DNS OF SWIRLING FLOW IN A ROTATING PIPE

Abstract

Numerical simulation is carried out to study the combined effects of rotation and induced swirl on the fully developed turbulent pipe flow at Reynolds number Reb = 4900, based on the bulk velocity and the pipe diameter. The swirl is induced by a body force in the tangential momentum equation, which produces a tangential velocity field in the near wall region. Results from a single swirl along with five different strengths of the rotation are considered. The effects of rotation and swirl on turbulent structures are investigated in detail. Also instantaneous axial velocity fluctuations are provided to visualize the effects on the turbulent structures. Introduction Turbulent flows of liquids or gases through long straight pipes occur in a variety of different industrial applications. Such flows have received considerable attention throughout the years and are fairly well understood today, although some uncertainties still prevails at very high Reynolds numbers; see e.g. Hultmark et al. (2012). Under certain circumstances, however, the streamlines are helical rather than straight lines and the mean flow becomes twocomponential rather than one-componential. This happens if a swirling motion arises or if the pipe is subjected to axial rotation. Swirl may result from a swirl generator or an upstream elbow, whereas axially rotating pipes are found in turbo machinery cooling systems. In both cases, a circumferential componentUθ of the mean velocity vector coexists with the axial mean velocity componentUz. The presence of a circumferential mean velocity component tends to orient the coherent near-wall structures with the local mean flow direction. Besides the tilting of the near-wall structures, the structures may be strengthened or weakened in a two-componential mean flow. Fully developed turbulent flow in axially rotating pipes has been studied experimentally by Murakami & Kikuyama (1980) and Imao et al. (1996) and by means of large-eddy simulations (LES) by Eggels & Nieuwstadt (1993) and direct numerical simulations (DNS) by Eggels et al. (1994) and Orlandi & Fatica (1997). It is observed that rotation results in drag reduction. Recent DNS studies of swirling pipe flow by Nygard & Andersson (2010) showed the same influence of the induced swirl on the axial mean velocity as axial rotation. However, the presence of swirl turned out to have less clear-cut effects on the turbulence field. In the cases with stronger swirl, even drag reduction was reported whereas weak swirl gave rise to excess drag. Swirl and axial rotation both give rise to helical streamlines and it is therefore not unexpected that similarities between these two circumstances can be found. The aim of the present study is to examine how an originally swirling pipe flow reacts to axial rotation. For a given swirl number, five different rotation rates (N = −1,−0.5,0,0.5,1) with both senses of rotation will be studied. To this end, the full Navier-Stokes equations are solved in three-dimensional space and in time on a computational mesh sufficiently fine to resolve the energetic large-eddy structures. Governing equations The governing equations are solved in cylindrical coordinates θ , r, and z. For practical reasons, the variables qθ = ruθ , qr = rur and qz = uz are introduced. Here uθ , ur, and uz are velocity components in the respective coordinate directions. All variables in the governing equations are non-dimensionalized with the centerline velocity of the Poiseuille profile, Up and the pipe radius, R. To simplify, the non-dimensionalized total pressure, ptotal is divided in to three parts as follows: ptotal = P(θ)+ P(z)+ p(θ ,r,z, t). (1) The first part, P(θ), is the artificial transverse pressure component. In order to introduce a swirl in the pipe flow, the azimuthal pressure gradient, dP/dθ , is introduced. The second part of Eq. (1) is the mean axial pressure, P(z) and finally, p(θ ,r,z, t) represents the remaining part of the total pressure. The Navier-Stokes equations in terms of the new variables, in a reference frame rotating with the pipe wall