An experimental investigation of the instability of a two-dimensional jet at low Reynolds numbers

1964 ◽  
Vol 20 (2) ◽  
pp. 337-352 ◽  
Author(s):  
Hiroshi Sato ◽  
Fujihiko Sakao
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Maximum Velocity ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Laminar Jet ◽  
Artificial Disturbance ◽  
Low Reynolds ◽  
The Stability

An experimental investigation was made of the stability of a two-dimensional jet at low Reynolds numbers with extremely small residual disturbances both in and around the jet. The velocity distribution of a laminar jet is in agreement with Bickley's theoretical result. The stability and transition of a laminar jet are characterized by the Reynolds number based on the slit width and the maximum velocity of the jet. When the Reynolds number is less than 10, the whole jet is laminar. When the Reynolds number is between 10 and around 50, periodic velocity fluctuations are found in the jet. They die out as they travel downstream without developing into irregular fluctuations. When the Reynolds number exceeds about 50, periodic fluctuations develop into irregular, turbulent fluctuations. The frequency of the periodic fluctuation is roughly proportional to the square of the jet velocity.The stability of the jet against an artificially imposed disturbance was also investigated. Sound was used as an artificial disturbance. The disturbance is either amplified or damped in the jet depending on its frequency. The conventional stability theory was modified by considering the streamwise increase of Reynolds number. The experimental results are in agreement with the theoretical results.

A Modified Turbulence Model for Low Reynolds Numbers: Application to Hydrostatic Seals

2005 ◽  
Vol 127 (1) ◽  
pp. 130-140 ◽  
Author(s):  
Noe¨l Brunetie`re
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Axial Stiffness ◽  
Low Reynolds Numbers ◽  
Order Of Magnitude ◽  
Low Reynolds ◽  
The Stability

A modification of the Elrod and Ng turbulence model is presented. The order of magnitude of the Reynolds number in thin lubricant films varies between 102 and 105. For Reynolds numbers higher than 103, the fluid flow becomes turbulent. It is well accepted in lubrication to use a zero-equation turbulence model of the type developed by Constantinescu (1962, ASME J. Basic Eng., 84(1), pp. 139–151), Ng (1964, ASLE Trans., 7, pp. 311–321), Ng and Pan (1965, ASME J. Basic Eng., 87, pp. 675–688), Elrod and Ng (1967, ASME J. Lubr. Technol., 89, pp. 346–362), or Hirs (1973, ASME J. Lubr. Technol., 95, pp. 137–146). The Elrod and Ng approach is certainly the most efficient for combined pressure and shear flows where the Reynolds number is above 104. This paper proposes a modification of the Elrod and Ng model in order to ensure a good correlation with experimental data obtained with low Reynolds number turbulent flows. The present model, coupled with a scaling factor for taking into account the transition to turbulence, is therefore accurate for all of the typical Reynolds number values recorded in lubrication. The model is then applied to hydrostatic noncontacting face seals, which usually operate at Reynolds numbers varying from 103 to 104. The accuracy of the model is shown for this particular application of radial rotating flow. A special study is made of the transition to turbulence. The results are compared with those obtained using the initial Elrod and Ng model. The axial stiffness coefficient and the stability threshold are significantly affected by the turbulence model.

scholarly journals Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers

1989 ◽  
Vol 206 ◽  
pp. 579-627 ◽  
Author(s):  
C. H. K. Williamson
Keyword(s):  
Reynolds Number ◽  
Boundary Conditions ◽  
Vortex Shedding ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Cylinder Wake ◽  
Completely Continuous ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Central Flow

Two fundamental characteristics of the low-Reynolds-number cylinder wake, which have involved considerable debate, are first the existence of discontinuities in the Strouhal-Reynolds number relationship, and secondly the phenomenon of oblique vortex shedding. The present paper shows that both of these characteristics of the wake are directly related to each other, and that both are influenced by the boundary conditions at the ends of the cylinder, even for spans of hundreds of diameters in length. It is found that a Strouhal discontinuity exists, which is not due to any of the previously proposed mechanisms, but instead is caused by a transition from one oblique shedding mode to another oblique mode. This transition is explained by a change from one mode where the central flow over the span matches the end boundary conditions to one where the central flow is unable to match the end conditions. In the latter case, quasi-periodic spectra of the velocity fluctuations appear; these are due to the presence of spanwise cells of different frequency. During periods when vortices in neighbouring cells move out of phase with each other, ‘vortex dislocations’ are observed, and are associated with rather complex vortex linking between the cells. However, by manipulating the end boundary conditions, parallel shedding can be induced, which then results in a completely continuous Strouhal curve. It is also universal in the sense that the oblique-shedding Strouhal data (Sθ) can be collapsed onto the parallel-shedding Strouhal curve (S0) by the transformation, S0 = Sθ/cosθ, where θ is the angle of oblique shedding. Close agreement between measurements in two distinctly different facilities confirms the continuous and universal nature of this Strouhal curve. It is believed that the case of parallel shedding represents truly two-dimensional shedding, and a comparison of Strouhal frequency data is made with several two-dimensional numerical simulations, yielding a large disparity which is not clearly understood. The oblique and parallel modes of vortex shedding are both intrinsic to the flow over a cylinder, and are simply solutions to different problems, because the boundary conditions are different in each case.

A Modified Turbulence Model for Low Reynolds Numbers: Applications to Hydrostatic Seals

2004 ◽  
Author(s):  
Noe¨l Brunetie`re
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Axial Stiffness ◽  
Low Reynolds Numbers ◽  
Order Of Magnitude ◽  
Low Reynolds ◽  
The Stability

The order of magnitude of the Reynolds number in thin lubricant films varies between 102 and 105. For Reynolds numbers higher than 103, the fluid flow becomes turbulent. It is well accepted in lubrication to use a zero equation turbulence model of the type developed by Constantinescu [1] or Elrod, Ng and Pan [2–4] or Hirs [5]. The Elrod and Ng approach is certainly the most efficient for combined pressure and shear flows where the Reynolds number is above 104. This paper proposes a modification of the Elrod and Ng model in order to ensure a good correlation with experimental data obtained with low Reynolds number turbulent flows. The present model, coupled with a scaling factor for taking into account the transition to turbulence, is therefore accurate for all the typical Reynolds number values recorded in lubrication. The model is then applied to hydrostatic noncontacting face seals, which usually operate at Reynolds numbers varying from 103 to 104. The accuracy of the model is shown for this particular application of radial rotating flow. A special study is made of the transition to turbulence. The results are compared with those obtained using the initial Elrod and Ng model. The axial stiffness coefficient and the stability threshold are significantly affected by the turbulence model.

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.

A Computational Study on Airfoils at a Low Reynolds Number

2000 ◽  
Author(s):  
Ajit Pal Singh ◽  
S. H. Winoto ◽  
D. A. Shah ◽  
K. G. Lim ◽  
Robert E. K. Goh
Keyword(s):  
Reynolds Number ◽  
Computational Analysis ◽  
Computational Study ◽  
Low Reynolds Number ◽  
Micro Air Vehicles ◽  
Reynolds Numbers ◽  
Aerodynamic Performance ◽  
Low Reynolds Numbers ◽  
Study Results ◽  
Low Reynolds

Abstract Performance characteristics of some low Reynolds number airfoils for the use in micro air vehicles (MAVs) are computationally studied using XFOIL at a Reynolds number of 80,000. XFOIL, which is based on linear-vorticity stream function panel method coupled with a viscous integral formulation, is used for the analysis. In the first part of the study, results obtained from the XFOIL have been compared with available experimental data at low Reynolds numbers. XFOIL is then used to study relative aerodynamic performance of nine different airfoils. The computational analysis has shown that the S1223 airfoil has a relatively better performance than other airfoils considered for the analysis.

Experimental characterization of three-dimensional corner flows at low Reynolds numbers

2012 ◽  
Vol 707 ◽  
pp. 37-52 ◽  
Author(s):  
J. Sznitman ◽  
L. Guglielmini ◽  
D. Clifton ◽  
D. Scobee ◽  
H. A. Stone ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Channel Cross Section ◽  
Experimental Characterization ◽  
Low Reynolds Numbers ◽  
Low Reynolds

AbstractWe investigate experimentally the characteristics of the flow field that develops at low Reynolds numbers ($\mathit{Re}\ll 1$) around a sharp $9{0}^{\ensuremath{\circ} } $ corner bounded by channel walls. Two-dimensional planar velocity fields are obtained using particle image velocimetry (PIV) conducted in a towing tank filled with a silicone oil of high viscosity. We find that, in the vicinity of the corner, the steady-state flow patterns bear the signature of a three-dimensional secondary flow, characterized by counter-rotating pairs of streamwise vortical structures and identified by the presence of non-vanishing transverse velocities (${u}_{z} $). These results are compared to numerical solutions of the incompressible flow as well as to predictions obtained, for a similar geometry, from an asymptotic expansion solution (Guglielmini et al., J. Fluid Mech., vol. 668, 2011, pp. 33–57). Furthermore, we discuss the influence of both Reynolds number and aspect ratio of the channel cross-section on the resulting secondary flows. This work represents, to the best of our knowledge, the first experimental characterization of the three-dimensional flow features arising in a pressure-driven flow near a corner at low Reynolds number.

Viscous constraints on microorganism approach and interaction

2018 ◽  
Vol 851 ◽  
pp. 715-738 ◽  
Author(s):  
Mehdi Jabbarzadeh ◽  
Henry Chien Fu
Keyword(s):  
Reynolds Number ◽  
Near Field ◽  
Reynolds Numbers ◽  
Suspended Particles ◽  
The Other ◽  
Direct Approach ◽  
Low Reynolds Numbers ◽  
Physical Constraints ◽  
Low Reynolds ◽  
Viscous Hydrodynamics

Microorganisms must approach other suspended organisms or particles in order to interact with them during a host of life processes including feeding and mating. Microorganisms live at low Reynolds number where viscosity dominates and strongly affects the hydrodynamics of swimmer and nearby cells and objects. Viscous hydrodynamics makes it difficult for two surfaces to approach closely at low Reynolds numbers. Nonetheless, it is observed that microorganisms in fluid are still able to approach closely enough to interact with each other or suspended particles. Here, we study how the physical constraints provided by viscous hydrodynamics affects the feasibility of direct approach of flagellated and ciliated microorganisms to targets of different sizes. We find that it is feasible for singly flagellated swimmers to approach targets that are the same size or bigger. On the other hand, for squirmers, the feasibility of approach depends on near-field flows that can be controlled by the details of their swimming strokes.

Low Reynolds-Number Experiments in an Axial-Flow Turbomachine

1964 ◽  
Vol 86 (3) ◽  
pp. 257-295 ◽  
Author(s):  
J. Neustein
Keyword(s):  
Reynolds Number ◽  
Guide Vane ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Low Flow ◽  
Working Fluid ◽  
Low Reynolds Numbers ◽  
Blade Row ◽  
Overall Performance ◽  
Low Reynolds

The performance of a single-stage, axial-flow turbomachine was studied experimentally at low Reynolds numbers. The study was made with a turbomachine modeled from a large jet-engine type of axial-flow compressor. Low Reynolds numbers were obtained by using a mixture of glycerine and water as the working fluid. The overall performance was determined over a range of Reynolds numbers RT (based on rotor-tip speed and rotor chord) from 2000 to 150,000. The flow rate at each Reynolds number was varied from near shutoff to the maximum permitted by the turbomachine-tunnel systems. Blade-row characteristics were studied by means of quantitative flow surveys before and after each blade row, and by means of extensive flow-visualization experiments within each blade row. The investigation established that sudden or critical changes in performance do not occur in the type of machine tested, between RT of 150,000 and 20,000. Below 20,000 the performance deteriorated more rapidly. A relatively sharp change in performance occurred between RT of 20,000 and 10,000. The results clarified many of the viscous flow details in each blade row which are associated with the deterioration of performance. These effects were very pronounced at RT of 4000 and below. Consequently, a considerable part of the paper is concerned with results obtained at these lower Reynolds numbers. From the point of view of a designer, information is presented in regard to overall performance, guide-vane turning, and guide-vane and stator total-pressure losses, all as functions of Reynolds number. These results are expected to be indicative of performance in turbomachines similar to the one tested here. Other details are concerned with problems such as wall boundary layers, flow reversal at low flow coefficients, lip-clearance flow, flow patterns near shutoff, and flow comparisons in stators with rotating and stationary hubs.

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