74 Engineering

8/8/2019 74 Engineering

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ENGINEERING JUDGMENT

AND NATURALCIRCULATION CALCULATIONS

Conferencia pronunciada por el Dr. Juan Carlos Ferreri

el 23 de agosto de 2003

en la Academia Nacional de Ciencias de Buenos Aires,

acto organizado por el Instituto de Investigacin y Desarrollo

Instituto de Investigacin y Desarrollo

2007


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INSTITUTO DE INVESTIGACIN Y DESARROLLO

Director: Dr. AMLCAR E. ARGELLES

Todos los derechos reservadosHecho el depsito que establece la Ley 11.723IMPRESO EN ARGENTINA

ACADEMIANACIONALDE CIENCIASDE BUENOS AIRESAvda. Alvear 1711, 3er. Piso - 1014 Ciudad de Buenos Aires - Argentinae-mail: [email protected]

ISBN-10: 987-537-063-0

ISBN-13: 978-987-537-063-0

La publicacin de los trabajos de los Acadmicos y disertantes invitados serealiza bajo el principio de libertad acadmica y no implica ningn grado deadhesin por parte de otros miembros de la Academia, ni de sta como en-tidad colectiva, a las ideas o puntos de vista de los autores.


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ANTECEDENTES CIENTFICOS

Ing. Juan Carlos Ferreri graduated as Aeronautical Engineer at theLa Plata University in 1967 and has dedicated his professionalcareer to the particular field of computational fluid mechanicsand heat and mass transfer.

For more than twenty years he has devoted his work to NuclearEngineering.

He is currently an Honorary Consultant Member to the Researchand Development Institute at the National Academy of Sciencesof Buenos Aires; Principal Staff Member and Manager at theScientific and Technical Support Branch of the NuclearRegulatory Authority and Independent Researcher at theCONICET.

He has received the Senior 2004 Award to Research, Professionaland Teaching Achievements in Argentina from the Argentinean

Association for Computational Mechanics (AMCA).He has been Member and President of the Argentine Committee for

Heat and Mass Transfer. He has also been part time professorat different universities and a member of advisory committees

at the university, CONICET and other institutions.He has taught in numerical methods, mainly at post graduate

courses, and is usually part of examination staffs for PhD thesisand has been external peer in Advisory Committees for NuclearEngineering and Aeronautical Engineering professors selectionin many opportunities.

In the last decade he developed an intense research activity incollaboration with researchers at the University of Pisa, in theparticular field of systems computer codes for nuclear safety

analysis.He has published eighty papers in his field of expertise and has

delivered tens of seminars and invited to conferences inArgentina and abroad.


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INTRODUCCIN

Ing. PEDRO VICIEN

La conferencia de hoy estar a cargo del Ingeniero AeronuticoJuan Carlos Ferreri, egresado de la Universidad Nacional de La Pla-ta en el ao 1967. Naci en el ao 1944, casi en el ao en que comien-za nuestra decadencia y que todava se extiende hasta nuestros das.Sin embargo el conocimiento que an circula en nuestros crculosuniversitarios nos entrega estudiosos de su calibre, que deberan pro-porcionarnos una cuota de optimismo.

Sera bastante fatigoso para ustedes que yo les leyera los ttulosde los 73 trabajos publicados con su firma junto con algunos de suscolegas. Tambin su mochila tiene la mencin de 14 informes parainstituciones o contratistas en temas serios vinculados principalmen-

te a la CNEA, la Fuerza Area y firmas industriales. Su carrera aca-dmica se puede clasificar de brillante. Ense en la Universidad deBuenos Aires y en la Nacional de La Plata, dirige tesis de doctoradoy de maestras de la UBA, UNLP y en el Instituto Balseiro.

Ha participado como miembro referee en varias revistas impor-tantes del mbito cientfico y tecnolgico del pas y extranjero. Ac-tualmente es Director de Proyectos de la Autoridad ReguladoraNuclear de la Argentina y revista en la carrera de investigador delCONICET.

La especialidad del ingeniero Ferreri es ahora su actividad enmtodos computacionales y simulacin numrica y su participacinen un proyecto internacional de mtodos informticos, aplicados a latermo-hidrulica.

El tema elegido para la conferencia es Engineering judgmentand natural circulation calculations. La ciencia de la transmisin decalor ha sido siempre un tema muy difcil de abordar con desarrollosmatemticos, especialmente en conveccin. Los clculos de transmi-sin de calor por conveccin son muy complicados por el gran nmero

de variables diferentes que se presentan.


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Afortunadamente en la mayora de las aplicaciones estas varia-bles pueden agruparse en relativamente pocos grupos adimensiona-les o nmeros sin dimensin y, de esa manera, reduciendo el nmerode variables efectivas con las que trabajar experimentalmente. Laagrupacin de estas variables se hace mediante el mtodo de anli-sis dimensional que es muy usado en los trabajos cientficos. Aqutermina la cita del libro de Fishenden & Saunders de 1950. EnMcAdams se mencionan alguno de esos nmeros y en la tabla depresentacin se enumeran 20 grupos.

Las ecuaciones que se utilizan en ingeniera trmica para el tra-tamiento de la conveccin provienen de desarrollos experimentalesms que de desarrollos tericos, por lo menos era as en mis pocasde estudio y profesionales.

Modernamente se usan herramientas computacionales, am-pliando considerablemente el anlisis de los problemas que se pre-sentan en la prctica de la ingeniera. Aspectos de ese tratamientonos sern ofrecidos ahora.

No quiero terminar sin manifestar mi personal complacencia portener entre nosotros, en esta tribuna, a un ingeniero que tiene unafuerte capacidad cientfica que se ha desarrollado en nuestro medioy que es un ejemplo de lo que debe ser la formacin de los ingenie-ros argentinos para afrontar los desafos del futuro.


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No hay hombre que, fuera de su especialidad, no sea crdulo

Jorge Luis Borges, El milagro Secreto, Ficciones

ENGINEERING JUDGMENT AND NATURALCIRCULATION CALCULATIONS

Dr. JUAN CARLOS FERRERI

Abstract

The analysis performed to establish the validity of computer coderesults in the particular field of natural circulation flow stabilitycalculations is presented in the light of usual engineering practice. Theeffects of discretization and closure correlations are discussed and somehints to avoid undesired mistakes in the evaluations performed are given.

Resumen

El anlisis que se realiza para establecer la validez de los resultadosdel clculo realizado mediante programas de cmputo en el campo particu-lar de la estabilidad de la circulacin natural de fluidos es presentado a laluz de la prctica usual de la ingeniera. Los efectos de la discretizacin yde las correlaciones de cierre son discutidos y se dan, adems, algunas guaspara evitar errores no deseados en la evaluaciones.

Introduction

The concept engineering judgment (EJ) is sometimes invoked tosupport the validity of technical assertions based on the subjective

judgment of experts. This is particularly true when uncertaintyprevails regarding the data at hand, in opposition to statistically

valid data sets. Many relevant technical decisions are based on thistype of EJ. In particular, the assignment of subjective probabilities

to rarely occurring events is a usual example of this particular use


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of EJ. The statement educated guessing used to be an alternativenomenclature to denominate this somewhat arbitrary, non-scientific,way of value assignment to parameters. The nuclear corporation issensitive to these aspects and one of the general conclusions of anuclear safety specialists meeting [1] was to Minimize need forexpert judgment as far as practicable.Needless to say, this is alsothe more common cause for public and non-governmentalorganizations complaints regarding risk and cost-benefit analyses ofinstallations. Public and NGOs opposition to chemical, nuclear andmany other types of industrial emplacements are, quite frequently,the consequence of their negative perception of said risk-benefitstudies.

EJ is really at the base of the usual way of engineering dataanalysis. It is the case of deciding whether or not a calculated set ofresults can be considered a valid one. In this paper, applications ofEJ deal with the computer prediction of the stability of naturalcirculation (NC) flows (jargon for natural thermal convective flows)in hydraulic loops of interest in the nuclear industry.

The simplest approximation will be considered, namely one-dimensional (1D), almost incompressible flow in single phase. It maybe argued that it is a rather simplistic problem, because real lifeinstallations show much more complicated situations. However, most

of the calculations performed under these restrictive hypotheses posesome challenges that must be solved on the basis of EJ if this isunderstood, as mentioned above, as the process performed todetermine the validity of a given set of computer results. Theemphasis of this paper is not on the two basic steps of computer codedevelopment, namely: verification and validation. These steps areassumed as done. Here, the verified and validated codes are used toanalyze quite simple loops, either theoretical or experimental ones,with the main interest focused on assessing the results. As a

consequence, some insights are derived to account for the effects ofdiscretization and closure correlations. One aspect that will deserveparticular consideration is whether to stop for the search ofperfection in the achieved results, this in the light of lack of really

valid experimental data allowing for partial validation or lack ofexact solutions for the problem under analysis (the vast majority ofreal life engineering problems) with different codes.

Perhaps, before starting the analysis, it may be useful to excerptsome considerations by Scananpieco and Harlow [2] on the role of

computational predictions: In as much as we can simulate reality,


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we can use the computer to make predictions about what will occur

in a certain set of circumstances. Finite-difference techniques can

create an artificial laboratory for examining situations which would

be impossible to observe otherwise, but we must always remain

critical of our results. Finite-differencing can be an extremely

powerful tool, but only when it is firmly set in a basis of physical

meaning. In order for a finite-difference code to be successful, we must

start from the beginning, dealing with simple cases and examining

our logic each step of the way. F.H. Harlow was one of the mosttalented experts in Computational Fluid Dynamics, who leaded thefamous Group T3 at Los Alamos Scientific Laboratory in the 70-80s.

From the regulatory point of view, the need for independentsafety analysis can not be sufficiently emphasized. It must beunderstood that the same engineering data most probably willgenerate different results, even using the same code and the same(agreed with the licensee) criteria for discretization. Differenceswould arise from choosing different code options or what is the codeuser interpretation of the agreed criteria. In passing, the importanceof EJ may be, once again exemplified by the following excerpt from[3]: It should be stressed that the staff does not rely solely incomputer analyses, but rather use the analyses as a tool to help guideunderstanding of plant behavior in conjunction with EJ, hand

calculations, data analysis, and experience with plant operation.Also: It must be continually emphasized that code results mustalways be used with cautionary engineering judgment. This is trueeven for those uses where the code has been explicitly assessedagainst data because user choices and input deck errors mayinfluence the calculation results.

In what follows, some examples coming from previous work bythe author and his colleague at the University of Pisa, ProfessorWalter Ambrosini, are reviewed and presented. These results will be

the support for the present contribution. It must be mentioned thatthe subject herein discussed is one of the more important aspects ofsafety evaluations and only a brief, quite restricted discussion will bepresented.

The search for convergence of results

This is, perhaps, the easiest step in computational analysis of

engineering problems but only conceptually. In fact, it means that


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grid size, as measured by some suitable norm, is compatible with theaccuracy of resolution of some type of boundary layer. This may bea momentum boundary layer as in the vicinity of a wall, the depthof heat penetration in a solid or the time history of some suitabledependent variable as a function of its time scale, among many otherpossible examples. What must be considered is that a given boundarylayer behavior must be solved accurately enough. Searching for gridconvergence is not a too costly activity in simple integration domains,like the 1D cases herein considered. In multi-dimensional domains,the use of multiple scale calculations tends to keep detail andaccuracy at an appropriate level in the entire integration domain.Shape and size variation of computational cells affect the globalaccuracy.

In the case of natural circulation in unstable flow conditionsanalyzed using time domain computer codes, the problem consists inusing a spatial discretization fine enough as to minimize the amountof numerical diffusion. It is sometimes added in the process ofsolution as a consequence of the inherent properties of the discretescheme. This diffusion is usually associated with first-order spatialdiscretization. It may be argued that usingO(1) numerical schemesshould not be recommended in general. However, most engineeringthermal-hydraulic systems codes use this approximation to

circumvent a worse limitation: the ill-posedness of governingequations.

The interaction of flow stabilization and discretization maybe exemplified resorting to results in [4], as shown in Figure 1, wherethe flow rate in a toroidal loop was obtained using a finite-differencescheme O(x, t) known as forward time (Euler) upstream space(FTUS in short), 1000 spatial nodes and a cell Courant number(U.t/x), C=0.8. The results are compared with the ones obtainedusing a modal expansion- it is free of numerical diffusion- with 500

modes and adding the numerical diffusion corresponding to theprevious approximation. It may be observed that the results arenearly the same. Then, it may be concluded that the usualinteraction between numerics and physics persists in this non-linearcase.

The results in [4] showed how using different order schemescould be useful to get improved convergence of results to somelimiting accuracy. Perhaps the most interesting results were showinghow usual approximations of piping systems related to nuclear

industry could be non-conservative from the point of view of safety.


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In fact, revisiting a pioneering work by P. Welander [5], a stabilitymap was determined. It corresponds to a two pipes loop 10 m highand 0.1 m in diameter, with a concentrated heat source at the bottomand an opposite heat sink at the top, as the one shown in Figure 2.

The analytical stability map is the one in Figure 3, where aworking point corresponding to an unstable flow condition was set.Then the map was constructed by calculation with the FTUSapproximation and the effect of the number of nodes was determined.

Figure 1. The flow rate for the FTUS scheme using 1000 nodes and itssimulation using a modal expansion of 500 modes and adding the numerical

viscosity corresponding to 1000 nodes.

Heating

Cooling

Source

Sink

s = 0

s =1

s = 2

a) b)

Figure 2. A schematicview of a natural

circulation loop, adapted

from Welander (1967)

Figure 3. Theoretical stability map for the positiveflow steady-state conditions

0

1

2

3

4

5

6

0 100 200 300 400 500 600

Stable

Unstable

Reference Unstable Case

( = 339, = 2.3)


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In the maps following, and are two non dimensional parametersthat measure, respectively, the buoyancy driving force and theresisting friction force in the loop.

Figure 4 shows that, as the number of nodes increases, theunstable region in the map progressively converges to the theoreticalstability boundary (SB). Then, for the point under analysis, flowchanges from a stable condition to an unstable one. Then, theevaluation of this system goes from a non-conservative stabilitycondition evaluation towards a conservative, real unstable one.Predicting system stability is, obviously a non-correct, dangeroussituation in this case.

The interesting consideration here is that discretizing a pipe 10m long and 0.1 m internal diameter in volumes 0.3 m long seemsnatural to a systems code user, at least as a compromise betweencomputational cost and expected system behavior. Then, assumingthat the system is expected to perform in a stable way, EJ must beused to decide on various aspects, namely: a) the system satisfies thedesign goals; b) the numerical model is appropriate; c) the computercode is applicable; d) the discretization is adequate and does notmask some unexpected behavior and e) results are converged. Thesequestions are of great importance for the safety evaluation of nuclearinstallations. Furthermore, as they seem natural, they have been

also considered in the so-called Code Scaling, Applicability andUncertainty (CSAU) evaluation methodology [6], an United StatesNuclear Regulatory Commissions major documented way to assessthe traceability of nuclear safety analyses. Also, the need for thequalification of codes and their users arises in a natural way and this,incidentally, has also been the subject of much analysis, see forexample, the discussions in [7], among others.

0 100 200 300 400 500 600 700 800 900 1000

0

2

4

6

8

10

Stable Region

Unstable

Theoretical SB

Test Case

0 100 200 300 400 500 600 700 800 900 100

0

2

4

6

8

10

Stable Region

Unstable Region

Theoretical SB

Test Case

Figure 4a. Stability map with 30

nodes per leg

Figure 4b. Stability map with 100

nodes per leg


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Another problem arises when two independent code results arecompared. A general, sophisticated thermal-hydraulic systems codelike RELAP5 [8] and another of restricted validity can be bothapplied to a particular physical situation for which the second isknown to be applicable. In NC flows in single phase, the mass flowrate scales with the 1/third power of the heat input in the system.Then, a difference of 10 % in heat input leads to only 3.2 % in flowrate. This last difference is small and acceptable in most situations,given the uncertainties in codes and their closure correlations, butcovers a significant one in power. Deciding when it is possible toaccept this difference pose some challenge for large, complex systemsand requires applying EJ again. Regarding convergence of results,some care must be also taken when lumped parameter simulationsare used. In [9], a lumping criterion for concentrated heat source/sinkwas developed, which eliminates the lack of convergence due toheated length in a FTUS finite-differences scheme applied to theabove mentioned problem. These results arose from applying EJ tothis lack of convergence.

The effect of closure correlations

Related to the previous search for convergence of results, thereis another aspect to be taken into account. It is whether an accepted,usually applied closure correlation is appropriate to describe thephysics of the problem under analysis. Closure correlations serve toset a system of conservation equations closed. Most commonly, theyinclude interface and interphase relations like friction laws, heattransfer correlations, phase slip velocity specification and manyothers. In this section, the effects of using different versions of themacroscopic friction law will be discussed. It is important to say, from

the very beginning, that if the results of an engineering computerprediction are not known (the usual case in engineering calculations),then using accepted closure correlations is a basic tenet. There isnothing to be argued against this practice. On the contrary, it issupported by common sense and EJ.

It may be interesting to consider firstly the effect of frictionlaw in the stability map of a toroidal loop. This geometry is amenableto analytical and numerical analysis and has been the subject ofresearch since decades ago. An example of this may be found in [11]

and Figure 5 shows, without makeup, how the system behaved


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Figure 5,A toroidal loop with fixed input heat and dynamic heat exchanger

Figure 6a. The variation of friction factor with Reynolds number

changing the nodalization, showing the usual damping of the FTUSfinite-differences scheme.Far more recently, in [4], the effects of the friction laws on the

stability maps of a similar system were analyzed. Figure 6a showsthe most usual correlations for the friction factor in a tube, as afunction of the Reynolds number. The one signaled as Churchill lawis an adequate fitting to the Moodys law used for smooth tubes inengineering calculations. Figure 6b shows how the neutral stabilityboundary is affected by the particular choice of the friction factor

variation at the transition of the flow from laminar to turbulent. Thevariation is also predicted using the FTUS methodology and a modal


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expansion solution of the governing equations. Now, a more realisticsituation will be analyzed.

Let us now consider the following experimental results [12],dealing with NC flow in a simple square loop. The loop consists of a23.2 mm I.D. glass pipe, having 2.1 m vertical legs and equipped with0.8 m long electrically heated and fluid cooled horizontal sections.The latter consists of a pipe-in-pipe heat exchanger, fed by relativelycold water and at prescribed flow rates.This loop showed unstableNC flow conditions for a heat power input of 420 W. These resultshave been simulated by a set of two codes described in [13]. Figures7 and 8 show the results of the predictions using Churchills

Figure 6b. The stability map as a function of the friction law

Figure 7.Flow rate variation for 450 W


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25 26 27 28 29 30 31 32 33 34 35

Secondary Coolant Temperature [C]

100

200

300

400

500

600

700

800

900

1000

H

eaterPower[W

]

0.0232 m I.D. Loop of Vijayan et al. (1995)

1st Order Schem e, Fine Nodalisation, Dt = 0.1 s, Churchill's Friction Law

UNSTABLE

UNSTABLE

STABLE

STABLE

Figure 8. Stability map using Churchills law

25 26 27 28 29 30 31 32 33 34 35

Secondary Coolant Temperature [C]

100

200

300

400

500

600

700

800

900

1000

H

eaterPower[W

]

0.0232 m I.D. Loop of Vijayan et al. (1995)

1st Order Schem e, Fine Nodalisation, Dt = 0.1 s, Friction law suggested by Vijayan et al

ALW AYS UNSTABLE

Figure 9.Stability map using Vijayans suggested friction law


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approximation. As may be observed, the map shows a band of stableflow condition. Figure 9 shows the map for the same conditions usingthe friction law as suggested in [12]. The flow is always unstable, asthe experiments also indicate. The calculation using the codes of [13]with the correlation in [12] permitted to recover a condition similarto the one in Figure 9, i.e. a completely unstable map. Now, thefollowing may be concluded: the transition laws adopted to linkcorrelations for laminar and turbulent flow adopted in thermal-hydraulic codes are under question in unstable flows. It was shownthat a non monotonous transition branch in the correlating curvemay lead to predict stability, whereas experimental observationsshow unstable behaviour. Again the condition is not conservative.

It is somewhat difficult to establish an EJ criterion to deal withthis situation. Perhaps, the conclusion in [10] can be repeated here:the validity of the traditional claim for the inapplicability of theforced convection friction correlations in natural circulation conditionsappears to be rather dependent on the geometry of the loop. In fact,though in some literature works, including comprehensive reviews,recommendations are given to use friction laws providing largerfriction factors than in forced flow, the work in [12] seems to suggestthat classical laminar and turbulent friction correlations performreasonably well in rectangular loops. It is so when appropriate

localised pressure drop coefficients are included in the models toaccount for the effect of bends and other discontinuities.Nevertheless, what is clear is that transitional flows must beevaluated quite carefully, testing the effects even of the mostclassical closure correlations.

Conclusions

This presentation dealt with some particular applications ofengineering judgment to evaluate the results of computer codesapplication to unstable, one-dimensional, natural circulation flows insingle phase. Despite the simplicity of the systems analyzed, someproblems have been exemplified that pose a challenge to the commonreasoning. Perhaps, the only way to circumvent the questions ofconvergence of results and the effects of closure correlations is toresort to sensitivity to parameters analysis. This author and hiscolleague W. Ambrosini have also contributed on this subject that is

an active field of research, as summarized in [4]. If a concluding


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assertion is needed, it may be that EJ and non dogmatism gotogether and that accepting clichs as working rules must be avoided.In the authors opinion, the few examples considered fully supportthe previous assertion.

References

1) 1998, N. Aksan (Compiler), Best estimate methods in thermalhydraulic safety analysis, Summary and Conclusions of OECD/CSNISeminar 29 June - 1 July, 1998, Ankara, Turkey, NEA/CSNI/R(99)22.

2) 1995, E. Scannapieco and F. H. Harlow, Introduction to Finite-Difference Methods for Numerical Fluid Dynamics, LA-12984 (UC-700).

3) 1996, L.M. Shotkin, Development and assessment of U.S. NRCthermal-hydraulic system computer codes, Nuclear Technology, 116,pp. 231-244.

4) 2002, J.C. Ferreri and W. Ambrosini, On The Analysis of ThermalFluid Dynamic Instabilities via Numerical Discretisation ofConservation Equations, Nuclear Eng. and Design, 215, pp. 153-170.

5) 1967, P. Welander, On the oscillatory instability of a differentiallyheated fluid loop, J. Fluid Mech., 29, part. 1, pp. 17-30.

6) 1989, Quantifying Safety Margins: Application of Code Scaling,Applicability, and Uncertainty Evaluation Methodology to a LargeBreak Loss-of-Coolant Accident, NUREG/CR-5249, EGG-2659 also inNuclear Engineering and Design, 119, 1990.

7) 1998, IAEA, IAEA Specialist Meeting on User Qualification for andUser Effect on Accident Analysis for Nuclear Power Plants, Vienna, 31

August - 3 September, 1998.8) 1990, K.E. Carlson et al., RELAP5/MOD3 Code Manual Volume I:

Code Structure, System Models and Solution Methods, NUREG/CR-5535.

9) 1991, G.M. Grandi and J.C. Ferreri, Limitations of the use of a HeatExchanger Approximation for a Point Heat Source, Internal Memo,

CNEA, GSRN, Argentina Included in: 1999, Ferreri and W. Ambrosini, Verification of RELAP5/MOD3 with theoretical and numericalstability results on single-phase, natural circulation in a simple loop,US Nuclear Regulatory Commission, NUREG IA/151.

10) 2004, W. Ambrosini, N. Forgione, J.C. Ferreri and M. Bucci, The effectof wall friction in single-phase natural circulation stability at thetransition between laminar and turbulent flow, Annals of NuclearEnergy, 31, pp. 1833-1865.

11) 1984, J.C. Ferreri and A.S. Doval, Sobre los efectos de la discretizacinen el cmputo de la circulacin natural en loops, Seminarios del

CAMAT, 24, pp. 181-212.


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12) 1995, P.K. Vijayan, H. Austregesilo, V. Teschendorff, 1995. Simulationof the unstable behaviour of single-phase natural circulation withrepetitive flow reversals in a rectangular loop using the computer code

ATHLET, Nuclear Engineering and Design, 155, pp. 623-641.

13) 2003, W. Ambrosini and J.C. Ferreri, Prediction of Stability of One-dimensional Natural Circulation with a Low Diffusion NumericalScheme, Annals of Nuclear Energy, 30, pp 1505-1537.


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MESA DIRECTIVA

- 2005-2007 -

Presidente

Dr. JULIO H. G. OLIVERA

Vicepresidente 1Dr. ROBERTO J. WALTON

Vicepresidente 2Dr. AMLCAR E. ARGELLES

Secretario

Dr. HUGO

F. BAUZ

ProsecretarioDr. JORGE SAHADE

TesoreroIng. PEDRO VICIEN

ProtesoreroDr. FAUSTO T. L. GRATTON


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