Numerical models of jet flows of a viscous incompressible fluid

Abstract

We give the numerical models of two-dimensional and axisymmetric stationary jet flows, which are based on the approximation of a boundary layer and the simplest nonstationary grids. We carried out the numerical experiments that demonstrate the convergence of the algorithms considered. Using the modified turbulent e -ε model, we numerically simulate the dynamics of two-dimensional and axisymmetric turbulent wakes with zero and small nonzero excess momenta.The approximation of a boundary (thin shear) layer is a classical approximation when studying the two-dimensional and axisymmetric jet flows [21,23], The methods of calculating the boundary-layer equations were considered in a sufficiently large number of works [4][5][6]11,12,[15][16][17][19][20][21]23,26,27] (a more complete bibliography can be found therein). Analysing the works on the numerical integration of the boundarylayer equations, we can emphasize the trend associated with the use of adaptive grids [15,18,21,23,27]. First of all, this is the use of Euler -Lagrange Prandtl-Mises variables [18,21,23]. The finite difference method and the collocation grid method with the use of adaptive grids were developed in [15,27], respectively. The flows in the boundary layer itself were considered in [15,27]. Both laminar and turbulent flows were studied in the above works. Turbulent wakes belong to the familiar jet flows of a viscous incompressible fluid. The property of conservativeness of the algorithm with respect to the law of conservation of momentum is an important property of the methods of calculating wake flows. This problem has been rigorously solved only for wakes with nonzero excess momentum [5]. The law of conservation of momentum is of special importance in studying the wakes with zero or small excess momentum [19]. The momentumless turbulent wakes (see, e.g. [2]) are shearless even at a distance of several diameters from a body. In this case the defect of a longitudinal component in the wake becomes practically equal to zero. Thus, we can hardly rely on the efficiency of Prandtl-Mises variables in their classical interpretation when numerically simulating the asymptotic (at large distances from a body) behaviour of the wake.In this paper we attempt to construct a simple and sufficiently efficient algorithm for calculating the jet flows of a viscous incompressible fluid, using nonstationary grids.

Numerical modelling of momentumless wakes using semiempirical turbulence models of second and third order

“…The initial distributions ε, U d , u 2 , v 2 , w 2 were given at a distance x x 0 10 from the body based on Aleksenko and Kostomakha's experimental data [1] (see also [4,14,29]). The initial distributions ε, U d , u 2 , v 2 , w 2 were given at a distance x x 0 10 from the body based on Aleksenko and Kostomakha's experimental data [1] (see also [4,14,29]).…”

Invariant Manifolds in Parametric turbulent Models

“…The initial distribution of the tangential stress u v is specified by formula (5). A finite difference algorithm for calculating, its test and realization, and the results of its application to the problem of turbulent wake dynamics were detailed in [19]. The computations are performed to double accuracy.…”

Compatible differential constraints to an infinite chain of transport equations for cumulants

“…It has been shown (see, for example [19]) that the momentumless turbulent wakes behave quite differently from the turbulent wakes with a nonzero excess impulse. In particular, we may account that the momentumless turbulent wake is also a shearless turbulent flow.…”

“…In particular, we may account that the momentumless turbulent wake is also a shearless turbulent flow. There exists a sufficiently large number of publications [19][20][21][22][23] (comprehensive references can be found therein) in which the results of experimental and theoretical investigations are discussed. The results of laboratory and numerical experiments demonstrate a faster decrease of the defect of the longitudinal velocity component in comparison with a wake flow behind a towed body.…”