Turbulent rotating flow calculations: An assessment of two-equation anisotropic and Reynolds stress models

Abstract

The stress field in a rotating turbulent internal flow is highly anisotropic. This is true irrespective of whether the axis of rotation is aligned with or normal to the mean flow plane. Consequently, turbulent rotating flow is very difficult to model. This paper attempts to assess the relative merits of three different ways to account for stress anisotropies in a rotating flow. One is to assume an anisotropic stress tensor, another is to model the anisotropy of the dissipation rate tensor, while a third is to solve the stress transport equations directly. Two different near-wall two-equation models and one Reynolds stress closure are considered. All the models tested are asymptotically consistent near the wall. The predictions are compared with measurements and direct numerical simulation data. Calculations of turbulent flows with inlet swirl numbers up to 1.3, with and without a central recirculation, reveal that none of the anisotropic two-equation models tested is capable of replicating the mean velocity field at these swirl numbers. This investigation, therefore, indicates that neither the assumption of anisotropic stress tensor nor that of an anisotropic dissipation rate tensor is sufficient to model flows with medium to high rotation correctly. It is further found that, at very high rotation rates, even the Reynolds stress closure fails to predict accurately the extent of the central recirculation zone. NOTATION b ijanisotropy tensor (u i u j À 2kä ij =3)=(2k) C D dimensionless constant with an assigned value of 1.68 C s model constant with an assigned value of 0.11 C 1 , C Ã 1 , C 2 , C Ã 3 , C 5 model constants = 3.4, 1.8, 4.2, 1.3 and 0.4 respectively C å , C å1 , C å2 , C å3 , C å5 model constants = 0.12, 1.5, 1.83, (1.9), 2.9556 and 5.8 respectively C ì model constant with an assigned value of 0.096 (0.09) D pipe diameter D ij production tensor D T ij turbulent diffusion tensor f w1 damping function exp[À(Re t =200) 2 ] f w2 damping function exp[À(Re t =40) 2 ] f å damping function 1 À 2 9 exp[À(Re t =6) 2 ] f ì damping function h channel half-width k turbulent kinetic energy L, M, N model constants 2:25, 0:5 and 0.57 respectively n i wall unit normal vector (0, 1, 0) p fluctuating pressure P mean pressure P ij production tensor P production of turbulent kinetic energy Àu i u j (@U i =@x j ) r radial coordinate R pipe radius Re Reynolds number U m D=í Re t turbulent Reynolds number k 2 =åí Re å turbulent Reynolds number (åí) 1=4 y=í Ro rotation number W 0 =U m or 2jÙjh=U m S swirl number [2 R 0 U W r 2 dr]=(R 3 U 2 m ) S ij mean strain rate tensor (@U i =@x j @U j =@x i )=2 S Ã ij dimensionless strain rate tensor S ij (k=å) 193 The MS was

Prediction of strongly swirling flow within an axial hydrocyclone using two commercial CFD codes

“…When the same authors (Chen and Lin, 1999) modelled the Kitoh (1991) swirling flow, the SSG model performed better, however, the centreline backflow was still difficult to model especially far downstream. Similar difficulties with the SSG model and variants were also experienced by Yuan and So (1998). Yeh and Lin (2000) and Lu and Semião (2003) found that for strongly swirling flows the SSG model predicted slightly better results than the linear pressure-strain models.…”

“…This occurred because of a number of reasons: (1) the near wall velocities and therefore the shear stresses were predicted correctly, and (2) the swirl number is the ratio of two integrals which have a higher weighting in the correctly predicted annular and near wall regions. Good swirl number matches with poor recirculation zone predicted velocity profiles were also found by Yuan and So (1998) when they compared their simulated results with the experiments (S = 0.97) of Kitoh (1991). Alekseenko et al (1999) also found during their experiments that the swirl number was not a unique parameter by which quite different swirling flow structures can be characterised.…”

“…Examples in the literature of the DRSM applied to the prediction of the turbulent swirling flow without core recirculation include: Chen and Lin (1999), Hogg and Leschziner (1989), Jones and Pascau (1989), Sharif and Wong (1995), Spall and Ashby (2000), Tsai et al (1995), Yeh and Lin (2000), Yuan and So (1998). These flows are easier to model numerically because the equations of motion are parabolic and as a result some simplifications can be made.…”

“…Turbulent swirling flow with core recirculation is more difficult to model because the equations of motion are elliptic and no simplifying assumptions can be made. Examples in the literature include: Chen and Lin (1999), Nikjooy and Mongia (1991), Sharif and Wong (1995), Wennerberg and Obi (1993), Xia et al (1997), Yuan and So (1998). The present work belongs in this category.…”