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.

Mathematical modeling of steady stratified flows

2003 ◽  
Vol 3 ◽  
pp. 195-207
Author(s):  
A.M. Ilyasov ◽  
V.N. Kireev ◽  
S.F. Urmancheev ◽  
I.Sh. Akhatov
Keyword(s):  
Stokes Equations ◽  
Approximate Model ◽  
Immiscible Liquid ◽  
Stratified Flows ◽  
Navier Stokes ◽  
Flat Channel ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Flow Parameters ◽  
Direct Numerical Solution

The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

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.

ON THE EXISTENCE AND UNIQUENESS OF TWO‐FLUID CHANNEL FLOWS

2005 ◽  
Vol 9 (1) ◽  
pp. 67-78 ◽  
Author(s):  
J. Socolowsky
Keyword(s):  
Stokes Equations ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Density Ratios ◽  
Steady State Solutions ◽  
Two Fluid

iscous two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations. In this paper the solvability of the related stationary problems is discussed and computational results are presented. Furthermore, it is shown that depending on the flow parameters like viscosity or density ratios and on the fluxes there can happen nonexistence of steady‐state solutions. For other parameter sets the solution is even unique. Dvieju, tekančiu kanale, klampiu skysčiu srauto uždavinys iškyla taikant ivairias skirtingu rušiu paviršiu padengimo technologijas. Atitinkamas matematinis modelis išreiškiamas dvimačiu kraštiniu uždaviniu su laisvu paviršiumi Navje-Stokso lygtims. Straipsnyje nagrinejamas santykinai stacionaraus uždavinio išsprendžiamumas ir pateikiami skaičiavimo rezultatai. Be to parodoma, kad priklausomai nuo sroves parametru kaip ir nuo klampumo ir tankio santykio stacionarus sprendiniai gali neegzistuoti. Su kitais parametrais egzistuoja tiksliai vienas sprendinys.

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.

Vortex core identification in viscous hydrodynamics

2005 ◽  
Vol 363 (1833) ◽  
pp. 1937-1948 ◽  
Author(s):  
Lucas I Finn ◽  
Bruce M Boghosian ◽  
Christopher N Kottke
Keyword(s):  
Software Package ◽  
Message Passing ◽  
Message Passing Interface ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Steering ◽  
Navier Stokes Equations ◽  
Viscous Hydrodynamics ◽  
Knots And Links ◽  
User Intervention

We describe a software package designed for the investigation of topological fluid dynamics with a novel algorithm for locating and tracking vortex cores. The package is equipped with modules for generating desired vortex knots and links and evolving them according to the Navier–Stokes equations, while tracking and visualizing them. The package is parallelized using a message passing interface for a multiprocessor environment and makes use of a computational steering library for dynamic user intervention.

The Effect of Constriction Size on the Pulsatile Flow in a Channel

1995 ◽  
Vol 117 (4) ◽  
pp. 571-576 ◽  
Author(s):  
Moshe Rosenfeld ◽  
Shmuel Einav
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Thrombus Formation ◽  
Propagation Speed ◽  
Navier Stokes ◽  
Flow Structures ◽  
Incoming Flow ◽  
Noninvasive Methods ◽  
Navier Stokes Equations ◽  
Potential Damage

The effect of the constriction size on the pulsatile flow in a channel is studied by solving the time-dependent incompressible Navier-Stokes equations. A pulsating incoming flow is specified at the upstream boundary and the flow is investigated for several constriction sizes. Large flow structures are developed downstream of the constriction even for very small constriction size. The flow structures consist of several vortices that are created in each cycle and propagate downstream until they are washed away with the acceleration of the incoming flow. Additional vortices are created by a vortex multiplication process. The strength and total number of vortices generated in each cycle increase with the severity of the constriction. The maximal size of the vortices as well as their propagation speed are independent of the constriction size. These findings may be used for devising noninvasive methods for detecting the severity of stenoses in blood vessels and the potential damage to blood elements and thrombus formation caused by vortices.

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.

Study of Supersonic Flowfield With Secondary Injection

2004 ◽  
Author(s):  
D. Sun ◽  
R. S. Amano
Keyword(s):  
Total Pressure ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Weighted Essentially Nonoscillatory ◽  
Secondary Injection ◽  
Total Pressure Ratio

Two and three-dimensional steady flowfields generated by transverse secondary injection into a supersonic flow, was simulated by solving the Favre-averaged Navier-Stokes equations using the weighted essentially nonoscillatory (WENO) schemes. Both the two-dimensional and three-dimensional results are given. Some parameters affecting the penetration height and separation length of the interactive flowfield, including the total pressure ratio of the jet to the freestream, the boundary layer thickness, slot width, the Mach number of the freestream and injection, the jet angle, and the shape of the injection orifice in the 3D flowfield, were calculated in more detail.

scholarly journals To the issue of evaluating sonic boom overpressure and loudness

2019 ◽  
Vol 304 ◽  
pp. 02003
Author(s):  
Igor G. Bashkirov ◽  
Sergey L. Chernyshev ◽  
Vladlen S. Gorbovskoy ◽  
Andrey V. Kazhan ◽  
Vyacheslav G. Kazhan ◽  
...  
Keyword(s):  
Software Package ◽  
Stokes Equations ◽  
Aerodynamic Drag ◽  
Near Field ◽  
Theoretical Data ◽  
Aerodynamic Characteristics ◽  
Sonic Boom ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Computational Mesh

At present, in the world there is a growing interest in the development of a new generation of supersonic passenger aircraft. One of the main problems of creating such aircraft is to ensure both an acceptable sonic boom level and high aerodynamic characteristics in the supersonic cruising mode. This requires the development of reliable methods for obtaining the near field under the plane with taking into account the influence of the boundary layer, calculation of overpressure signature on the ground and evaluation of sonic boom loudness. In this work four variants of the equivalent body of revolution of minimum sonic boom with different nose sharpening were investigated for an aircraft weighing 19 tons in supersonic cruising flight at Mach number of 1.7 and altitude of 15.5 km using the software package for solving the Reynolds–averaged Navier–Stokes equations (RANS) ANSYS CFX. A macro for calculating the overpressure signature on the ground for the distribution of disturbances in the near field under the aircraft and a program for evaluating the sonic boom loudness in various metrics were developed. Computational mesh verification of the results was carried out, the obtained overpressure signatures were compared with theoretical data and calculation results from the software package for the integration of complete system of Euler equations by finite–difference method X–CODE. The effect of the sharpening of the nose part on aerodynamic drag and sound boom characteristics was shown. The work was done in the interests of the international project RUMBLE (RegUlation and norM for low sonic Boom LEvels).

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