Shear-flow instability due to a wall and a viscosity discontinuity at the interface

1987 ◽  
Vol 179 ◽  
pp. 201-225 ◽  
Author(s):  
A. P. Hooper ◽  
W. G. C. Boyd
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Flow Instability ◽  
Short Wave ◽  
Linear Instability ◽  
Wave Instability ◽  
New Type ◽  
Lower Fluid ◽  
Superposed Fluids ◽  
Shear Flow Instability

Consider the Couette flow of two superposed fluids of different viscosity with the depth of the lower fluid bounded by a wall and the interface while the depth of the upper fluid is unbounded. The linear instability of this flow configuration is studied at all values of flow Reynolds number and disturbance wavelength using both asymptotic and numerical methods. Three distinct forms of instability are found which are dependent on the magnitude of two dimensionless parameters β and (α R)1/3, where β is a dimensionless wavenumber measured on a viscous lengthscale, α is a dimensionless wavenumber measured on the scale of the depth of the lower fluid and R is the Reynolds number of the lower fluid. At large β there is the short-wave instability found previously by Hooper & Boyd (1983). At small β and small (αR)1/3 there is the long-wave instability first discovered by Yih. At small β and large (αR)1/3 there is a new type of instability which arises only if the kinematic viscosity of the lower bounded fluid is less than the kinematic viscosity of the upper fluid.

scholarly journals Nonlinear Vortex Structures Driven by Small-Scale Non-helical Forces in Obliquely Rotating Stratified Fluids

2021 ◽  
Vol 66 (6) ◽  
pp. 478
Author(s):  
M.I. Kopp ◽  
A.V. Tur ◽  
V.V. Yanovsky
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Linear Instability ◽  
Vortex Structures ◽  
Small Scale ◽  
Third Order ◽  
Nonlinear Modes ◽  
The Third ◽  
New Type ◽  
Scale Turbulence

We study a new type of large-scale instability in obliquely rotating stratifi ed fl uids with small-scale nonhelical turbulence. The small-scale turbulence is generated by the external force with zero helicity and low Reynolds number. The theory uses the method of multiscale asymptotic expansions. The nonlinear equations for large-scale motions are obtained in the third order of perturbation theory. We consider a linear instability and stationary nonlinear modes. Solutions in the form of nonlinear Beltrami waves and localized vortex structures such as kinks of a new type are obtained.

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

scholarly journals Movement of a finite body in channel flow

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160164 ◽  
Author(s):  
Frank T. Smith ◽  
Edward R. Johnson
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Flow Instability ◽  
Flow Direction ◽  
Finite Size ◽  
The Body ◽  
Thin Body ◽  
Shear Stresses ◽  
Unsteady Interaction ◽  
High Reynolds

A body of finite size is moving freely inside, and interacting with, a channel flow. The description of this unsteady interaction for a comparatively dense thin body moving slowly relative to flow at medium-to-high Reynolds number shows that an inviscid core problem with vorticity determines much, but not all, of the dominant response. It is found that the lift induced on a body of length comparable to the channel width leads to differences in flow direction upstream and downstream on the body scale which are smoothed out axially over a longer viscous length scale; the latter directly affects the change in flow directions. The change is such that in any symmetric incident flow the ratio of slopes is found to be cos ⁡ ( π / 7 ) , i.e. approximately 0.900969, independently of Reynolds number, wall shear stresses and velocity profile. The two axial scales determine the evolution of the body and the flow, always yielding instability. This unusual evolution and linear or nonlinear instability mechanism arise outside the conventional range of flow instability and are influenced substantially by the lateral positioning, length and axial velocity of the body.

scholarly journals Effect of the Reynolds Number and Clearance Flow on the Aerodynamic Characteristics of a New Variable Inlet Guide Vane

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 172
Author(s):  
Hengtao Shi
Keyword(s):  
Reynolds Number ◽  
Guide Vane ◽  
Three Dimensional ◽  
High Growth ◽  
Aerodynamic Characteristics ◽  
Inlet Guide Vane ◽  
Separation Region ◽  
Clearance Flow ◽  
New Type ◽  
Variable Inlet Guide Vane

Recently, a new type of low-loss variable inlet guide vane (VIGV) was proposed for improving a compressor’s performance under off-design conditions. To provide more information for applications, this work investigated the effect of the Reynolds number and clearance flow on the aerodynamic characteristics of this new type of VIGV. The performance and flow field of two representative airfoils with different chord Reynolds numbers were studied with the widely used commercial software ANSYS CFX after validation was completed. Calculations indicate that, with the decrease in the Reynolds number Rec, the airfoil loss coefficient ω and deviation δ first increase slightly and then entered a high growth rate in a low range of Rec. Afterwards, a detailed boundary-layer analysis was conducted to reveal the flow mechanism for the airfoil performance degradation with a low Reynolds number. For the design point, it is the appearance and extension of the separation region on the rear portion; for the maximum incidence point, it is the increase in the length and height of the separation region on the former portion. The three-dimensional VIGV research confirms the Reynolds number effect on airfoils. Furthermore, the clearance leakage flow forms a strong stream-wise vortex by injection into the mainflow, resulting in a high total-pressure loss and under-turning in the endwall region, which shows the potential benefits of seal treatment.

scholarly journals The impact of magnetic fields on momentum transport and saturation of shear-flow instability by stable modes

2021 ◽  
Vol 28 (2) ◽  
pp. 022309
Author(s):  
A. E. Fraser ◽  
P. W. Terry ◽  
E. G. Zweibel ◽  
M. J. Pueschel ◽  
J. M. Schroeder
Keyword(s):  
Magnetic Fields ◽  
Shear Flow ◽  
Flow Instability ◽  
Momentum Transport ◽  
Shear Flow Instability ◽  
The Impact

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).

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Amplitude propagation in slowly varying trains of shear-flow instability waves

1986 ◽  
Vol 170 ◽  
pp. 21-51 ◽  
Author(s):  
J. M. Russell
Keyword(s):  
Variational Principles ◽  
Flow Instability ◽  
Near Field ◽  
Equations Of Motion ◽  
Wave Action ◽  
Small Disturbance ◽  
Instability Waves ◽  
Action Density ◽  
Spatial Coordinates ◽  
Shear Flow Instability

The analog of Whitham's law of conservation of wave action density is derived in the case of Rayleigh instability waves. The analysis allows for wave propagation in two space dimensions, non-unidirectionality of the background flow velocity profiles and weak horizontal nonuniformity and unsteadiness of those profiles. The small disturbance equations of motion in the Eulerian flow description are subject to a change of dependent variable in which the new variable represents the pressure-driven part of a disturbance material coordinate function as a function of the Cartesian spatial coordinates and time. Several variational principles expressing the physics of the small disturbance equations of motion are presented in terms of this new variable. A law of conservation of ‘bilinear wave action density’ is derived by a method intermediate between those of Jimenez and Whitham (1976) and Hayes (1970a). The distinction between the observed square amplitude of an amplified wavetrain and the wave action density is discussed. Three types of algebraic focusing are discussed, the first being the far-field ‘caustics’, the second being near-field ‘movable singularities’, and the third being a focusing mechanism due to Landahl (1972) which we here derive under somewhat weaker hypotheses.

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