scholarly journals Asymptotically based self-similarity solution of the Navier–Stokes equations for a porous tube with a non-circular cross-section

2017 ◽  
Vol 826 ◽  
pp. 396-420 ◽  
Author(s):  
M. Bouyges ◽  
F. Chedevergne ◽  
G. Casalis ◽  
J. Majdalani
Keyword(s):  
Cross Section ◽  
Similarity Solution ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Internal Flow ◽  
Navier Stokes ◽  
Solid Rocket Motor ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Radial Deviation

This work introduces a similarity solution to the problem of a viscous, incompressible and rotational fluid in a right-cylindrical chamber with uniformly porous walls and a non-circular cross-section. The attendant idealization may be used to model the non-reactive internal flow field of a solid rocket motor with a star-shaped grain configuration. By mapping the radial domain to a circular pipe flow, the Navier–Stokes equations are converted to a fourth-order differential equation that is reminiscent of Berman’s classic expression. Then assuming a small radial deviation from a fixed chamber radius, asymptotic expansions of the three-component velocity and pressure fields are systematically pursued to the second order in the radial deviation amplitude. This enables us to derive a set of ordinary differential relations that can be readily solved for the mean flow variables. In the process of characterizing the ensuing flow motion, the axial, radial and tangential velocities are compared and shown to agree favourably with the simulation results of a finite-volume Navier–Stokes solver at different cross-flow Reynolds numbers, deviation amplitudes and circular wavenumbers.

Influence of Surface Roughness on Shear Flow

2004 ◽  
Vol 71 (4) ◽  
pp. 459-464 ◽  
Author(s):  
S. Bhattacharyya ◽  
S. Mahapatra ◽  
F. T. Smith
Keyword(s):  
Cross Section ◽  
Numerical Solutions ◽  
Flat Surface ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Uniform Shear

The local planar flow of incompressible fluid past an obstacle of semi-circular cross section is considered, the obstacle being mounted on a long flat surface. The far-field motion is one of uniform shear. Direct numerical solutions of the Navier-Stokes equations are described over a range of Reynolds numbers. The downstream eddy length and upstream position of maximum pressure gradient are found to agree with increased Reynolds number theory; in particular the agreement for the former quantity is close for Reynolds numbers above about 50.

Linear Analysis of the Currents in a Pipe

1986 ◽  
Vol 41 (9) ◽  
pp. 1141-1153
Author(s):  
U. Brosa
Keyword(s):  
Exact Solutions ◽  
Cross Section ◽  
Bulk Viscosity ◽  
Stokes Equations ◽  
Simple Procedure ◽  
Circular Cross Section ◽  
Linear Analysis ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Infinite Set

A simple procedure to find solutions of the hydrodynamic Stokes equations is given. The procedure is used to determine the linear modes of a newtonian fluid in a pipe of circular cross section. Compressibility, shear and bulk viscosity are included, and no restrictions on the symmetry of the modes are made. Furthermore an infinite set of exact solutions of the Navier-Stokes equations is presented.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

Analytical and Semi-empirical Models of Tornadoes and Downbursts

2021 ◽  
Author(s):  
Djordje Romanic ◽  
Horia Hangan
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Empirical Models ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Simplifying Assumptions ◽  
The Individual ◽  
Semi Empirical

Analytical and semi-empirical models are inexpensive to run and can complement experimental and numerical simulations for risk analysis-related applications. Some models are developed by employing simplifying assumptions in the Navier-Stokes equations and searching for exact, but many times inviscid solutions occasionally complemented by boundary layer equations to take surface effects into account. Other use simple superposition of generic, canonical flows for which the individual solutions are known. These solutions are then ensembled together by empirical or semi-empirical fitting procedures. Few models address turbulent or fluctuating flow fields, and all models have a series of constants that are fitted against experiments or numerical simulations. This chapter presents the main models used to provide primarily mean flow solutions for tornadoes and downbursts. The models are organized based on the adopted solution techniques, with an emphasis on their assumptions and validity.

Low-Frequency Fluctuations In The Flow Over Confined Cylinder In A Narrow Rectangular Duct At Re = 3 750

2017 ◽  
Vol 12 (1) ◽  
pp. 43-49
Author(s):  
Egor Palkin ◽  
Rustam Mullyadzhanov
Keyword(s):  
Stokes Equations ◽  
Low Frequency ◽  
Horseshoe Vortex ◽  
Navier Stokes ◽  
Infinite Cylinder ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Frequency Modulations ◽  
Bounding Surfaces

Flows between two closely spaced bounding surfaces are frequently appear in engineering applications and natural flows. In current paper the flow over a cylinder in a narrow rectangular duct was investigated by numerical computations of Navier-Stokes equations using Large eddy simulations (LES) at ReD = 3 750 based on cylinder diameter and the bulk velocity at inflow boundary. The influence of the bounding walls was demonstrated by comparing mean flow streamlines with the flow over an infinite cylinder at close Reynolds numbers. A comparison between the time-averaged velocity field in front and past the cylinder with experimental from the literature data showed good agreement although the characteristic horseshoe vortex structures are highly sensitive to Reynolds number and turbulence level at inflow boundary. Most energetic modes in recirculating region were revealed by spectral analysis. These low-frequency modulations were characterized by the pair of dominating vortices which are expected to have high influence on the heat transfer in near wake of the cylinder.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

The Research on Numerical Simulation of the Centrifugal Pump and Configuration Perfected

2013 ◽  
Vol 694-697 ◽  
pp. 56-60
Author(s):  
Yue Jun Ma ◽  
Ji Tao Zhao ◽  
Yu Min Yang
Keyword(s):  
Numerical Simulation ◽  
Centrifugal Pump ◽  
Unstructured Grid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Internal Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Phenomena ◽  
Simplec Algorithm

In the paper, on the basis of three-dimensional Reynolds-averaged Navier-Stokes equations and the RNG κ-ε turbulence model, adopting Three-dimensional unstructured grid and pressure connection the implicit correction SIMPLEC algorithm, and using MRF model which is supported by Fluent, this paper carries out numerical simulation of the internal flow of the centrifugal pump in different operation points. According to the results of numerical simulation, this paper analyzes the bad flow phenomena of the centrifugal pump, and puts forward suggests about configuration perfected of the centrifugal pump. In addition, this paper is also predicted the experimental value of the centrifugal pump performance, which is corresponding well with the measured value.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

The effects of secondary flow on the laminar dispersion of an injected substance in a curved tube

1970 ◽  
Vol 315 (1520) ◽  
pp. 99-113 ◽  
Keyword(s):  
Secondary Flow ◽  
Cross Section ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Flux Ratio ◽  
Original Method ◽  
Asymptotic Solutions ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Mean Velocity

The numerical solution by McConalogue & Srivastava (1968) of Dean’s simplified Navier–Stokes equations for the laminar flow of an inviscid fluid through a tube of circular cross-section of radius a , coiled in a circular arc of radius L , and valid for k in the range (16.6, 77.1), where k = Re √( a / L ), Re the Reynolds number, is compared with experiment, correlated to the asymptotic solutions for k > 100, and extended to study the convective axial dis­persion of a substance injected into the tube. The variation of the calculated flux ratio agrees closely with White’s (1929) measurements of the inverse quantity over the same range, and the field patterns for the upper end of the range establish the validity of the two basic assumptions of the asymptotic solutions. The original method is extended to calculate the mean axial velocity of a typical particle of the fluid and to present the statis­tical distribution of mean velocity over the particles of a substance injected as a thin disk uniformly over the cross section of the tube. These distributions are used to display the varia­tion with k of the shape of indicator concentration-time curves. The expected effect of secondary flow, in producing a more uniform distribution of velocity over the fluid than in Poiseuille flow, is evident.

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