11 其它文档找的一些论文developing a cfd ology for the analysis of flow stability

1、Annals of Nuclear Energy 54 (2013) 251262Developing a CFD methodology for the analysis of ow stabilityin heated channels with uids at supercritical pressuresEmmanuel Ampomah-Amoako a, Walter Ambrosini b,a University of Ghana, School of Nuclear and Allied Sciences, Department of Nuclear Engineering,

2、P.O. Box AE 1, Atomic Energy, Kwabenya, Accra, Ghanab Dipartimento di Ingegneria Civile e Industriale, Universit di Pisa, Largo Lucio Lazzarino 2, 56126 Pisa, Italya r t i c l e i n f oa b s t r a c tArticle history:Received 9 August 2012Received in revised form 1 November 2012 Accepted 2 November 2

3、012Available online 23 December 2012The paper presents the rst results of a systematic methodology aimed at assessing the feasibility of anal- yses by CFD codes of ow instabilities in heated channels containing supercritical uids. The research makes use of features presently available in CFD models,

4、 in the aim to move step-by-step from simple channel cases towards the analysis of more realistic fuel bundle subchannels.In the present step, basing on previous experience, the STAR-CCM+ code is adopted to solve ow sta- bility problems in circular channels and fuel bundle slices without heating str

5、uctures, in the aim to char- acterise the response of CFD models in the analysis of purely thermalhydraulic instability phenomena. Some of the effects related to numerical discretisation, ow direction with respect to gravity and uid properties are studied, comparing the stability thresholds identied

6、 by transient calculations with maps set up by in-house 1D codes developed and adopted in previous work. Both static and dynamic instabil- ities are observed, clearly showing the contiguity of these two kinds of phenomena as a function of inlet uid subcooling.Conclusions are nally drawn about the pr

7、omising features of CFD codes for such applications, sketch- ing the lines of the work already going on in order to address more realistic reactor scale conditions.2012 Elsevier Ltd. All rights reserved.Keywords: Supercritical pressure StabilityFluid-to-uid comparison Numerical discretisation CFD1.

8、Introductionet al., 2005; Chatoorgoon, 2006, 2008; Ortega Gmez et al., 2008; Ambrosini and Sharabi, 2008).The researches on SCWR instabilities inherit a considerable body of knowledge and analysis tools from boiling water reactor studies. Many of the recent complex stability analyses developed for S

9、CWR conceptual design (see e.g., Yi et al., 2004a, 2004b; Cai et al., 2009) clearly derive methodologies and analytical tools from the wealth of methodologies and tools developed for BWR design. In fact, the similarities existing between boiling and supercritical pressure instability phenomena are,

10、as expected, quite striking (Ambrosini, 2007). The techniques adopted for stability analysis of boiling water reactors are based on 1D thermalhydraulic mod- elling and subchannel analysis, also because CFD techniques seem not to be mature enough to tackle efciently so complex two- phase unsteady phe

11、nomena.Most of the recently adopted models for SCWR stability anal-yses are based on 1D cross section averaged mass, momentum and energy equations; nevertheless, the absence of interfaces accompanying the remarkable property changes occurring at supercritical pressure allows applying CFD approaches

12、basing on the more mature techniques available for single-phase uids. Though the ow of supercritical pressure uids in heated chan- nels is topologically simpler with respect to boiling ows, the presence of very dense and very light uid regions has clear con- sequences in the resulting mixed convecti

13、on conditions, whichThe prediction of ow stability of nuclear reactor cores has rel- evance in the design of existing boiling water reactors as well as of the supercritical water reactors (SCWRs) proposed for GenerationIV. Indeed, these two reactor concepts share the common feature that a dense uid

14、enters the reactor core, being subjected to con- siderable expansion and acceleration along the fuel channels; this phenomenon is at the basis of possible unstable behaviour that may occur especially in conditions of high power-to-ow ratios.Boiling channel instabilities have received attention for d

15、ecades by the scientic community and many details are known about the reasons for their occurrence and the means to avoid them or to mitigate their consequences by proper design and operating proce- dures (see, e.g., the reviews published by Bour et al. (1973), March-Leuba and Rey (1993), DAuria et

16、al. (1997) and Kaka and Bon (2008). On the other hand, the study of instabilities in super- critical and near-critical systems is also dated back to several dec- ades ago (Zuber, 1966), though it has received renewed attention in recent times owing to the interest for SCWR systems (Zhao Correspondin

17、g author. Tel.: +39 050 836673; fax: +39 050 2218065.E-mail addresses: (E. Ampomah-Amoako), walter.am- brosiniing.unipi.it (W. Ambrosini).0306-4549/$ - see front matter 2012 Elsevier Ltd. All rights reserved. /10.1016/j.anucene.2012.11.002Contents lists available at

18、 SciVerse ScienceDirectAnnals of Nuclear Energyjournal homepage: /locate/anucene252E. Ampomah-Amoako, W. Ambrosini / Annals of Nuclear Energy 54 (2013) 251262stronglyaffect the macroscopically observed heat transferand by limitations in the hardware adopted for computations at the ti

19、me. Recently, it was considered worth to start from these re- sults for planning a more systematic analysis of the capabilities of CFD codes in predicting ow stability with uids at supercritical pressure. The presently adopted code is STAR-CCM+ (see the re- lated website) in its versions 5 to 7. The

20、 code is being used for dif- ferent studies related to supercritical uids performed at the University of Pisa also in the frame of the EU THINS Project, mainly in relation to heat transfer and hydraulic resistance, and of the Coordinated Research Project of IAEA on SCWRs, by addressing also the eld

21、of natural circulation (Angelucci et al., 2011; Ambrosini, 2011a; Molfese et al., 2011; Ambrosini and De Rosa, 2011; De Rosa et al., 2011).The present systematic analysis is aimed at a better qualica-tion of the capabilities of the considered CFD code, exploiting some of its features that can be use

22、ful for simulating real reactor channel behaviour. A relatively realistic model of a fuel bundle subchannel equipped with the conducting regions of UO2, gap and cladding, in addition to the coolant uid, also including point kinetics feedback, was already developed on the basis of the rst results of

23、the per- formed analyses (Ambrosini et al., 2012) and is presently subjected to further assessment considering the experience gained dealing with simple problems.It must be claried that a limitation of the present work is in the choice to use only wall functions (i.e., high y+ approaches) for near w

24、all treatment. This is a consequence of the observed over- prediction of wall temperature obtained by presently available low-Reynolds number models in case of heat transfer deterioration (see e.g., De Rosa et al., 2011). On the other hand, the use of wall functions in CFD models leads to completely

25、 disregard heat trans- fer deterioration, making predictions more similar to those of pres- ent 1D models. While waiting for the development of CFD models suitable for an accurate prediction of heat transfer deterioration, it seemed wiser to avoid mixing different sources of inaccuracy, rul- ing out

26、 the high temperatures predicted by many low-Re turbu- lence models when dealing with mixed convection conditions to supercritical uids. In this respect, the use of CFD performed in this work does not yet exploit all the potential of this technique, mainly focusing on numerical discretisation effect

27、s and on uid-to-uid comparison, in order to compare the results obtained with those of 1D models.It must be mentioned that a problem currently open in thiseld is the poor availability of experimental data to be used forphenomena.The use of CFD in the stability analysis of supercritical pressure ow s

28、tability problems is a rather recent approach. Sharabi et al. (2008), making use of the FLUENT code (Fluent Inc., 2004), noted that by linearly increasing in time the power supplied to a vertical heated channel it is possible to bring it to unstable behaviour, simulating self-sustained oscillations

29、even in the lack of specic external pertur- bations. This behaviour, initially noted in a circular channel with 2D axial symmetric discretisation, was also obtained in 3D triangular and square pitch subchannel slices (Sharabi et al., 2009), showing approximately the same phenomenological features.Th

30、ere are several motivations to explore the applicability of CFD to stability analyses of supercritical uid ow in heated channels. A rst one is the greater detail that can be granted by CFD, counter- balanced by a larger computational price that is anyway decreasing as the hardware and software are p

31、rogressively developed. CFD also offers a more fundamental approach in terms of constitutive laws, introducing empiricism at a more basic level than 1D models. The use of both CFD and 1D system codes is also aligned with the present tendency to adopt different models for addressing larger and smalle

32、r scale effects.The rst analyses performed in previous work for the circular channel and those for the subchannel slices were initially per- formed making use of the conventional near-wall treatment based on the use of wall functions. In such a case, the obtained oscilla- tions were quite similar to

33、 those predicted by 1D models, except for the greater richness in spatial description of the phenomenon. However, in the case of the circular channel it was also tried to make use of a low Reynolds number k e model, obtaining lessregular oscillation patterns, quite far from sinusoidal amplied ordamp

34、ed, involving also cycles of alternating heat transfer deterio- ration and restoration (Sharabi et al., 2008). This behaviour is sim- ilar to that postulated during severe oscillations in boiling water reactor fuel, involving cycles of boiling transition and rewet. Sincethe evaluation of heat transf

35、er deterioration by CFD models is still a challenge, with most of k e models predicting excessive overes- timates of wall temperatures with respect to experimental data, this interesting prediction was considered only a qualitative mimic of what could be possibly observed in real conditions.The expe

36、rience gained in previous analyses paved the way for further studies, though its results were limited in accuracy by the character of rst attempts made with no prior experienceNomenclatureRoman lettersGreek lettersCmaxmaximum value of the Courant numberbisobaric thermal expansion coefcient (K 1)Cpsp

37、ecic heat at constant pressure (J/(kg K)Kfriction dimensionless group (Euler number)Dhhydraulic diameter (m)qdensity (kg/m3) or spectral radiusf friction factorFrFroude numberSubscriptsg gravity (m/s2)ininleth uid specic enthalpy (J/kg)pconstant pressureKin, Kout inlet and outlet singular pressure d

38、rop coefcientpcpseudocriticalLchannel length (m)NSPCsub-pseudocritical numberSuperscriptsNTPCtrans-pseudocritical numberstarred variables indicate dimensionless valuesQ_power (W)Ttemperature (K) or period (s)Abbreviationsttime (s)BWRBoiling Water Reactorv specic volume (m3/kg)CFDComputational Fluid

39、Dynamicsw velocity (m/s)SCWRSupercritical Water Reactorygeneral variableE. Ampomah-Amoako, W. Ambrosini / Annals of Nuclear Energy 54 (2013) 251262253comparison with code predictions; only recently experiments that could be useful for such purpose have been made available (Xiong et al., 2012; TJoen

40、and Rohde, 2012). As a consequence, the mate- rial presented in this paper is limited to provide a preliminary basis for phenomenological assessment, addressing simple problems and comparing the results obtained for their stability as predicted by the CFD models with those available from 1D codes. T

41、his com- parison, made in a more meaningful and comprehensive way than it was possible in previous analyses (Sharabi et al., 2008), provides a picture of the capabilities of CFD models in predicting unstable behaviour in heated channels with supercritical uids.From the point of view of time discreti

42、sation, a Coupled Impli- cit, Implicit Unsteady advancement scheme was used, considering both the rst and the second order time advancement schemes with different time steps and internal Courant numbers. Some cal- culations were run also with a Segregated Flow and Energy ap-proach, in which ow and e

43、nergy equationsaresolvedseparately; however, it was preferred to use the coupled implicit approach with a very large internal Courant number (mostly equal to 20,000), obtaining a rather robust time advancement and a good degree of convergence in the 20 iterations allowed for the advance- ment at eac

44、h time step. This strategy of running the calculations represents one of the possible ways to use the STAR-CCM+ code for such problems and it was nally selected because it was found suitable in all the addressed cases.As it will be shown later on in this paper, on the basis of numer-ical diffusion c

45、onsiderations, a time step of 0.1 s with the use of a second order time advancement scheme were found a suitable choice compromising between accuracy and computational ef- ciency. In all the equations, advection terms were discretised at second order, being the default choice in STAR-CCM+.Concerning

46、 the turbulence model, a standard k e model withhigh y+ treatment (i.e., with wall functions) was selected for thecircular channel, while a realisable k e model is currentlyadopted in subchannel slice analyses. As already mentioned in the Introduction, at the moment it was anyway tried to avoid de-

47、tailed wall treatments that could lead to strong overestimates in wall temperatures, as observed in analyses related to the predic- tion of heat transfer deterioration (see e.g., De Rosa et al., 2011). Similarly, it was avoided to introduce inlet and outlet throttling, e.g., simulated by porous inte

48、rfaces, or conjugated heat transfer modelling of the solid wall. All these aspects are being considered in the research presently performed, but they were ruled out in these rst phases in order to avoid masking the pure thermal hydraulic effects being the target of the study. In this purpose, a unif

49、orm heat ux was imposed at the inner wall surface disregard- ing heat conduction effects. From the hydraulic point of view, the surface was assumed to be smooth, but sensitivity analyses on roughness are also underway.Fluid properties were assigned as polynomial functions of tem-perature (for densit

50、y and specic heat) or as eld functions (for thermal conductivity and dynamic viscosity), making use in all the cases of a cubic spline piecewise interpolation of values pro- vided by the NIST package (NIST, 2002). A home-made FORTRAN program was used to semi-automatically adjust the values of the re

51、quired temperature intervals to a reasonable number, assuring relatively high accuracy.2.2. Adopted methodology of analysis2. Considered systems and methodology of analysis2.1. Geometry, discretisation and modelling choicesBasing on previous work, three different systems are addressed in the present

52、 analysis, with main emphasis on the rst, being the simplest one: a circular pipe having a length 4.2672 m (14 ft) and an internal diameter of 8.36 mm, already addressed in previous works (Sharabi et al., 2008) as a simplied system, having realistic cross section and length with respect to bundle su

53、bchannel; a square and a triangular pitch rod bundle slices having the fol- lowing characteristics (see Sharabi et al., 2009): for the square pitch subchannel: rod diameter = 10.2 mm; pitch = 11.2 mm; active height = 4.2 m; for the triangular pitch subchannel: rod diameter = 7.6 mm; pitch = 8.664 mm

54、; active height = 3 m.The geometries of the two bundle slices, shown in Fig. 1, are coherent with previous proposals about different core congura- tions of thermal and fast supercritical water reactors (Yamaji et al., 2001; Yoo et al., 2006).On the basis of previous experience (Sharabi et al., 2008)

55、 and of several preliminary calculations made in the frame of this work with different choices for the radial and the axial numbers of nodes, a reasonable axi-symmetric 2D discretisation of the circular pipe was selected as having 40 uniform 0.1 mm nodes plus a single node with a size of 0.18 mm clo

56、se to the wall, in order to allow for the applicability of wall functions. On the other hand, the axial dis- cretisation was xed in 200 uniform nodes.For the fuel bundle slices, instead, the base size of the radial mesh was selected to be 0.1 mm, except close to the wall, where it was selected to be

57、 0.19 mm, to make a reasonable use of wall functions. Axially, 200 nodes were used for the case of the square pitch and 100 for the triangular pitch one, resulting respectively a bit ner and a bit coarser than the ones used in previous work (150 axial nodes adopted for both cases by Sharabi et al.,

58、2009).The methodology of analysis was slightly changed with respect to past work. In particular, the following steps were performed for each calculation:(a) 1/8 square pitch assembly slice(b) 1/6 triangular pitch assembly sliceFig. 1. Fuel bundle slices considered in the present work with their radial discretisation.254E. Ampomah-Amoako, W. Ambrosini / Annals of Nuclear Energy 54 (2013) 251262 a mass ow (orvelocity) inlet boundary condition is rs