[雙語(yǔ)翻譯]外文翻譯---管道流動(dòng)中液固兩相流的數(shù)值模擬（英文）

1、Numerical investigations of liquid–solid slurry flows in a fully developed turbulent flow regionJ. Ling, P.V. Skudarnov, C.X. Lin, M.A. Ebadian *Hemispheric Center for Environmental Technology, Center for Engineering and

2、 Applied Sciences, Florida International University, 10555 West Flagler Street, EAS-2100, Miami, FL 33174, USAReceived 6 December 2001; accepted 14 February 2003AbstractIn this paper, a simplified 3D algebraic slip mixtu

3、re (ASM) model is introduced to obtain the numerical solution in sand–water slurry flow. In order for the study to obtain the precise numerical solution in fully developed turbulent flow, the RNG K–e turbulent model was

4、used with the ASM model. An unstructured (block-structured) non-uniform grid was chosen to discretize the entire computational domain, and a control volume finite difference method was used to solve the governing equatio

5、ns. The mean pressure gradients from the numerical solutions were compared with the authors? experimental data and that in the open literature. The solutions were found to be in good agreement when the slurry mean veloci

6、ty is higher than the corresponding critical deposition velocity. Moreover, the numerical investigations have displayed some important slurry flow characteristics, such as volume fraction distributions, slurry density, s

7、lip velocity magnitude, slurry mean velocity distributions, and slurry mean skin friction coefficient distributions in a fully developed section, that have never been displayed in the experiments. ? 2003 Elsevier Science

8、 Inc. All rights reserved.Keywords: Granular flow; Multiphase flow; Numerical analysis; Slurries; Turbulence1. IntroductionSlurry pipeline transportation is a popular mode of transportation in various industries. It has

9、several ad- vantages, such as its friendliness to the environment and its relatively low operation and maintenance costs. In general, slurry transportation is divided into three major flow patterns: (1) pseudo-homogeneou

10、s flow (or homo- geneous flow) and heterogeneous flow; (2) heteroge- neous and sliding bed flow (or moving bed flow), and (3) saltation and stationary bed flow (Doron and Barnea, 1996). Pseudo-homogeneous flow is a slurr

11、y flow pattern in which the slurry flows at a very high velocity and all solid particles are distributed nearly uniformly across the pipe cross-section. With a decrease in slurry flow rate, the heterogeneous flow pattern

12、 occurs when there is a concentration gradient in the direction perpendicu- lar to the pipe axis, with more particles transported at the lower part of the pipe cross-section, as is the case inmost practical applications.

13、 As the slurry flow rate is reduced further, the solid particles accumulate at the bottom of the pipe and form a moving bed layer, while the upper part of the pipe cross-section is still occupied by a heterogeneous mixtu

14、re. When the slurry flow rate is too low to suspend all solid particles, a stationary bed layer at the bottom of the pipe cross-section is observed. This is the saltation and stationary bed flow (Vocaldo and Charles, 197

15、2; Parzonka et al., 1981). The slurry velocity associated with the formation of a stationary bed layer is called the critical deposition velocity. A bed layer in the slurry pipeline is unstable and dangerous during the o

16、peration of pipeline transportation. It probably enhances pipe wear and causes plugging or blockage of the pipeline. As a result, it should be avoi- ded in design and operation of the pipeline transporta- tion system. Sl

17、urry flow is very complex. In a survey of the open literature on slurry transportation investigations, it was found that most investigations were made in labora- tories to determine pressure gradients and critical de- po

18、sition velocities in slurry flows. Doron et al. (1987) and Doron and Barnea (1993) proposed two-layer and* Corresponding author. Tel.: +1-305-348-3585; fax: +1-305-348- 4176. E-mail address: ebadian@hcet.fiu.edu (M.A. Eb

19、adian).0142-727X/03/$ - see front matter ? 2003 Elsevier Science Inc. All rights reserved. doi:10.1016/S0142-727X(03)00018-3International Journal of Heat and Fluid Flow 24 (2003) 389–398www.elsevier.com/locate/ijhffsity,

20、 and lm is the viscosity of the mixture, which are expressed asqm ¼ X nk¼1 akqk and lm ¼ X nk¼1 aklk ð3Þ~ um and ~ uDk are mass-averaged velocity and drift veloci- ties, which are expressed

21、as~ um ¼Pn k¼1 akqk~ uk qm and ~ uDk ¼ ~ uk ?~ um ð4ÞThe slip velocity is defined as the velocity of the secondary phase (p) relative to the primary phase (q) velocity:~ vqp ¼ ~ up ?~ uq 

22、40;5ÞThe drift velocity and slip velocity are connected by the following expression:~ uDp ¼~ vqp ? X ni¼1aiqi qm ~ vqi ð6ÞThe basic assumption in the ASM model is that, to prescribe an algebraic

23、relation for the relative velocity, a local equilibrium between the phases should be reached over short spatial length scales. The form of the slip velocity is~ vqp ¼ðqm ? qpÞd2 p 18lqfdrag ~ g? o~ um ot!&

24、#240;7Þwherefdrag ¼ 1 þ 0:15 Re0:687 Re 6 1000 0:0183 Re Re > 1000?The volume fraction equation for the secondary phase isoot ðapqpÞ þ ooxi ðapqpum;iÞ ¼ ? ooxi ðapqpuD

25、p;iÞ ð8ÞThis ASM model can be applied in the laminar and turbulent two-phase flows. In practice, since slurry transportation is in the fully developed turbulent flow, the RNG K–e turbulent model is used wi

26、th the ASM model in this study. The turbulent kinetic energy in RNG K–e turbulent model isoot ðqmkÞ þ ooxi ðqmum;ikÞ ¼ ooxi aklmokoxi? ? ? ?þ ltS2 ? qme ð9ÞDissipation rate of

27、 the turbulent kinetic energy isoot ðqmeÞ þ ooxi ðqmum;ieÞ¼ ooxi aelmoeoxi? ? ? ?þ C1eek ltS2 ? C2eqme2k ? R ð10Þwhere the coefficients ak and ae are the inverse effect Prandt

28、l numbers for k and e, respectively. In the high-Reynolds-number limit, ak ¼ ae ffi 1:393. C1e and C2e are equal to 1.42 and 1.68. b and Prt are the coefficient of thermal expansion and the turbulent Prandtl number

29、for energy. S is the modulus of the mean rate-of-strain tensor, Sij, which is defined asS ¼ ffiffiffiffiffiffiffiffiffiffiffiffi 2SijSij p and Sij ¼ 12oui oxj?þ ouj oxi?ð11ÞR in Eq. (10) was expr

30、essed asR ¼ Clqmg3ð1 ? g=g0Þ1 þ fg3 ? e2k ð12Þwhere g ¼ S ? k=e, g0 ? 4:38, f ¼ 0:012, and Cl ¼ 0:085.2.2. Boundary conditionsNon-slip boundary condition is imposed on the wal

31、ls, and heat transfer is not considered in the entire com- putational domain. For this paper, in the near-wall zone, the standard wall function proposed by Launder and Spalding (1974) was chosen due to its wide appli- ca

32、tion in industrial flows. When the mesh is such that y? 6 11:225 at the wall-adjacent cells, the viscous force is dominant in the sublayer. The laminar stress–strain relationship can be applied:u? ¼ y? ð13Þ

33、;y? ¼qmC1=4 l k1=2 p yplm ð14ÞThe logarithmic law for the mean velocity is known to be valid for y? ? 11:225 (Fluent Inc., 1996). It can be expressed asu? ¼ 1k lnðEy?Þ ð15Þwhere k

34、is von Karman?s constant, Cl is turbulent model constant, and kp and yp are the turbulent kinetic energy at point p and distance from point p to the wall, respectively. To simplify the simulations, the mean velocity inle

35、t boundary condition and pressure outlet boundary con- dition are imposed on the inlet and outlet of slurry pipeline:ux;inlet ¼ constant; uy;inlet ¼ uz;inlet ¼ 0; andpoutlet ¼ constant ð16Þ3

36、. Numerical computation3.1. Physical problems and grid systemThe geometry and physical problem studied in this paper are as follows: Horizontally straight pipeline length, L ¼ 1.4 m; inner diameter of the pipe, d &#