Two Dimensional Jet at Low Reynolds Numbers

2007 ◽  
Author(s):  
Akinori Muramatsu ◽  
Tatsuo Motohashi
Keyword(s):  
Reynolds Number ◽  
Outer Part ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Momentum Conservation ◽  
Control Surface ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Vortical Motion ◽  
The Difference

A numerical simulation of two-dimensional jets was carried out using a SOLA method. The two-dimensional jets were discharged from a slit in a wall at Reynolds numbers below 50. The difference between the calculated flow fields and those of the Bickley jet is due to the non-uniformity of the pressure field near the jet exit at the wall. The jet spreads faster than the Bickley jet. The decay of the streamwise velocity on the center line is more rapid than that of the Bickley jet. The streamwise velocity profile is different from that of the Bickley jet, and a reversed flow is generated in the outer part of the jet. The jet develops instability through two processes. First, small fluctuations grow exponentially. Second, vortical motion such as so-called ‘flapping motion’ of the jet develops in the downstream region. The critical Reynolds number, as determined by the growth of an integral of kinetic energy, is approximately 16.5. Integrals of momentum and pressure are calculated on a control surface in order to confirm the momentum conservation law. When the Reynolds number exceeds 20, the generation of fluctuations contributes to streamwise variations in the integrals of momentum and pressure.

scholarly journals Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers

2017 ◽  
Vol 826 ◽  
Author(s):  
Dileep Chandran ◽  
Rio Baidya ◽  
Jason P. Monty ◽  
Ivan Marusic
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Spatial Spectrum ◽  
Two Dimensional ◽  
Hot Wire ◽  
Self Similarity ◽  
Low Reynolds Numbers ◽  
High Reynolds

Here, we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high-Reynolds-number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26 000. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise ($\unicode[STIX]{x1D706}_{x}$) and spanwise ($\unicode[STIX]{x1D706}_{y}$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows$\unicode[STIX]{x1D706}_{y}/z\sim (\unicode[STIX]{x1D706}_{x}/z)^{1/2}$behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship ($\unicode[STIX]{x1D706}_{y}\sim \unicode[STIX]{x1D706}_{x}$), as required for self-similarity and predicted by the attached eddy hypothesis.

The Flow Over Two-Dimensional Surface-Mounted Obstacles at Low Reynolds Numbers

1985 ◽  
Vol 107 (4) ◽  
pp. 489-494 ◽  
Author(s):  
C. D. Tropea ◽  
R. Gackstatter
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Laser Doppler Anemometer ◽  
Height Ratio ◽  
Low Reynolds Numbers ◽  
Step Flow ◽  
Streamwise Velocity Component ◽  
Recirculation Zones ◽  
The Mean

The flow over a fence and a block mounted in a fully developed channel flow is experimentally investigated as a function of the Reynolds number, blockage ratio and length-to-height ratio using a laser-Doppler-anemometer. The information obtained includes the location and size of the primary and secondary recirculation zones, and profiles of the mean streamwise velocity component. The experiments were carried out in a channel for a Reynolds number in the range 150 < ReH < 4500. Comparisons are drawn between the obstacle flow and the backward-facing step flow.

Flow past a flat plate at low Reynolds numbers

1958 ◽  
Vol 3 (4) ◽  
pp. 329-343 ◽  
Author(s):  
E. Janssen
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Truncation Error ◽  
Reynolds Numbers ◽  
Experimental Result ◽  
Total Drag ◽  
Low Reynolds Numbers ◽  
Flow Past ◽  
The Difference

The flow past a flat plate at Reynolds numbers in the range 0·1 to 10·0 is investigated by an analogue method. The solution gives the stream function and the vorticity in the flow field surrounding the plate. From these are obtained the local coefficient of friction, the pressure distribution along the plate, and the total drag coefficient. The drag coefficient approaches the analytical values of Haaser (1950) and of Tomotika & Aoi (1953) as the Reynolds number decreases toward 0·1. The drag coefficient approaches the Blasius solution as the Reynolds number increases. At Reynolds number 10·0 the drag coefficient is still above the Blasius value, but is below the value obtained experimentally by Janour (1951). The difference from the experimental result is attributed for the most part to truncation error.

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.

Experimental and Computational Investigation of the Two-Dimensional Channel Flow Over Two Fences in Tandem

1988 ◽  
Vol 110 (1) ◽  
pp. 48-54 ◽  
Author(s):  
F. Durst ◽  
M. Founti ◽  
S. Obi
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Channel Flow ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Blockage Ratio ◽  
Two Dimensional ◽  
Computational Investigation ◽  
Recirculation Zones ◽  
The Mean

Measurements and computations of the mean streamwise velocity and its fluctuations are reported for an arrangement of two similar fences mounted in tandem in fully developed channel flow. The influence of Reynolds number and blockage ratio, in terms of the size and location of the primary and secondary recirculation zones, were investigated. The flow field around each fence was found to be similar to one another as well as to the corresponding single fence flow, for Reynolds numbers (based on the fence height) of up to 100. For higher Reynolds numbers, the shear layer developing from the first fence was significantly disturbed by the second fence resulting in earlier transition and higher turbulence intensities. This effect was most evident in the measured differences of the recirculation lengths downstream of each fence.

Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures

1997 ◽  
Vol 336 ◽  
pp. 267-299 ◽  
Author(s):  
H. C. KUHLMANN ◽  
M. WANSCHURA ◽  
H. J. RATH
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Single Vortex ◽  
Low Reynolds Numbers ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
The Difference ◽  
Convective Cells ◽  
Highly Strained

The steady flow in rectangular cavities is investigated both numerically and experimentally. The flow is driven by moving two facing walls tangentially in opposite directions. It is found that the basic two-dimensional flow is not always unique. For low Reynolds numbers it consists of two separate co-rotating vortices adjacent to the moving walls. If the difference in the sidewall Reynolds numbers is large this flow becomes unstable to a stationary three-dimensional mode with a long wavelength. When the aspect ratio is larger than two and both Reynolds numbers are large, but comparable in magnitude, a second two-dimensional flow exists. It takes the form of a single vortex occupying the whole cavity. This flow is the preferred state in the present experiment. It becomes unstable to a three-dimensional mode that subdivides the basic streched vortex flow into rectangular convective cells. The instability is supercritical when both sidewall Reynolds numbers are the same. When they differ the instability is subcritical. From an energy analysis and from the salient features of the three-dimensional flow it is concluded that the mechanism of destabilization is identical to the destabilization mechanism operative in the elliptical instability of highly strained vortices.

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.

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.

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

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