained for several η, because of their dependence on η. Since the transitional APF is still unclear, we investigate annular Poiseuille flows in the transitional regime through the large-domain simulations in a range of the friction Reynolds number from Reτ = 150 down to 56. At a transitional Reynolds number, weak-fluctuation regions occur intermittently and regularly in the flow field, and the localized turbulence appears in the form of banded patterns same as in plane Poiseuille flow (PPF). The flow system of APF with a high radius ratio η ≈ 1 can be regarded as PPF and, hence, the transition regime in high radius-ratio of APF and in PPF should be analogous. However, in APF, the banded structure takes on helical shape around the inner cylinder, since APF is a closed system in the spanwise (azimuthal) direction. In this paper, the (dis-)similarity between APF and PPF is discussed.

Recent Research on Cascade-Flow Problems

1966 ◽  
Vol 88 (1) ◽  
pp. 221-228 ◽  
Author(s):  
H. Schlichting ◽  
A. Das
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
High Speed ◽  
Research Work ◽  
Reynolds Numbers ◽  
Tip Clearance ◽  
Flow Problems ◽  
Flow Losses ◽  
Cascade Flow ◽  
Wide Range

A survey is given of extensive research work on cascade-flow problems carried out in recent years in Germany. A considerable part of this work was done in the Variable Density High Speed Cascade Wind Tunnel of the Deutsche Forschungsanstalt fu¨r Luftfahrt at Braunschweig, in which the Reynolds number and the Mach number of the cascade can be varied independently. For compressor cascades with blades of different thickness ratio extensive measurements of the aerodynamic coefficients have been carried out in a wide range of Mach numbers and Reynolds numbers. For very low Reynolds numbers, as they occur for jet engines in high-altitude flight, the influence of turbulence level on loss coefficients has been investigated. Furthermore, comprehensive investigations on secondary-flow losses are reported. The most important parameters in this connection are the ratio of blade length to blade chord, the tip clearance, the Reynolds number, and the deflection of the flow in the cascade. The influence of all these parameters on the secondary-flow losses has been clarified to a certain extent.

Formation of vortex rings from falling drops

1967 ◽  
Vol 29 (1) ◽  
pp. 177-185 ◽  
Author(s):  
David S. Chapman ◽  
P. R. Critchlow
Keyword(s):  
Reynolds Number ◽  
Vortex Ring ◽  
Liquid Drop ◽  
Prolate Spheroid ◽  
Ring Formation ◽  
Vortex Rings ◽  
Surface Tensions ◽  
Wide Range ◽  
The Moment

A study of the formation of vortex rings when a liquid drop falls into a stationary bath of the same liquid has been made. The investigation covered liquids with a wide range in surface tensions, densities and viscosities. The results confirm the reported existence of optimum dropping height from which the drop develops into a superior vortex ring. The optimum heights are analysed, by a photographic study, in terms of the liquid drop oscillation. It is found that vortex rings are formed best if the drop is spherical and changing from an oblate to a prolate spheroid at the moment of contact with the bath. A Reynolds number has been determined for vortex rings produced at optimum dropping heights; these numbers are approximately 1000. A possible mechanism for the ring formation is suggested.

scholarly journals Compressible starting jet: pinch-off and vortex ring–trailing jet interaction

2017 ◽  
Vol 817 ◽  
pp. 560-589 ◽  
Author(s):  
Juan José Peña Fernández ◽  
Jörn Sesterhenn
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Vortex Ring ◽  
Pressure Ratio ◽  
Reynolds Numbers ◽  
Chamber Pressure ◽  
Vortex Interaction ◽  
Dominant Feature ◽  
Chamber Temperature ◽  
Starting Jet

The dominant feature of the compressible starting jet is the interaction between the emerging vortex ring and the trailing jet. There are two types of interaction: the shock–shear layer–vortex interaction and the shear layer–vortex interaction. The former is clearly not present in the incompressible case, since there are no shocks. The shear layer–vortex interaction has been reported in the literature in the incompressible case and it was found that compressibility reduces the critical Reynolds number for the interaction. Four governing parameters describe the compressible starting jet: the non-dimensional mass supply, the Reynolds number, the reservoir to unbounded chamber temperature ratio and the reservoir to unbounded chamber pressure ratio. The latter parameter does not exist in the incompressible case. For large Reynolds numbers, the vortex pinch-off takes place in a multiple way. We studied the compressible starting jet numerically and found that the interaction strongly links the vortex ring and the trailing jet. The shear layer–vortex interaction leads to a rapid breakdown of the head vortex ring when the flow impacted by the Kelvin–Helmholtz instabilities is ingested into the head vortex ring. The shock–shear layer–vortex interaction is similar to the noise generation mechanism of broadband shock noise in a continuously blowing jet and results in similar sound pressure amplitudes in the far field.

Numerical investigation of wake flow regimes behind a high-speed rotating circular cylinder in steady flow

2019 ◽  
Vol 878 ◽  
pp. 875-906
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu ◽  
Lin Lu
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Rotation Rate ◽  
High Speed ◽  
Three Dimensional ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Rotating Circular Cylinder

Flow around a high-speed rotating circular cylinder for $Re\leqslant 500$ is investigated numerically. The Reynolds number is defined as $UD/\unicode[STIX]{x1D708}$ with $U$, $D$ and $\unicode[STIX]{x1D708}$ being the free-stream flow velocity, the diameter of the cylinder and the kinematic viscosity of the fluid, respectively. The aim of this study is to investigate the effect of a high rotation rate on the wake flow for a range of Reynolds numbers. Simulations are performed for Reynolds numbers of 100, 150, 200, 250 and 500 and a wide range of rotation rates from 1.6 to 6 with an increment of 0.2. Rotation rate is the ratio of the rotational speed of the cylinder surface to the incoming fluid velocity. A systematic study is performed to investigate the effect of rotation rate on the flow transition to different flow regimes. It is found that there is a transition from a two-dimensional vortex shedding mode to no vortex shedding mode when the rotation rate is increased beyond a critical value for Reynolds numbers between 100 and 200. Further increase in rotation rate results in a transition to three-dimensional flow which is characterized by the presence of finger-shaped (FV) vortices that elongate in the wake of the cylinder and very weak ring-shaped vortices (RV) that wrap the surface of the cylinder. The no vortex shedding mode is not observed at Reynolds numbers greater than or equal to 250 since the flow remains three-dimensional. As the rotation rate is increased further, the occurrence frequency and size of the ring-shaped vortices increases and the flow is dominated by RVs. The RVs become bigger in size and the flow becomes chaotic with increasing rotation rate. A detailed analysis of the flow structures shows that the vortices always exist in pairs and the strength of separated shear layers increases with the increase of rotation rate. A map of flow regimes on a plane of Reynolds number and rotation rate is presented.

Numerical Modeling of Spores Dispersal of Sphagnum Moss Using ANSYS FLUENT

2017 ◽  
Author(s):  
Dwight L. Whitaker ◽  
Robert Simsiman ◽  
Emily S. Chang ◽  
Samuel Whitehead ◽  
Hesam Sarvghad-Moghaddam
Keyword(s):  
Vortex Ring ◽  
High Speed ◽  
Cost Effective ◽  
Video Data ◽  
Vortex Rings ◽  
Peat Moss ◽  
Ansys Fluent ◽  
Formation Number ◽  
Piston Stroke ◽  
First Time

The common peat moss, Sphagnum, is able to explosively disperse its spores by producing a vortex ring from a pressurized sporophyte to carry a cloud of spores to heights over 15 cm where the turbulent boundary layer can lift and carry them indefinitely. While vortex ring production is fairly common in the animal kingdom (e.g. squid, jellyfish, and the human heart), this is the first report of vortex rings generated by a plant. In other cases of biologically created vortex rings, it has been observed that vortices are produced with a maximum formation number of L/D = 4, where L is the length of the piston stroke and D is the diameter of the outlet. At this optimal formation number, the circulation and thus impulse of the vortex ring is maximized just as the ring is pinched off. In the current study, we modeled this dispersal phenomenon for the first time using ANSYS FLUENT 17.2. The spore capsule at the time of burst was approximated as a cylinder with a thin cylindrical cap attached to it. They were then placed inside a very large domain representing the air in which the expulsion was modeled. Due to the symmetry of our model about the central axis, we performed a 2D axisymmetric simulation. Also, due the complexity of the fluid domain as a result of the capsule-cap interface, as well as the need for a dynamic mesh for simulating the motion of the cap, first a mesh study was performed to generate an efficient mesh in order to make simulations computationally cost-effective. The domain was discretized using triangular elements and the mesh was refined at the capsule-cap interface to accurately capture the ring vortices formed by the expulsed cap. The dispersal was modeled using a transient simulation by setting a pressure difference between inside of the capsule and the surrounding atmospheric air. Pressure and vorticity contours were recorded at different time instances. Our simulation results were interpreted and compared to high-speed video data of sporophyte expulsions to deduce the pressure within the capsule upon dispersal, as well as the formation number of resulting vortex rings. Vorticity contours predicted by our model were in agreement with the experimental results. We hypothesized that the vortex rings from Sphagnum are sub-optimal since a slower vortex bubble would carry spores more effectively than a faster one.

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