An experimental study of the instability of a stably stratified free shear layer

1975 ◽  
Vol 71 (3) ◽  
pp. 563-575 ◽  
Author(s):  
Yu-Hwa Wang
Keyword(s):  
Flow Field ◽  
Shear Layer ◽  
Richardson Number ◽  
Open Channel ◽  
Salt Water ◽  
Stability Boundary ◽  
Water Channel ◽  
Free Shear Layer ◽  
Circulating Water ◽  
The Stability

A stably stratified free shear layer is created in a continuously circulating water channel in the laboratory. Two streams of salt water of different concentrations are brought together at the entrance to the open channel and a layered uniform flow field with a distinct sharp interface is produced in the test section. The maximum density difference between the two layers is Δρx = 0·0065ρw, where ρw is the density of water. The velocity of each layer can be adjusted at will to create free shear across the interface. At the end of the open channel, a mechanical device to separate the layers for recirculation is provided. The resulting flow field has a viscous region approximately 15 times larger than the scale of the salinity diffusion layer. Visual observations are made with hydrogen bubbles and dye traces. Interfacial waves are initiated by artificial excitation. The perturbation frequencies range from 0·476 to 10·40Hz. The measured wavelengths range from 0·46 to 3·02 cm. Damped waves as well as growing waves are observed at various exciting frequencies. Velocity profiles and instantaneous velocities are measured by a hot-film anemometer designed for use in salt water. Experimental values of the Richardson number, the dominant parameter characterizing the instability process, range from 1·23 to 14·45. The stability boundary is determined experimentally. Comparisons with Hazel's numerical results and the earlier results of Scotti & Corcos for low values of the Richardson number are also made.

An experiment on the stability of small disturbances in a stratified free shear layer

1972 ◽  
Vol 52 (3) ◽  
pp. 499-528 ◽  
Author(s):  
R. S. Scotti ◽  
G. M. Corcos
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Test Section ◽  
Richardson Number ◽  
Molecular Diffusion ◽  
Free Shear Layer ◽  
Horizontal Beam ◽  
Theoretical Predictions ◽  
Critical Richardson Number ◽  
The Stability

A statically stable stratified free shear layer was formed within the test section of a wind tunnel by merging two uniform streams of air after uniformly heating the top stream. The two streams were accelerated side by side in a contraction section. The resulting sheared thermocline thickened gradually as a result of molecular diffusion and was characterized by nearly self-similar temperature (odd), velocity (odd) and Richardson number (even) profiles. The minimum Richardson numberJ0could be adjusted over the range 0·07 ≥J0≥ 0·76; the Reynolds number Re varied between 30 and 70. Small periodic disturbances were introduced upstream of the test section by a fine wire oscillating in the thermocline. The wire generated a narrow horizontal beam of internal waves, which propagated downstream and remained confined within the thermocline. The growth or decay of these waves was observed in the test section. The results confirm the existence of a critical Richardson number the value of which is in plausible agreement with theoretical predictions (J0≅ 0·22 for the Reynolds number of the experiment). The growth rate is a function of the wavenumber and is somewhat different from that computed for the same Reynolds and Richardson numbers, but the calculation assumed velocity and density profiles which were also somewhat different.

Numerical studies of the stability of inviscid stratified shear flows

1972 ◽  
Vol 51 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Philip Hazel
Keyword(s):  
Richardson Number ◽  
Shear Flows ◽  
Stability Boundary ◽  
Phase Speed ◽  
Neutral Curve ◽  
Free Shear Layer ◽  
Density Profiles ◽  
Complex Phase ◽  
Numerical Studies ◽  
The Stability

The infinitesimal stability of inviscid, parallel, stratified shear flows to two-dimensional disturbances is described by the Taylor-Goldstein equation. Instability can only occur when the Richardson number is less than 1/4 somewhere in the flow. We consider cases where the Richardson number is everywhere non- negative. The eigenvalue problem is expressed in terms of four parameters,Ja ‘typical’ Richardson number, α the (real) wavenumber andcthe complex phase speed of the disturbance. Two computer programs are developed to integrate the stability equation and to solve for eigenvalues: the first findscgiven α andJ, the second finds α andJwhenc≡ 0 (i.e. it computes the stationary neutral curve for the flow). This is sometimes,but not always, the stability boundary in the α,Jplane. The second program works only for cases where the velocity and density profiles are antisymmetric about the velocity inflexion point. By means of these two programs, several configurations of velocity and density have been investigated, both of the free-shear-layer type and the jet type. Calculations of temporal growth rates for particular profiles have been made.

The stability of a thermally radiating stratified shear layer, including self-absorption

1974 ◽  
Vol 64 (1) ◽  
pp. 65-83 ◽  
Author(s):  
Joseph J. Dudis
Keyword(s):  
Shear Layer ◽  
Optical Depth ◽  
Richardson Number ◽  
Stability Boundary ◽  
Lower Troposphere ◽  
Neutral Stability ◽  
Viscous Effects ◽  
The Earth ◽  
Critical Richardson Number ◽  
The Stability

A linear stability analysis is applied to a stably stratified, thermally radiating shear layer. The grey Milne–Eddington approximation is employed as a radiation model. In contrast to a previously reported optically thin analysis, no inviscid instability exists, in the limit of vanishing horizontal wavenumber, for this selfabsorbing model. The inviscid neutral-stability boundary (Richardson number us. dimensionless wavenumber) for the Milne–Eddington approximation converges to the optically thick limit as the optical depth of the shear layer is increased. As the optical depth of the shear layer is decreased, the inviscid Milne–Eddington neutral-stability boundary approaches the optically thin limit, although not uniformly in the wavenumber. For fixed mean velocity gradient and fluid properties, the inviscid critical Richardson number approaches infinity as the optical depth of the shear layer approaches zero. Viscous effects neutralize this radiative destabilization, and the critical Richardson number eventually returns to zero as the optical depth continues to decrease. A shearlayer thickness exists for which the viscous critical Richardson number is a maximum. For shear depths greater than this thickness, self-absorption effects increase the stability; and for shear depths less than this thickness, viscous effects increase the stability. Results of the analysis are applied to the atmospheres of Venus and the earth. A critical Richardson number somewhat above the non-radiating value of 3 (although below the previously reported optically thin value) is found for the lower troposphere of the earth. No substantial effect is found for the earth's lower stratosphere or for the 100 km level above Venus.

Interference Between a Square and a Circular Cylinder

2015 ◽  
Author(s):  
Nithin S. Kumar ◽  
R. Ajith Kumar ◽  
Jayalakshmi Mohan
Keyword(s):  
Circular Cylinder ◽  
Flow Visualization ◽  
Shear Layer ◽  
Flow Pattern ◽  
Water Channel ◽  
Flow Patterns ◽  
Observation Time ◽  
Square Cylinder ◽  
Circulating Water ◽  
Layer Flow

The flow visualization studies around a square cylinder (upstream) and a circular cylinder arranged in tandem configuration is studied experimentally to identify the interference flow patterns. Flow visualization studies are carried out in a re-circulating water channel. The investigations are carried out for tandem arrangement varying the center-to-center distance (L) between the cylinders; L/B ratio is varied from 1 to 5 where B is the characteristic length. Experiments were conduct at a Reynolds number of 2100 (based on B). The results are also obtained for two tandem square cylinder configuration. The flow patterns observed are: Alternate Shear Layer Reattachment with and without gap flow, Simultanous shear layer reattachment and detached shear layer flow pattern. The time of persistence (in percentage) for each flow pattern is estimated over a sufficiently long period of observation time to identify the most influential, predominant flow pattern. Though these patterns are identical for square-square and square-circular tandem configurations, their order of predominance is different for both the configurations.

Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers

1971 ◽  
Vol 49 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Kanefusa Gotoh
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Electrically Conducting ◽  
The Stability ◽  
The Magnetic Field

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.

On the stability of a heterogeneous shear layer subject to a body force

1961 ◽  
Vol 11 (2) ◽  
pp. 284-290 ◽  
Author(s):  
J. Menkes
Keyword(s):  
Shear Layer ◽  
Richardson Number ◽  
Body Force ◽  
Density Variation ◽  
The Body ◽  
Neutral Stability ◽  
Horizontal Shear ◽  
Critical Richardson Number ◽  
The Stability ◽  
Small Disturbances

The effects of density variation and body force on the stability of a heterogeneous horizontal shear layer are investigated. The density is assumed to decrease exponentially with height, and the body force is assumed to be derivable from a potential; the velocity distribution in the shear layer is taken to be U(y) = tanh y. The method of small disturbances is employed to obtain a family of neutral stability curves depending on the choice of the Richardson number. It is demonstrated, furthermore, that the value of the critical Richardson number depends on the magnitude of the non-dimensional density gradient.

Effects of Non-Axisymmetric Volute On Rotating Stall in the Vaneless Diffuser of Centrifugal Compressors

2022 ◽  
Author(s):  
Zitian Niu ◽  
Zhenzhong Sun ◽  
Baotong Wang ◽  
Xinqian Zheng
Keyword(s):  
Flow Field ◽  
Stability Boundary ◽  
Rotating Stall ◽  
Vaneless Diffuser ◽  
Unstable Flow ◽  
Centrifugal Compressors ◽  
Cfd Simulations ◽  
Specific Location ◽  
Stable Operating ◽  
The Stability

Abstract Rotating stall is an important unstable flow phenomenon that leads to performance degradation and limits the stability boundary in centrifugal compressors. The volute is one of the sources inducing non-axisymmetric flows in centrifugal compressors, which has an important effect on compressors' aerodynamic performance. However, the influence of volute on rotating stall is unclear. Therefore, the effects of volute on rotating stall behavior have been explored in this paper by experiments and numerical simulations. The frequency of the rotating stall captured by the experiments is 43.9% of the impeller passing frequency, while it is 44.7% of IPF calculated from the numerical results, which proves the accuracy and capability of the numerical method in this work to study the rotating stall behavior. The flow fields from CFD simulations further reveal that one stall cell initializing in a particular location deforms into several stall cells while rotating along the circumferential direction and becomes much smaller in a specific location during the evolution process, and finally, it is suppressed in another specific location as a result of the distorted flow field caused by the volute. By optimizing volute geometry to reduce the distortion of the flow field, it is expected that the rotating stall can be weakened or suppressed, which is helpful to extend the stable operating range of centrifugal compressors.

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