The stability of countercurrent mixing layers in circular jets

1991 ◽  
Vol 227 ◽  
pp. 309-343 ◽  
Author(s):  
P. J. Strykowski ◽  
D. L. Niccum
Keyword(s):  
Shear Layer ◽  
Critical Velocity ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Mean Velocity ◽  
Axisymmetric Vortex ◽  
Circular Jets ◽  
Axisymmetric Shear ◽  
The Stability

A spatially developing countercurrent mixing layer was established experimentally by applying suction to the periphery of an axisymmetric jet. A laminar mixing region was studied in detail for a velocity ratio R = ΔU/2U between 1 and 1.5, where ΔU describes the intensity of the shear across the layer and U is the average speed of the two streams. Above a critical velocity ratio Rr = 1.32 the shear layer displays energetic oscillations at a discrete frequency which are the result of very organized axisymmetric vortex structures in the mixing layer. The spatial order of the primary vortices inhibits the pairing process and dramatically alters the spatial development of the shear layer downstream. Consequently, the turbulence level in the jet core is significantly reduced, as is the decay rate of the mean velocity on the jet centreline. The response of the shear layer to controlled external forcing indicates that the shear layer oscillations at supercritical velocity ratios are self-excited. The experimentally determined critical velocity ratio of 1.32, established for very thin axisymmetric shear layers, compares favourably with the theoretically predicted value of 1.315 for the transition from convective to absolute instability in plane mixing layers (Huerre & Monkewitz 1985).

scholarly journals Effect of Mean Velocity-to-Critical Velocity Ratios on Bed Topography and Incipient Motion in a Meandering Channel: Experimental Investigation

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 883
Author(s):  
Nargess Moghaddassi ◽  
Seyed Habib Musavi-Jahromi ◽  
Mohammad Vaghefi ◽  
Amir Khosrojerdi
Keyword(s):  
Experimental Investigation ◽  
Critical Velocity ◽  
Velocity Ratio ◽  
Scour Depth ◽  
Incipient Motion ◽  
Mean Velocity ◽  
Straight Path ◽  
Meandering Channel ◽  
Bed Topography ◽  
The Mean

As 180-degree meanders are observed in abundance in nature, a meandering channel with two consecutive 180-degree bends was designed and constructed to investigate bed topography variations. These two 180-degree mild bends are located between two upstream and downstream straight paths. In this study, different mean velocity-to-critical velocity ratios have been tested at the upstream straight path to determine the meander’s incipient motion. To this end, bed topography variations along the meander and the downstream straight path were addressed for different mean velocity-to-critical velocity ratios. In addition, the upstream bend’s effect on the downstream bend was investigated. Results indicated that the maximum scour depth at the downstream bend increased as a result of changing the mean velocity-to-critical velocity ratio from 0.8 to 0.84, 0.86, 0.89, 0.92, 0.95, and 0.98 by, respectively, 1.5, 2.5, 5, 10, 12, and 26 times. Moreover, increasing the ratio increased the maximum sedimentary height by 3, 10, 23, 48, 49, and 56 times. The upstream bend’s incipient motion was observed for the mean velocity-to-critical velocity ratio of 0.89, while the downstream bend’s incipient motion occurred for the ratio of 0.78.

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

2000 ◽  
Vol 421 ◽  
pp. 229-267 ◽  
Author(s):  
JONATHAN B. FREUND ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Velocity Difference ◽  
Mean Velocity ◽  
The Mean ◽  
Mach Numbers ◽  
High Mach ◽  
Compressibility Effects

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

On the stability of an inviscid shear layer which is periodic in space and time

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Finite Amplitude ◽  
Periodic Component ◽  
Periodic Flow ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

The potential flow bounded by a mixing layer and a solid surface

1984 ◽  
Vol 395 (1809) ◽  
pp. 265-290 ◽  
Keyword(s):  
Shear Layer ◽  
Solid Surface ◽  
Turbulent Mixing ◽  
Potential Flow ◽  
Near Field ◽  
Mixing Layer ◽  
Detailed Comparison ◽  
Mixing Layers ◽  
Turbulent Shear ◽  
Spatial Correlations

Phillips's ( Proc. Camb. Phil. Soc . 51, 220 (1955)) analysis of the potential 'near field' forced by a turbulent shear layer is extended to include calculation of velocity spectra, spatial correlations and the effect of a solid surface at a finite distance from the shear layer. In the region away from the influence of the wall the theory predicts that correlation scales depend principally on the effective distance from the turbulence. This result suggests that the large correlation scales measured outside turbulent mixing layers do not necessarily demonstrate the essential tow-dimensionality of the large turbulent eddies and shows why mixing layers are more influenced by potential flow effects than are other shear layers. The detailed comparison of the theory to measurements made outside a high Reynolds number single-stream turbulent mixing layer results in an unphysical negative regions are caused by an error in a basic assumption of the theory. However, all the measured correlation scales appear to increase linearly with distance from the turbulence and therefore are consistent with the main result of the analysis. As the potential flow becomes affected by the wind tunnel floor, u 2 — and w 2 — are amplified significantly more than the theory predicts, while v 2 — is not attenuated. These discrepancies are attributed partly to the streamwise inhomogeneity of the flow, which was not incorporated into the analysis.

Dynamics of Large-Scale Structures for Jets in a Crossflow

1999 ◽  
Vol 121 (3) ◽  
pp. 577-587 ◽  
Author(s):  
F. Muldoon ◽  
S. Acharya
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Computational Study ◽  
Near Field ◽  
Velocity Ratio ◽  
Leeward Side ◽  
Dynamic Features ◽  
Mean Velocity ◽  
Large Scale Structures ◽  
Scale Structures

Results of a three-dimensional unsteady computational study of a row of jets injected normal to a crossflow are presented with the aim of understanding the dynamics of the large-scale structures in the region near the jet. The jet to crossflow velocity ratio is 0.5. A modified version of the computer program (INS3D), which utilizes the method of artificial compressibility, is used for the computations. Results obtained clearly indicate that the near-field large-scale structures are extremely dynamic in nature, and undergo breakup and reconnection processes. The dynamic near-field structures identified include the counterrotating vortex pair (CVP), the horseshoe vortex, wake vortex, wall vortex, and shear layer vortex. The dynamic features of these vortices are presented in this paper. The CVP is observed to be a convoluted structure interacting with the wall and horseshoe vortices. The shear layer vortices are stripped by the crossflow, and undergo pairing and stretching events in the leeward side of the jet. The wall vortex is reoriented into the upright wake system. Comparison of the predictions with mean velocity measurements is made. Reasonable agreement is observed.

A numerical study of shear layer characteristics of low-speed transverse jets

2016 ◽  
Vol 790 ◽  
pp. 275-307 ◽  
Author(s):  
Prahladh S. Iyer ◽  
Krishnan Mahesh
Keyword(s):  
Velocity Profile ◽  
Shear Layer ◽  
Convective Instability ◽  
Numerical Study ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Dominant Frequencies

Direct numerical simulation (DNS) and dynamic mode decomposition (DMD) are used to study the shear layer characteristics of a jet in a crossflow. Experimental observations by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129) at velocity ratios ($R=\overline{v}_{j}/u_{\infty }$) of 2 and 4 and Reynolds number ($Re=\overline{v}_{j}D/{\it\nu}$) of 2000 on the transition from absolute to convective instability of the upstream shear layer are reproduced. Point velocity spectra at different points along the shear layer show excellent agreement with experiments. The same frequency ($St=0.65$) is dominant along the length of the shear layer for $R=2$, whereas the dominant frequencies change along the shear layer for $R=4$. DMD of the full three-dimensional flow field is able to reproduce the dominant frequencies observed from DNS and shows that the shear layer modes are dominant for both the conditions simulated. The spatial modes obtained from DMD are used to study the nature of the shear layer instability. It is found that a counter-current mixing layer is obtained in the upstream shear layer. The corresponding mixing velocity ratio is obtained, and seen to delineate the two regimes of absolute or convective instability. The effect of the nozzle is evaluated by performing simulations without the nozzle while requiring the jet to have the same inlet velocity profile as that obtained at the nozzle exit in the simulations including the nozzle. The shear layer spectra show good agreement with the simulations including the nozzle. The effect of shear layer thickness is studied at a velocity ratio of 2 based on peak and mean jet velocity. The dominant frequencies and spatial shear layer modes from DNS/DMD are significantly altered by the jet exit velocity profile.

scholarly journals Effect of Mean Velocity to Critical Velocity Ratios on Bed Topography and Incipient Motion in a Meandering Channel: Experimental Investigation

2021 ◽  
Author(s):  
Nargess Moghaddassi ◽  
Seyed Habib Musavi-Jahromi ◽  
Mohammad Vaghefi ◽  
Amir Khosrojerdi
Keyword(s):  
Experimental Investigation ◽  
Critical Velocity ◽  
Velocity Ratio ◽  
Scour Depth ◽  
Incipient Motion ◽  
Mean Velocity ◽  
Straight Path ◽  
Meandering Channel ◽  
Bed Topography ◽  
The Mean

As 180-degree meanders are observed in abundance in nature, a meandering channel with two consecutive 180-degree bends was designed and constructed to investigate bed topography variations. These two 180-degree mild bends are located between two upstream and downstream straight paths. In this study, different mean velocity to critical velocity ratios have been tested at the upstream straight path to determine the meander's incipient motion. To this end, bed topography variations along the meander and the downstream straight path were addressed for different mean velocity to critical velocity ratios. In addition, the upstream bend's effect on the downstream bend has been investigated. Results indicated that the maximum scour depth at the downstream bend has increased as a result of changing the mean velocity to critical velocity ratio from 0.8 to 0.84, 0.86, 0.89, 0.92, 0.95, and 0.98 by respectively 1.5, 2.5, 5, 10, 12, and 26 times. Moreover, increasing the ratio increased the maximum sedimentary height by 3, 10, 23, 48, 49, and 56 times. The upstream bend's incipient motion was observed for the mean velocity to critical velocity ratio of 0.89, while the downstream bend was equal to 0.78.

scholarly journals Effects of roof configuration on natural ventilation for an isolated building

2021 ◽  
Vol 15 (3) ◽  
pp. 8379-8389
Author(s):  
Lip Kean Moey ◽  
Man Fai Kong ◽  
Vin Cent Tai ◽  
Tze Fong Go ◽  
Nor Mariah Adam
Keyword(s):  
Kinetic Energy ◽  
Natural Ventilation ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Flow Characteristics ◽  
Mean Velocity ◽  
Gable Roof ◽  
Building Models ◽  
Large Vortex ◽  
Field Information

Numerical analyses based on CFD steady RANS were conducted to investigate the effects of roof configuration on wind-induced natural ventilation for an isolated roofed building. Gable roof and saltbox roof building models were tested with 15˚, 25˚, 35˚ and 45˚ roof pitch in present study. The flow field information and flow characteristics were obtained from the contours and plots generated by CFD. In accordance to the increment of roof pitch, the turbulence kinetic energy and mean velocity ratio show vigorous response. The flow separated at the windward corner do not reattach onto the roof, thus induced higher velocity gradient and form a large vortex at the roof ridge. The vortices behind then building caused by the flow separation at the roof ridge extend along the mixing layer and spread up to the roof. The pressure differences mainly rely on the roof shapes. Greater pressure differences between the upstream, interior and downstream was observed in saltbox roof cases. This is due to the extended roof height which boosted the impinging effect caused by the incoming wind. Generally, the saltbox roof configuration exhibit better performance than gable roof in terms of the measured parameters.

Dynamics of Large-Scale Structures for Jets in a Crossflow

1998 ◽  
Author(s):  
Frank Muldoon ◽  
Sumanta Acharya
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Computational Study ◽  
Near Field ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Leeward Side ◽  
Mean Velocity ◽  
Large Scale Structures ◽  
Scale Structures

Results of a three dimensional unsteady computational study of a row of jets injected normal to a cross-flow are presented with the aim of understanding the dynamics of the large scale structures in the region near the jet. The jet to cross-flow velocity ratio is .5. A modified version of the computer program (INS3D) which utilizes the method of artificial compressibility is used for the computations. Results obtained clearly indicate that the near field large scale structures are extremely dynamical in nature, and undergo breakup and reconnection processes. The dynamical near field structures identified include the counter rotating vortex pair (CVP), the horseshoe vortex, wake vortex, wall vortex and the shear layer vortex. The dynamical features of these vortices are presented in this paper. The CVP is observed to be a convoluted structure interacting with the wall and horseshoe vortices. The shear layer vortices are stripped by the crossflow, and undergo pairing and stretching events in the leeward side of the jet. The wall vortex is reoriented into the upright wake system. Comparison of the predictions with mean velocity measurements is made. Reasonable agreement is observed.

The interaction between the mean flow and coherent structures in turbulent mixing layers

1994 ◽  
Vol 260 ◽  
pp. 81-94 ◽  
Author(s):  
J. Cohen ◽  
B. Marasli ◽  
V. Levinski
Keyword(s):  
Velocity Profile ◽  
Coherent Structures ◽  
Turbulent Mixing ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Mean Flow ◽  
Mean Velocity ◽  
Turbulent Mixing Layer ◽  
Self Similar ◽  
The Mean

The nonlinear interaction between the mean flow and a coherent disturbance in a two-dimensional turbulent mixing layer is addressed. Based on considerations from stability theory, previous experimental results, in particular the modification of the mean velocity profile, the peculiar growth of the forced shear-layer thickness and the spatial growth of the disturbance amplitude, are explained. A model that assumes a quasi-parallel mean flow having a self-similar mean velocity profile is developed. The model is capable of predicting the downstream evolution of turbulent mixing layers subjected to external excitations.

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