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.

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.

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

2011 ◽  
Vol 681 ◽  
pp. 411-433 ◽  
Author(s):  
HEMANT K. CHAURASIA ◽  
MARK C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Vortical Flow ◽  
Forced Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Dimensional Instability

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

Large eddy simulation of a circular jet: effect of inflow conditions on the near field

2009 ◽  
Vol 620 ◽  
pp. 383-411 ◽  
Author(s):  
JUNGWOO KIM ◽  
HAECHEON CHOI
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Reynolds Numbers ◽  
Momentum Thickness ◽  
Potential Core ◽  
Initial Momentum ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Mode 2 ◽  
Inflow Conditions

In the present study, the effects of the jet inflow conditions such as the initial momentum thickness (θ) and background disturbances on the downstream evolution of a circular jet are investigated using large eddy simulation (LES). We consider four different initial momentum thicknesses,D/θ = 50, 80, 120 and 180, and three different Reynolds numbers,ReD=UJD/ν = 3600, 104and 105, whereUJis the jet inflow velocity andDis the jet diameter. The present study shows that the jet characteristics significantly depend on both the initial momentum thickness and the Reynolds number. For all the Reynolds numbers considered in this study, vortex rings are generated at an earlier position with decreasing initial momentum thickness. In case of a relatively low Reynolds number ofReD= 3600, at smaller initial momentum thickness, early growth of the shear layer due to the early generation of vortex ring leads to the occurrence of large-scale coherent structures in earlier downstream locations, which results in larger mixing enhancement and more rapid increase in turbulence intensity. However, at a high Reynolds number such asReD= 105, with decreasing initial momentum thickness, rapid growth of the shear layer leads to the saturation of the shear layer and the generation of fine-scale turbulence structures, which reduces mixing and turbulence intensity. With increasingReθ(=UJθ/ν), the characteristic frequency corresponding to the shear layer mode (Stθ=fθ/UJ) gradually increases and reaches near 0.017 predicted from the inviscid instability theory. On the other hand, the frequency corresponding to the jet-preferred mode (StD=f D/UJ) varies depending onReDandD/θ. From a mode analysis, we show that, in view of the energy of the axial velocity fluctuations integrated over the radial direction, the double-helix mode (mode 2) becomes dominant past the potential core, but the axisymmetric mode (mode 0) is dominant near the jet exit. In view of the local energy, the disturbances grow along the shear layer near the jet exit: for thick shear layer, mode 0 grows much faster than other modes, but modes 0–3 grow almost simultaneously for thin shear layer. However, past the potential core, the dominant mode changes from mode 0 near the centreline to mode 1 and then to mode 2 with increasing radial direction regardless of the initial shear layer thickness.

scholarly journals The Effect of Reynolds Number on the Performance of Partial Admission and Re-Entry Axial Turbines

1965 ◽  
Author(s):  
Robert G. Adams
Keyword(s):  
Reynolds Number ◽  
Power Systems ◽  
Pressure Ratio ◽  
Reynolds Numbers ◽  
Test Program ◽  
Optimum Pressure ◽  
Auxiliary Power ◽  
Partial Admission ◽  
Open Cycle ◽  
Axial Turbines

In turbines designed for open-cycle auxiliary power systems for orbital and reentry vehicles, turbine blade Reynolds numbers of less than 1000 are not uncommon. An investigation of the effect of Reynolds number in this range on the performance of partial admission and reentry axial turbines, which are the predominant types of turbine used in this class of power system, was recently conducted. This paper describes the test program carried out, the results of the investigation, and examines the implications of the results on the design of turbines for this application. In general, it was found that the drop in efficiency with reduced Reynolds number was not so rapid with the types of turbine studied as with the full-admission turbine. The optimum pressure-ratio split was also found to be significantly affected by the Reynolds numbers encountered in the turbine stages.

Measurements of Turbulent Transport in a Square Channel with One Ribbed Wall

2022 ◽  
Author(s):  
Sebastian Ruck ◽  
Frederik Arbeiter
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Shear Layer ◽  
Reynolds Shear Stress ◽  
Turbulent Transport ◽  
Reynolds Numbers ◽  
Flow Structures ◽  
Channel Height ◽  
Height Ratio ◽  
Square Channel

Abstract The velocity field of the fully developed turbulent flow in a one-sided ribbed square channel (rib-height-to-channel-height ratio of k/h = 0.0667, rib-pitch-to-rib-height ratio of p/k = 9) were measured at Reynolds numbers (based on the channel height h and the mean bulk velocity uB) of Reh = 50 000 and 100 000 by means of Laser-Doppler-Anemometry (LDA). Triple velocity correlations differed slightly between both Reynolds numbers when normalized by the bulk velocity and the channel height, similarly to the first- and second-order statistical moments of the velocity. Their near-wall behavior reflected the crucial role of turbulent transport near the rib crest and within the separated shear layer. Sweep events occurred with the elongated flow structures of the flapping shear layer and gained in importance towards the channel bottom wall, while strong ejection events near the rib leading and trailing edges coincided with flow structures bursting away from the wall. Despite the predominant occurrence of sweep events close to the ribbed wall within the inter-rib spacing, ejection events contributed with higher intensity to the Reynolds shear stress. Ejection and sweep events and their underlying transport phenomena contributing to the Reynolds shear stress were almost Reynolds number-insensitive in the resolved flow range. The invariance to the Reynolds number can be of benefit for the use of scale-resolving simulation methods in the design process of rib structures for heat exchange applications.

scholarly journals On vortex shedding from an airfoil in low-Reynolds-number flows

2009 ◽  
Vol 632 ◽  
pp. 245-271 ◽  
Author(s):  
SERHIY YARUSEVYCH ◽  
PIERRE E. SULLIVAN ◽  
JOHN G. KAWALL
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Vortex Shedding ◽  
Coherent Structures ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Frequency Scaling ◽  
Separated Shear Layer ◽  
Low Reynolds Number Flows ◽  
Low Reynolds

Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 103 ≤ Rec ≤ 210 × 103, and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.

Experimental Study of Swirling Jets and Axial Forcing on Round Jets

2013 ◽  
Author(s):  
Amy B. McCleney ◽  
Philippe M. Bardet
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Flow Behavior ◽  
Past Research ◽  
Reynolds Numbers ◽  
Industrial Applications ◽  
Water Stream ◽  
Swirling Jets ◽  
Round Jets ◽  
Large Tank

In jets, swirl can significantly enhance growth and mixing. This can lead to better chemical process efficiencies, increased combustion completeness, lower exhaust plume temperatures, and reduction in pollutant by-products. Exciting natural instabilities can enhance mixing further. Past research on forcing of swirling jets resulted in limited change in flow behavior. This could be attributed to either low Reynolds numbers or imposed modes that were solely axial or azimuthal. In our experiment, both round and free swirling jets are created by independently controlling the axial and azimuthal momentum injection rates; the resulting water stream discharges into a large tank. Axial forcing on a round jet is varied for Strouhal number ranging from 0 to 0.45 and Reynolds number, Re, of 5,700 for small amplitudes. An unforced swirling jet is also presented for Re of 1,100 and 5,800 with a Swirl of 0.05. While the highest Reynolds number studied here is relevant to industrial applications, there is a dearth of experimental data in this range. Flow structures in the shear layer are identified with PLIF. Fluorescent dye is injected uniformly in the circumference of the boundary layer; this allows visualizing the effect of forcing and swirl on the shear layer in the near and far field. The results offer insight into controlling the spacing of the vortex rings formed by axial forcing.

The Effect of Reynolds Number and Laminar Separation on Axial Cascade Performance

1975 ◽  
Vol 97 (2) ◽  
pp. 261-273 ◽  
Author(s):  
W. B. Roberts
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Separation Bubble ◽  
Axial Compressor ◽  
Leading Edge ◽  
Practical Method ◽  
Reynolds Numbers ◽  
Compressor Cascade ◽  
Laminar Separation ◽  
Semiempirical Theory

Testing over a range of Reynolds numbers was done for three NACA 65 Profiles in cascade. The testing was carried out in the VKI C-1 Low Speed Cascade Wind Tunnel; blade chord Reynolds number was varied from 250,000 to 40,000. A semiempirical theory is developed which will predict the behavior of the shear layer across a laminar separation bubble. The method is proposed for two-dimensional incompressible flow and is applicable down to short bubble bursting. The method can be used to predict the length of the laminar bubble, the bursting Reynolds number, and the development of the shear layer through the separated region. As such it is a practical method for calculating the profile losses of axial compressor and turbine cascades in the presence of laminar separation bubbles. It can also be used to predict the abrupt leading edge stall associated with thin airfoil sections. The predictions made by the method are compared with the available experimental data. The agreement could be considered good. The method was also used to predict regions of laminar separation in converging flows through axial compressor cascades (exterior to the corner vortices) with good results. For Reynolds numbers below bursting the semiempirical theory no longer applies. For this situation the performance of an axial compressor cascade can be computed using an empirical correlation proposed by the author. Comparison of performance prediction with experiment shows satisfactory agreement. Finally, a tentative correlation, based on the NACA Diffusion Factor, is presented that allows a rapid estimation of the bursting Reynolds number of an axial compressor cascade.

Transition of Mixtures of Polymers in a Dilute Aqueous Solution

1970 ◽  
Vol 92 (3) ◽  
pp. 411-418 ◽  
Author(s):  
W. D. White ◽  
D. M. McEligot
Keyword(s):  
Molecular Weight ◽  
Reynolds Number ◽  
Pressure Ratio ◽  
Polymer Concentration ◽  
Transition Process ◽  
Reynolds Numbers ◽  
Turbulent Regime ◽  
Calibration Data ◽  
Molecular Weight Polymer ◽  
Dilute Aqueous Solution

Data are presented for the flow of deionized water solutions of linear, unbranched polymers—Separan AP-30, Polyox WSR-35 and Polyox WSR-301, and mixtures of the latter two in a 0.0235 in. tube. The Reynolds numbers vary from about 1200 to about 12,000. Measurements were made at 4 deg C and near room temperature. Occurrence of transition is confirmed by oscillograph traces and pressure ratio calculations in addition to the usual “break” on a friction factor-Reynolds number graph. From the calibration data, it appears that for small tubes there is a critical parameter, such as molecular weight or polymer length, below which transition occurs as for water, but above which the transition Reynolds number depends on polymer concentration. The low and high polymers were mixed to vary molecular weight distribution of samples. It was found that the higher molecular weight polymer dominates the transition process, but in the turbulent regime the effects are roughly additive.

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