Investigation of developed flow of an incompressible conductive fluid in a circular pipe by using the equation for the turbulent viscosity

The equation for the turbulent viscosity is used to investigate the developed flow of a conductive fluid in a longitudinal magnetic field. The solution of this equation is analyzed in the transition region from laminar to turbulent flow. The influence of the magnetic field on the local and integrated flow characteristics is studied. The convective heat exchange is computed in the case of liquid-metal flow with constant heat flux to the wall. It is shown that the computed results are in good agreement with the results of experiments in a broad range of variation of the governing parameters.     

Exact and numerical solutions of a fully developed generalized second-grade incompressible fluid with power-law temperature-dependent viscosity

We compute exact and numerical solutions of a fully developed flow of a generalized second-grade fluid, with power-law temperature-dependent viscosity (μ=θ^-M), down an inclined plane. Analytical solutions are found for the case when M=m+1, m≠1, m being a constant that models shear thinning (m<0) or shear thickening (m>0). The exact solutions are given in terms of Bessel functions. The numerical solutions indicate that both the velocity and the temperature increase with decreasing Froude number and that there is a critical value of Fr below which temperature “overshoots” its free surface value of unity. This phenomena is not reported in the work of Massoudi and Phuoc [Fully developed flow of a modified second grade fluid with temperature dependent viscosity, Acta Mech. 150 (2001) 23-37.] for viscosity that depends exponentially on temperature.     

Free convection flow over an uniform-heat-flux surface with temperature-dependent viscosity

The role of temperature-dependent viscosity is studied in laminar free convection flow adjacent to a vertical surface with uniform heat flux. The resulting non-similar equations are solved by using a suitable variable transformation and employing an implicit finite difference method. It is shown that the constant viscosity results evaluated at the ambient fluid temperature underestimate the Nusselt number and overestimate the drag coefficient. The heat transfer predictions for large values of the viscosity parameter may be two times the constant viscosity parameter prediction. The present analysis is in good agreement with the corresponding correlation of previous experimental investigation.     

Numerical solution of the turbulent flow of an incompressible fluid in curved planar and axially symmetrical channels

The governing equations for axially symmetric flow, where the Reynolds stresses are expressed by scalar turbulent viscosity, are the Reynolds equations. The turbulence model k, ? is used in the well-known form for fully developed turbulent flow.The numerical method, a continuation of the MAC system¹, is adapted so that even for high Reynolds cell numbers precision (δx²) can be achieved for the steady flow. Irregular cells join the rectangular network on the curved surface. Von Neumann's stability condition of the linearised numerical system is investigated. Special problems concerning the numerical solution of the turbulence model equations are stated and a special procedure is worked out to ensure that the fields k, ? do not converge to physically meaningless values. The program for the computer is universal in that the boundary problems can be assigned by input data.As an example, an axially symmetrical diffuser with an area ratio of widening 1.40 is computed. Fields of velocity and pressure at the wall as well as fields v_T and k are assessed. The results are compared with an experiment. The conclusion is that this method is suitable for the problems mentioned in this study as well as for unsteady flow.     

Partial-average-based equations of incompressible turbulent flow

This paper presents a detailed study of incompressible turbulent flow based on a newly developed statistical partial average scheme. As the ensemble average is taken on two groups of turbulent fluctuations separately, the partial average scheme is able to capture the first-order statistical moment of the fluctuation field, providing valuable information in addition to what have been known in the past from the conventional Reynolds average. The first-order statistical moment serves as the foundation in formulating theories of orthotropic turbulence and a momentum transfer chain in the modeling of second-order correlation terms, and eventually leads to a complete set of equations of incompressible turbulent flow. Without any empirical coefficients, the same set of the equations is used to simulate statistical mean behaviors and coherent structures of various benchmark turbulent flows. The simulated results are in good agreement with experimental data.     

On the spiral form of instability of couette flow of a viscous fluid

Summary The instability of Couette flow caused by vortices with spiral symmetry is studied; the equations of motion in a suitable spiral metric turn out to be analogous with those describing vortices with axial symmetry. The approximate solution is obtained by discretization of the differential equations. Special numerical techniques reduce drastically the dimensions of the matrices involved in the calculations. The Taylor number for transition is computed; comparisons with known results are established. The results are shown in a number of graphs.

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Sommario Si studia la forma di instabilità del moto alla Couette per vortici con simmetria a spirale. In una opportuna metrica a spirale le equazioni risultano analoghe a quelle che descrivono i vortici a simmetria assiale. La soluzione approssimata delle equazioni è ottenuta per discretizzazione mediante differenze finite, usando opportuni accorgimenti per ridurre notevolmente le dimensioni delle matrici su cui si eseguono i calcoli. Viene fatto il calcolo del numero critico di Taylor per le equazioni linearizzate in funzione dei parametri significativi e si stabiliscono confronti con risultati noti. Alcuni grafici mostrano i risultati ottenuti.

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On solving the problem of an ideal incompressible fluid flow around large-aspect-ratio axisymmetric bodies

Based on Babenko’s fundamental mathematical ideas, principally new (unsaturated) algorithms are developed for the numerical solution of problems of a potential axisymmetric ideal fluid flow around bodies of revolution, in particular, an ellipsoid of revolution with an aspect ratio equal to 1000. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 56–67, September–October, 2006.     

Linear stability of plane couette flow of an upper convected maxwell fluid

We investigate the linear stability of plane Couette flow of an upper convected Maxwell fluid using a spectral method to compute the eigenvalues. No instabilities are found. This is in agreement with the results of Ho and Denn [1] and Lee and Finlayson [2], but contradicts “proofs” of instability by Gorodtsov and Leonov [3] and Akbay and Frischmann [4,5]. The errors in those arguments are pointed out. We also find that the numerical discretization can generate artificial instabilities (see also [1,6]). The qualitative behavior of the eigenvalue spectrum as well as the artificial instabilities is discussed.     

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time‐independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi–Babuska condition. The k–l model is used to complete the turbulence closure problem. The non‐symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a ‘V‐cycling’ schedule. These methods are all compared to the non‐symmetric frontal solver. Copyright © 1999 John Wiley & Sons, Ltd.     

High-order LES modeling of turbulent incompressible flow

This article presents the high-order algorithms that we have developed for large-eddy simulation of incompressible flows, and the results that have been obtained for the 3D turbulent wake of a cylinder at a Reynolds number of $\mathit{Re}=3900$. To cite this article: R. Pasquetti, C. R. Mecanique 333 (2005).     

Analytical model of motion of turbulent vortex rings in an incompressible fluid

An analytical model describing the motion of vortex rings in an incompressible fluid is constructed. The model is valid both for homogeneous and inhomogeneous vortices buoyant in the gravity field, as well as for combined vortices. The expansion angle of a buoyant vortex is found from the characteristic parameters that define the flow rather than specified on the basis of experiments. Significant differences in the expansion angles of homogeneous and buoyant vortex rings are explained. The calculation results for the proposed model are compared with the results of laboratory experiments and data on the rise of the cloud produced by an atomic explosion.     

Hydraulic jump in the shear flow of an ideal incompressible fluid

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 11–20, January–February, 1995.