外文翻譯--采用cfd錐流量計(jì)的特性研究頂角和上游漩渦對性能的影響 （英文）

1、Flow Measurement and Instrumentation 20 (2009) 69–74Contents lists available at ScienceDirectFlow Measurement and Instrumentationjournal homepage: www.elsevier.com/locate/flowmeasinstStudy on the effect of vertex angle a

2、nd upstream swirl on the performance characteristics of cone flowmeter using CFDR.K. Singh, S.N. Singh ?, V. SeshadriDepartment of Applied Mechanics, IIT Delhi, Hauz Khas, New Delhi – 110016, Indiaa r t i c l e i n f oAr

3、ticle history: Received 24 May 2007 Received in revised form 14 September 2007 Accepted 2 December 2008Keywords: Computational fluid dynamics Cone flowmeter Discharge coefficient Reynolds number Inlet swirl Cone vertex a

4、nglea b s t r a c tComputational Fluid Dynamics (CFD) has emerged as a revolutionary tool for optimizing the design of any flowmeter for given conditions. The flow features obtained with CFD are more extensive compared t

5、o experiments. In the present study, CFD code ‘FLUENT’’ after validation has been used to investigate the effect of cone vertex angle and upstream swirl on the performance of cone flowmeter. The values of discharge coeff

6、icient (Cd) evaluated for different vertex angles shows that the value of discharge coefficient is independent of Reynolds number and its value decreases with increase in vertex angle. In the presence of upstream disturb

7、ance in the form of swirl, the value of discharge coefficient is also independent of Reynolds number and its value is only marginally affected by the magnitude of swirl. The flow in a longitudinal plane shows the presenc

8、e of a pair of contra-rotating vortices in the recirculation region just downstream of the cone. The velocity profile downstream becomes stable after a distance of about 5D. © 2008 Elsevier Ltd. All rights reserved.

9、1. IntroductionFlowmeters used in industries are often subject to highly disturbed upstream flow conditions due to constraints on the space available for laying the pipeline network. The disturbances may be caused due to

10、 the presence of valve, elbow, pipe fitting, bend etc at the upstream of the flowmeter. Conventional flow measuring devices like Orifice meter, Rotameter, Flow nozzle etc., require minimum upstream and downstream straigh

11、t lengths and hence can not be used under these conditions. Over the years, cone flowmeter has emerged as one of the best alternatives for flow measurement under highly disturbed flow conditions [1]. It is rather insensi

12、tive to outside vibration, cone configuration and pressure tap location. It also provides flow measurement with high accuracy over for a turn down ratio as high as 30:1 with a much higher repeatability as compared to oth

13、er flow measuring devices. Besides these advantages, cone flowmeter has high durability and high resistance to abrasion due to its tapered design. Its taper design minimizes wear (erosion) by reduction in contact of prim

14、ary element with high velocity [2]. Liptak [3] has reported that velocity profile due to presence of cone element tends to flatten in the center resulting in uniform velocity profile in the transverse plane. This could b

15、e the reason that cone flowmeter does not require long straight pipe lengths upstream of the? Corresponding author. Tel.: +91 11 26591180; fax: +91 11 26581119.E-mail address: sidhnathsingh@hotmail.com (S.N. Singh).flowm

16、eter. Genisi et al. [4] have shown that the cone creates a controlled turbulence region that reshapes the velocity profile in the pipeline. Flow is also directed away from the cone edge due to the development of Boundary

17、 layer and hence makes the edge wear resistant. Ifft et al. [5] have concluded that cone flowmeter’s performance does not get affected by disturbances caused by the single and double elbows in different planes even if up

18、stream pipe length is small. Later Peter et al. [6] have shown that cone flowmeter is capable of measuring the flow of liquid and gas with same accuracy. In non-standard tests, they have observed less difference (±0

19、.5%) compared to base line tests and have also emphasized the need of additional tests to cover a wide range of parameters, to assess the performance of the meter at non- standard installation conditions. Prabhu et al. [

20、7] have shown that discharge coefficient of cone flowmeter is less sensitive to flow disturbances than the other flow metering devices and pumping requirements also reduce by about 50% compared to normal orifice meter. W

21、ith the development of powerful computers, Computational Fluid Dynamics (CFD) has become an effective tool which is being used extensively as an alternative to elaborate experiments. It has diverse applications in variou

22、s industries like aerodynamics, automobile, chemical engineering etc. Simulation of any flow measuring device using CFD is still a complex phenomena but it offers an opportunity to optimize the performance of a flowmeter

23、. Buckle et al. [8] have demonstrated the capability of CFD in the improvement of an existing design of rotameter and also emphasized that CFD gives a better insight to the flow structure particularly with respect to str

24、ong velocity gradient in the gap0955-5986/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2008.12.003R.K. Singh et al. / Flow Measurement and Instrumentation 20 (2009) 69–74

25、 71Fig. 1. Design and drawing details of V-cone flowmeter used for validation [18].where Gk is the generation of turbulent kinetic energy due to the mean velocity gradient and is calculated asGk = µtS2 (10)and ‘S’ i

26、s the mean rate of shear stress tensor defined asS = ?2SijSij and Sij = 12??ui?xj + ?uj?xi?. (11)The effective viscosity is modeled in the RNG theory using scale elimination procedure resulting in a differential equation

27、 for turbulent viscosity asd? ρ2√εµ?= 1.72 ? ν ?υ ? ? 1 + cγd? νwhere ? ν = µeffµ and cγ ～ = 100. (12)In the high Reynolds number limit, the above equation gives µt =ρCµ k2ε with Cµ = 0.0845

28、. The effective viscosity is calculated by using this expression. The additional term ‘R’ (rapid strain term) in the ε equation isR = Cµρη3 (1 ? η/η0)1 + βη3 ε2k (13)where, η = Sk/ε. The values of constants in the t

29、urbulence model used are the standard values reported in literature [C1ε = 1.42, C2ε = 1.68, Cµ = 0.0845, αk = αε = 0.7179, η0 = 4.38 and β = 0.012].4. Solution schemeFlow Investigations have been carried out using

30、CFD Code ‘‘FLUENT’’ [16] which is based on cell centered finite volume approach. Second order discretization scheme was used for all governing equations since the grid which consists of tetrahedral cells are usually not

31、collinear to the flow direction. Under relaxation factor has been used for all parameters to satisfy Scarborough condition for convergence. Coupling between thepressure and velocity field was established using PISO [17]

32、scheme which is based on the higher degree of the approximate relation between the corrections for pressure and velocity as it is more appropriate for swirling flows. All discretized equations have been solved using segr

33、egated solver. An implicit solution scheme with conjunction of Algebraic Multigrid (AMG) has been used for faster convergence. Double precision was used in the computation and solutions were converged until the sum of th

34、e all the residual terms was less than 10?6.5. Validation of the computer codeAny prediction made using CFD code is accepted only after the validation of the code. Validation of the CFD code establishes the extent of acc

35、uracy and reliability of the turbulence model. In the present investigation, CFD code ‘FLUENT’ has been validated against the experimental data of Singh et al. [18]. The geometry of the cone flowmeter used for validation

36、 of the CFD code is given in Fig. 1. Flow prediction using different turbulence models was carried out using different turbulence models with water as working fluid. It was found that RNG k–ε model gives best matching wi

37、th experimental results. Similar observation has also been made by Erdal and Andersson [9] who have also concluded that standard k–ε model fails to describe flow features of flowmeter. For sake of brevity, comparison of

38、RNG k–ε model results with experimental data is only presented. Fig. 2a shows the comparison of predicted Cd with corresponding experimental values for β = 0.64. The deviation of between the experimental values and the p

39、redicted values are of the same order as that of the experimental uncertainties with the computed values. Further, validation is carried out by predicting the flow for cone flowmeter having β = 0.77 and similar trends ar

40、e observed (Fig. 2b). The maximum difference between the experimental and predicted results for both configurations is of the order of 4%, which is within acceptable limits for validation. These deviations could be attri