I. Eigenmotion analysis

1965 ◽  
Vol 285 (1402) ◽  
pp. 382-399 ◽  
Keyword(s):  
Dihedral Angle ◽  
Stokes Equations ◽  
Slow Motion ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Weakly Singular ◽  
Complex Eigenvalues ◽  
Slow Motions

General wedge and comer problems lead to the introduction of complex Navier-Stokes equations of complex laminar motions the real parts of which describe real laminar flows. Under the non-slip condition at the surface of a dihedral angle the general solution of the complex Navier-Stokes equations is established on the basis of the corresponding integral of the Stokes equations of slow motions. The latter integration is accomplished in terms of slow-motion eigenfunctions with real and complex eigenvalues. The results render valuable information about the flow properties at the leading or trailing edge of a dihedral angle. Weakly singular solutions, which are characterized by an infinite pressure and a finite velocity at the edge of the dihedral angle, are shown to exist for all wedges under asymmetric attack and for sharp wedges under symmetric attack. The existence of critical and branching eigenvalues exhibits the non-analyticity of laminar flows around dihedral angles in their dependence upon the corresponding wedge or corner angles.

II. Analysis of regular and singular motions

1965 ◽  
Vol 285 (1402) ◽  
pp. 400-412 ◽  
Keyword(s):  
Stokes Equations ◽  
Separated Flow ◽  
Fluid Flows ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Weakly Singular ◽  
Simultaneous Existence ◽  
Additional Explanation

An eigenmotion analysis of viscous fluid flows around dihedral angles presented in part I of this paper revealed the simultaneous existence of regular and weakly singular motions which are characterized by finite and infinite pressures at the edge of a wedge. Since the derivation of the Navier-Stokes equations is based on the finiteness of the velocity and pressure, the physical meaning of an infinite pressure in the region of operation requires an additional explanation. The present investigations analyse the flow properties of regular and weakly singular motions past a semi-infinite flat plate under symmetric and asymmetric attack. Particular attention is directed to the attached and separated flow patterns which can develop around a sharp edge. The duality of regular and weakly singular motions is shown to exist for most of the typical flow patterns which can be observed in published photographs. The qualitative agreement with photographs is especially satisfactory for regular motions. A brief summary of the essential flow properties of both types is given.

scholarly journals Critical slope for laminar transcritical shallow-water flows

2015 ◽  
Vol 783 ◽  
Author(s):  
O. Thual ◽  
L. Lacaze ◽  
M. Mouzouri ◽  
B. Boutkhamouine
Keyword(s):  
Stokes Equations ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Critical Surface ◽  
Steady Flows ◽  
Surface Slope ◽  
Critical Height ◽  
Navier Stokes Equations ◽  
Shallow Water Flows ◽  
Critical Slope

Backwater curves denote the depth profiles of steady flows in a shallow open channel. The classification of these curves for turbulent regimes is commonly used in hydraulics. When the bottom slope $I$ is increased, they can describe the transition from fluvial to torrential regimes. In the case of an infinitely wide channel, we show that laminar flows have the same critical height $h_{c}$ as that in the turbulent case. This feature is due to the existence of surface slope singularities associated to plug-like velocity profiles with vanishing boundary-layer thickness. We also provide the expression of the critical surface slope as a function of the bottom curvature at the critical location. These results validate a similarity model to approximate the asymptotic Navier–Stokes equations for small slopes $I$ with Reynolds number $Re$ such that $Re\,I$ is of order 1.

Swirling Laminar Pipe Flow of Suspensions

1973 ◽  
Vol 40 (2) ◽  
pp. 331-336 ◽  
Author(s):  
S. K. Tung ◽  
S. L. Soo
Keyword(s):  
Pipe Flow ◽  
Stokes Equations ◽  
Fluid Phase ◽  
Navier Stokes ◽  
Swirl Ratio ◽  
Particulate Phase ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Flow Reynolds Number ◽  
Laminar Pipe Flow

Vortex pipe flow of suspensions with laminar motion in the fluid phase is treated. The pipe consists of two smoothly joined sections, one stationary and the other rotating with a constant angular velocity. The flow properties of the fluid phase are determined by solving the complete Navier-Stokes equations numerically. The governing parameters are the flow Reynolds number and swirl ratio. Subsequent numerical solution to the momentum equations governing the particulate phase provides for both particle velocity and concentration distributions.

scholarly journals Subcritical transition in channel flows

2002 ◽  
Vol 451 ◽  
pp. 35-97 ◽  
Author(s):  
S. JONATHAN CHAPMAN
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Domain Of Attraction ◽  
Reynolds Numbers ◽  
Linear Instability ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Plane Poiseuille Flow ◽  
Navier Stokes Equations ◽  
Laminar State

Certain laminar flows are known to be linearly stable at all Reynolds numbers, R, although in practice they always become turbulent for sufficiently large R. Other flows typically become turbulent well before the critical Reynolds number of linear instability. One resolution of these paradoxes is that the domain of attraction for the laminar state shrinks for large R (as Rγ say, with γ < 0), so that small but finite perturbations lead to transition. Trefethen et al. (1993) conjectured that in fact γ <−1. Subsequent numerical experiments by Lundbladh, Henningson & Reddy (1994) indicated that for streamwise initial perturbations γ =−1 and −7/4 for plane Couette and plane Poiseuille flow respectively (using subcritical Reynolds numbers for plane Poiseuille flow), while for oblique initial perturbations γ =−5/4 and −7/4 Here, through a formal asymptotic analysis of the Navier–Stokes equations, it is found that for streamwise initial perturbations γ =−1 and −3/2 for plane Couette and plane Poiseuille flow respectively (factoring out the unstable modes for plane Poiseuille flow), while for oblique initial perturbations γ =−1 and −5/4. Furthermore it is shown why the numerically determined threshold exponents are not the true asymptotic values.

Navier-Stokes Computations of Cavity Aeroacoustics with Suppression Devices

1994 ◽  
Vol 116 (1) ◽  
pp. 105-112 ◽  
Author(s):  
Oktay Baysal ◽  
Guan-Wei Yen ◽  
Kamran Fouladi
Keyword(s):  
Turbulent Flows ◽  
Cavity Length ◽  
Stokes Equations ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Time Series Analyses ◽  
Cavity Acoustics ◽  
Volume Method

Effectiveness of two devices to suppress the cavity acoustics was computationally investigated. Two dimensional, computational simulations were performed for the transonic, turbulent flows past a cavity, which was first equipped with a rear face ramp and then with a spoiler. The Reynolds-averaged, unsteady, compressible, full Navier-Stokes equations were solved time accurately by a second-order accurate, implicit, upwind, finite-volume method. The effect of turbulence was included through the Baldwin-Lomax model with modifications for the multiple-wall effects and for the highly vortical flow with a shear layer. The results included instantaneous and time-averaged flow properties, and time-series analyses of the pressure inside the cavity, which compared favorably with the available experimental data. These results were also contrasted with the computed aeroacoustics of the same cavity (length-to-depth ratio of 4.5), but without a device, to demonstrate the suppression effectiveness.

scholarly journals Dynamics of laminar flows with coaxial oppositely-rotating layers

Vestnik MGSU ◽  
2019 ◽  
pp. 332-346
Author(s):  
Andrey L. Zuikov
Keyword(s):  
Reynolds Number ◽  
Active Zone ◽  
Vortex Flow ◽  
Stokes Equations ◽  
Laminar Flows ◽  
Radial Velocities ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Vortex Flows ◽  
Navier Stokes Equations

Introduction. The work relates to the scientific foundations of hydraulic and energy construction and is devoted to the study of laminar flows with coaxial oppositely-rotating layers. In the literature, such flows are called counter-vortex. In the turbulent range, counter-vortex flows are characterized by intensive mixing of the medium, which is widely used in the technologies of mixing non-natural and multi-phase media in thermal and atomic energy, in systems of mass- and heat transfer, in chemistry and microbiology, ecology, engine and rocket production. The aim of the theoretical study is to study the physical laws of the hydrodynamics of counter-vortex flows. Research methods. The theoretical Navier-Stokes equations and continuity equation are the basis of the theoretical model of the laminar counter-vortex flow. Results. Assuming the radial velocities are much less than the azimuthal and axial velocities and taking the Oseen approximation, the solution of the Navier - Stokes equations is obtained as Fourier - Bessel series or products of Fourier - Bessel series. In particular, the following were obtained: formulas for calculating the radial-longitudinal distributions of the normalized azimuthal, axial and radial velocities in the flow under study, the velocities are presented graphically in the form of radial profiles; equations for the calculation of current lines and viscous vortex fields, which are also presented in the form of graphs, were obtained. The two-layer and four-layer counter-vortex flows are considered. The analysis of the obtained theoretical results is performed. Conclusions. On the axis at the beginning of the active zone, the formation of a return flow with significant negative velocities is characteristic. This leads to the formation of a recirculation region, the mass exchange between which and the external flow is absent. Cascades of concentric vortexes of such high intensity that are not found in streams of a different nature are generated in the active zone. Calculation formulas include exp (-λ2x/Re) exponent multiplied by Reynolds number in degree b = 0 or b = -1, therefore increasing Reynolds number when b = 0 leads to proportional transfer of arbitrary characteristic counter-vortex flow down the pipe; and at b = -1, the bias of characteristic is accompanied by a proportional decrease in its scale.

Turbulent Flow in Two-Inlet Channels

1993 ◽  
Vol 115 (4) ◽  
pp. 638-645 ◽  
Author(s):  
Hsiao C. Kao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
High Reynolds ◽  
Inflow Conditions ◽  
Number Form

The problem of turbulent flows in two-inlet channels has been studied numerically by solving the Reynolds-averaged Navier-Stokes equations with the k–ε model in a mapped domain. Both the high Reynolds number and the low Reynolds number form were used for this purpose. In general, the former predicts a weaker and smaller recirculation zone than the latter. Comparisons with experimental data, when applicable, were also made. The bulk of the present computations used, however, the high Reynolds number form to correlate different geometries and inflow conditions with the flow properties after turning.

scholarly journals Modelling of the flow in front of the jet obstacle at variation of oncoming flow parameters

2021 ◽  
pp. 1-14
Author(s):  
Alexander Evgenyevich Bondarev ◽  
Artyom Evgenyevich Kuvshinnikov ◽  
Tatiana Nikolaevna Mikhailova ◽  
Irina Gennadievna Ryzhova ◽  
Lev Zalmanovich Shapiro
Keyword(s):  
Software Package ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Incoming Flow ◽  
Oncoming Flow ◽  
Input Flow ◽  
Navier Stokes Equations ◽  
Flow Parameters

The results of numerical simulation of the problem of interaction of supersonic flow with a jet obstacle under variation of input flow parameters are considered. The problem is solved in the system of Navier-Stokes equations. Laminar flows are considered. The qualitative flow pattern has been studied under the variation of incoming flow velocity and boundary layer thickness in the incoming flow. The calculations were performed using the OpenFOAM software package.

scholarly journals Stability of bedforms in laminar flows with free surface: from bars to ripples

2009 ◽  
Vol 642 ◽  
pp. 329-348 ◽  
Author(s):  
O. DEVAUCHELLE ◽  
L. MALVERTI ◽  
É. LAJEUNESSE ◽  
P.-Y. LAGRÉE ◽  
C. JOSSERAND ◽  
...  
Keyword(s):  
Free Surface ◽  
Stability Analysis ◽  
Stokes Equations ◽  
Transport Model ◽  
Bedload Transport ◽  
Laminar Flows ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Stability

The present paper is devoted to the formation of sand patterns by laminar flows. It focuses on the rhomboid beach pattern, formed during the backswash. A recent bedload transport model, based on a moving-grains balance, is generalized in three dimensions for viscous flows. The water flow is modelled by the full incompressible Navier–Stokes equations with a free surface. A linear stability analysis then shows the simultaneous existence of two distinct instabilities, namely ripples and bars. The comparison of the bar instability characteristics with laboratory rhomboid patterns indicates that the latter could result from the nonlinear evolution of unstable bars. This result, together with the sensibility of the stability analysis with respect to the parameters of the transport law, suggests that the rhomboid pattern could help improving sediment transport models, so critical to geomorphologists.

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