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).

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.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

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.

Triple velocity correlations in isotropic turbulence

1951 ◽  
Vol 47 (1) ◽  
pp. 146-157 ◽  
Author(s):  
R. W. Stewart
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Mean Wind Speed ◽  
The Mean ◽  
Mesh Grid ◽  
Working Section

AbstractThe triple velocity correlation, in turbulence produced by inserting a square-mesh grid near the beginning of the working section of a wind tunnel, has been measured for mesh Reynolds numbers of RM = 5300, 21,200 and 42,400 (RM = UM/ν, where U is the mean wind speed in the working section of the tunnel and M is the centre to centre spacing of the rods making up the grid; ν is the kinematic viscosity of air). At the lowest Reynolds number the correlation has been measured at distances downstream of the grid varying from 20 to 120M. This range covers practically all of the initial period of the decay of turbulence, where the turbulent intensity varies as t−1.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

scholarly journals Turbulence model performance for ventilation components pressure losses

2021 ◽  
Author(s):  
Karsten Tawackolian ◽  
Martin Kriegel
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Pressure Loss ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Test Case ◽  
Pressure Losses ◽  
Loss Coefficients ◽  
Near Wall

AbstractThis study looks to find a suitable turbulence model for calculating pressure losses of ventilation components. In building ventilation, the most relevant Reynolds number range is between 3×104 and 6×105, depending on the duct dimensions and airflow rates. Pressure loss coefficients can increase considerably for some components at Reynolds numbers below 2×105. An initial survey of popular turbulence models was conducted for a selected test case of a bend with such a strong Reynolds number dependence. Most of the turbulence models failed in reproducing this dependence and predicted curve progressions that were too flat and only applicable for higher Reynolds numbers. Viscous effects near walls played an important role in the present simulations. In turbulence modelling, near-wall damping functions are used to account for this influence. A model that implements near-wall modelling is the lag elliptic blending k-ε model. This model gave reasonable predictions for pressure loss coefficients at lower Reynolds numbers. Another example is the low Reynolds number k-ε turbulence model of Wilcox (LRN). The modification uses damping functions and was initially developed for simulating profiles such as aircraft wings. It has not been widely used for internal flows such as air duct flows. Based on selected reference cases, the three closure coefficients of the LRN model were adapted in this work to simulate ventilation components. Improved predictions were obtained with new coefficients (LRNM model). This underlined that low Reynolds number effects are relevant in ventilation ductworks and give first insights for suitable turbulence models for this application. Both the lag elliptic blending model and the modified LRNM model predicted the pressure losses relatively well for the test case where the other tested models failed.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Thermoelectric Generation with Impinging Nano-Jets

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 492
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Oztop ◽  
Mikhail A. Sheremet
Keyword(s):  
Fluid Dynamics ◽  
Power Generation ◽  
Computational Fluid Dynamics ◽  
Reynolds Number ◽  
Conversion Efficiency ◽  
Reynolds Numbers ◽  
Thermoelectric Generation ◽  
Volume Fractions ◽  
Water Jets ◽  
Conversion Efficiencies

In this study, thermoelectric generation with impinging hot and cold nanofluid jets is considered with computational fluid dynamics by using the finite element method. Highly conductive CNT particles are used in the water jets. Impacts of the Reynolds number of nanojet stream combinations (between (Re1, Re2) = (250, 250) to (1000, 1000)), horizontal distance of the jet inlet from the thermoelectric device (between (r1, r2) = (−0.25, −0.25) to (1.5, 1.5)), impinging jet inlet to target surfaces (between w2 and 4w2) and solid nanoparticle volume fraction (between 0 and 2%) on the interface temperature variations, thermoelectric output power generation and conversion efficiencies are numerically assessed. Higher powers and efficiencies are achieved when the jet stream Reynolds numbers and nanoparticle volume fractions are increased. Generated power and efficiency enhancements 81.5% and 23.8% when lowest and highest Reynolds number combinations are compared. However, the power enhancement with nanojets using highly conductive CNT particles is 14% at the highest solid volume fractions as compared to pure water jet. Impacts of horizontal location of jet inlets affect the power generation and conversion efficiency and 43% variation in the generated power is achieved. Lower values of distances between the jet inlets to the target surface resulted in higher power generation while an optimum value for the highest efficiency is obtained at location zh = 2.5ws. There is 18% enhancement in the conversion efficiency when distances at zh = ws and zh = 2.5ws are compared. Finally, polynomial type regression models are obtained for estimation of generated power and conversion efficiencies for water-jets and nanojets considering various values of jet Reynolds numbers. Accurate predictions are obtained with this modeling approach and it is helpful in assisting the high fidelity computational fluid dynamics simulations results.

Sign in / Sign up

Export Citation Format

Share Document