by Dan Hughes
As is the case of a large number of other matters, designing and developing scaled experiments of complex engineered equipment for inherently complex, transient fluid flow, heat transfer, hydrodynamics, and thermodynamics has been somewhat contentious. My experience has been that there are no aspects whatsoever of transient, compressible, boiling and flashing two-phase flows that are not contentious. Spirited discussions about every aspect continue to this day.
I’m going to try to present a very short description of the focus on scaling that was underway at Camp NRTS in the 1970s. I think my brief review into the literature shows how important the Camp NRTS work has been in experimental investigations of reactor safety all round the world. No math will be involved.
The matter of designing scaled models of full-size Nuclear Power Plants (NPPs) was critically important at Camp NRTS from the earlest days, and became even more critical (is that possible?) for experimental investigations of Loss of Fluid Accidents (LOCAs). The Semiscale and Loss of Fluid Test (LOFT) facilities, along with other experiments at NRTS, were to provide data for Validation of the mathematical models that were the basis of the computer codes used for safety analyses of proposed and operating NPPs. An extremely important process that was getting underway in the 1970s. The importance cannot be over-stated.
I don’t have much experience in this activity: I usually develop dimensionless numbers directly from the model equations and do not give much thought to how these relate to scaled models for the phenomena and processes represented by the mathematical model. So basically I’m an outside observer looking in when it comes to designing experimental rigs.
The objectives of using scaled models include accurately representing, and accurately measuring, the critically important response functions of interest at reasonable overall costs. The activity includes also development of instrumentation; another aspect that was a focus area at Camp NRTS, and one on which several people, including George Brockett, were very focused. Again way outside my areas of knowledge.
The concept developed at Camp NRTS is called Power-to-Volume scaling. Peter R. Davis, aka Pete or Davis, tells me that the details of the scaling methodology are in an internal LOFT document, Program Requirements Document (PRD). Don’t know if there are any publicly available copies of that PRD. A paper from 1974 that is very widely cited to contain the methodology is:
Ybarrondo, L.Y., Griffith, P., Fabic, S., McPherson, G.O., 1974. Examination of LOFT Scaling, In Proceedings of the ASME Winter Meeting, New York, USA.
That would be Larry Ybarrondo, Peter Griffith, Stan Fabic, and Don McPherson. I have had no success in finding electronic copies of that paper. (I actually suspect that few who cite the paper have actually seen the real thing. It is very elusive.) Note the 1974 date, and I think the methodology was developed prior to then by a year or two.
There are now hundreds of reports and papers on scaling of NPPs, comprised of thousands of words and hundreds of equations, and tens of dimless numbers. As there are now many test rigs around the world devoted to different response functions of physical phenomena and processes.
There are several review papers in the literature. A somewhat recent review, which I think is quite complete is:
F. D’Auria and G.M. Galassi (2010), Scaling in nuclear reactor system thermal-hydraulics, Nuclear Engineering and Design, Vol. 240, pp. 3267–3293.
I am going to insert several paragraphs from the paper.
Note this sentence:
The power-to-volume scaling, typically associated with the full-pressure, full-height and time-preserving requirements can be seen as the first (in historical terms) proposed solution to the scaling problem in NRSTH [Nuclear Reactor System Thermal-Hydraulics]. [bold by edh]
Another excerpt from the paper follows.
Three sectors for scaling analyses are recognized with geometric dimensions playing a major role in the classification:
- The component-scale, or zone-scale, or phenomenon-scale. At first, one of the following should be identified: (a) a component, e.g. the pump, or the separator, or the core region, (b) a zone, e.g. the upper plenum, or the connection between cold leg and downcomer, (c) a phenomenon, e.g. the Two-Phase Critical Flow (TPCF) at the break, or the Countercurrent Flow Limiting (CCFL) at the Upper Tie Plate (UTP), or the Critical Heat Flux (CHF) in the core region. Then, the variables affecting the component performance, the phenomena occurring in the assigned zone or the time window for the evolution of the phenomenon, shall be identified. Finally, suitable links shall be established between evolutions of the variables in the model and in the prototype.
[bold by edh]
End of excerpt.
The procedures summarized in this excerpt exactly describe what George Brockett was doing in the late 1960s at Camp NRTS. The procedures also form the foundation of the massive PIRT/CSAU/UQ approach developed in the late 1980s, and continuing today. It is my impression that the known fact that the procedures originated and developed at Camp NRTS has not ever been acknowledged by the later work.
While the excerpt below mentions Novack Zuber and the 1960s together, the earlest cited Zuber publication dates to 1991. All the citations to Zuber, Ishii, Wulff, Owen Jones, at el., and several textbooks in which scaling is discussed were published after the NRTS results.
If you download, or take a look at, the paper at the URL link above, you’ll see that all the citations to scaling papers associated with NPPs and test rigs were published after the NRTS work in the early 1970s.
Section 2.2 introduces important aspects of scaling and outlines the structure of the paper. Power-to-Volume scaling is the subject of Section 2.2.1.
2.2. The classic approaches to scaling
How to simulate the transient performance of an up-to-4500 MWth LWR (also called prototype hereafter) by a less than approximately 10 MWth ITF [Integral Test Facility] (also called model hereafter), with the noticeable exception of LOFT (Loss of Fluid Test, OECD/NEA, 1991), constitutes the ‘classic’ scaling problem. Key aspects connected with the problem (see also the operating conditions values given in Section 1) can be summarized as follows:
The power-to-volume scaling, typically associated with the full-pressure, full-height and time-preserving requirements can be seen as the first (in historical terms) proposed solution to the scaling problem in NRSTH [Nuclear Reactor System Thermal-Hydraulics]. This is discussed in Section 2.2.1. In that section, design factors derived from basic principles (i.e. not even the balance equations) and suitable for building NPP [Nuclear Power Plant] simulators are listed all together.
It is easily seen that the power-to-volume scaling together with associated requirements has two main drawbacks, specifically in the case when transients governed by gravity heads are concerned: (a) cost of the facility; (b) strong impact upon the transient evolution of thermal power release from passive structures. In order to overcome these drawbacks, fundamental research has been performed by Ishii and is outlined in Section 2.2.2.
Starting from the 1960s, Zuber, primarily with the support from US NRC, provided a continuous contribution to key issues in thermal-hydraulics including the scaling. His ideas are discussed in Section 2.2.3.
At some point in the history of system thermal-hydraulics, i.e. beginning of 1980s, the issues of validation of computational tools and of evaluation of uncertainty associated with any calculated results became relevant. The connection between scaling and uncertainty is discussed in Section 2.2.4 dealing with the CSAU (Code Scaling, Applicability and Uncertainty) procedure. Otherwise, the connection between scaling and validation is mentioned primarily in Section 4.2. [note by edh. Validation at Camp NRTS started long before the 1980s. The primary objective of Semiscale, LOFT, and the other experiments there was to provide data for Validation of the models.]
During the last two decades, i.e. 1990s and 2000s, reactor specialists from Russia and Far East Countries (primarily South Korea and Taiwan) made available their contributions to the solution of the scaling issue and the same issue became important for the design of advanced reactors. Thus, a short survey of related scaling achievements is provided in Section 2.2.5.
As already mentioned (e.g., see J. NED [Nuclear Engineering and Design] Special Issue, 1998), a large number of top level scientists were engaged to address the scaling issue and excellent scaling reviews can be found (e.g. Yun et al., 2004). Selected findings are summarized in Section 2.2.6, where emphasis is given to selected-representative scaling factors that are cross-correlated with design factors from Section 2.2.1. The connection between scaling and licensing is emphasized in Section 2.2.7. [edh note. The Abstracts for all the papers are here.]
Within the present framework and consistently with Zuber recommendations the need of hierarchy among scaling factors (however, this idea is shared or accepted by the majority, or even by all researchers in the area), is recognized. Hereafter, inconsistently with Zuber recommendations (discussed below) the computer code is put at the center of the attention for performing the scaling process. This is characterized as the ‘key-to-scaling’.
2.2.1. The power-to-volume scaling and the design factors
The needs to design and to construct experimental facilities capable of ‘simulating’ the NPP performance, noticeably the PWR, constituted a challenge for the involved scientists due to the contradictory requirements coming from ‘safety relevance’ and ‘cost constraints’. This happened the first time in the 1960s when the US NRC (Nuclear Regulatory Commission, AEC at that time) requested a suitable evidence of the capabilities of the ECCS (Emergency Core Cooling Systems) to keep cooled the core following LOCA (Loss of Coolant Accident).
Primordial set of scaling parameters were introduced for justifying the design and the operation of Semiscale and Loft facilities in the US, see e.g. the pioneering works by Carbiener and Chudnik (1969) and Ybarrondo et al. (1974), that later on were put in an archival form by Navahandi et al. (1982), Larson et al. (1982), Karwat (1983), and Kiang (1985). Till the TMI-2 accident, i.e. 1979, the attention for the simulation was focused toward the LB-LOCA (Large Break LOCA), however in the ‘post-TMI’ the above referenced papers also considered SB-LOCA (Small Break LOCA) phenomena (additional details related to the role of Loft in relation to scaling, are given in Section 3.4 with focus to LB-LOCA).
Facilities like Lobi, Spes, Bethsy and the Rosa series (noticeably the Lstf) were designed and built (or modified) in Europe and in Japan for the simulation of SBLOCA in PWR, after the occurrence of the TMI-2 accident; see e.g. the data base collected by D’Auria et al. (1994) and Ingegneri et al. (1997).
At this point in the history of NRSTH, i.e. decades 1980s and 1990s, the power-to-volume scaling approach, time-preserving, full-height, full-pressure was the preferred practical way to address the scaling issue within the area of ITF design, as already mentioned. However, three kinds of principles were distinguished (e.g. Navahandi et al., 1982)
- (1) Time reducing or linear scaling.
- (2) Time preserving or volume scaling.
- (3) Idealized time preserving.
The first set implies the reduction of the linear dimensions of the prototype by a given factor and, in transient conditions, the reduction of time by the same factor. In this case, the amount of power transferred to the fluid is reduced as the square of the linear dimension factor. The second set of criteria is at the origin of the dimensionless design factors discussed below and the third set of criteria actually resembles the second set, with more flexibility left to the designer, being the ‘time preserving’ the main objective for the application.
The dimensionless design factors are applicable for the design of facilities and experiments. They can be derived directly from the principles of conservation of mass, momentum and energy. As a difference, the scaling factors are derived from the more or less complex balance equations for single and two phase flow. Scaling factors obtained from simplified balance equations can be used to derive design factors.
A synthesis list of design factors that characterize the power-to-volume scaling can be found in Table 1 (e.g. D’Auria and Vigni, 1985; D’Auria et al., 1988, in these papers, where a hypothetical PWR simulator and an experiment are designed, respectively). Two groups of design factors ‘K’ can be distinguished dealing with the ITF hardware and the test BIC [Boundary and Initial Conditions], respectively. Here, ‘K’ is the ratio ‘quantity value in the model/quantity value in the prototype’.
The hardware of the hypothetical ITF [Integral Test Facility] is subdivided into the following zones: (a) LP (Lower Plenum) of RPV (Reactor Pressure Vessel); (b) CO (Core); (c) CO-BY Core Bypass; (d) UP (Upper Plenum); (e) UH (Upper Head); (f) HL-h (Hot Leg, horizontal part); (f) HL-v (HL, vertical part); (g) PRZ (Pressurizer); (h) SU-LI (Surge Line of PRZ); (i) LS (Loop Seal); (j) MCP (Main Coolant Pump); (k) CLh (Cold Leg, horizontal part); (l) DC (Down-Comer) of RPV; (m) SGI (Steam Generator Inlet Plenum, Primary Side); (n) SGO (Steam Generator Outlet Plenum, Primary Side); (o) SG UT PS (Steam Generator, U-Tubes, Primary Side): (p) SG UT SS (Steam Generator, U-Tubes, Secondary Side); (q) SG DC (Down-Comer, Secondary Side); (r) SG UP-SEP (Upper Plenum and Separator, Secondary Side); (s) SG UHDRY (Upper Head and Dryer, Secondary Side).
The information in the table is self-explanatory. However it can be noted that the Kv value is the key for the design and its value is strictly connected with the available financial resources. Adopted criteria imply that mass and energy in themodel are properly scaled (according to Kv) in relation to the prototype.
In case of LOCA, the break area should be scaled according to the parameter at row 6 in the table, i.e. the ratio AR/V shall be preserved. Furthermore, the break location should also be preserved considering the proper geometric location and the curve ‘pressure-drop vs loop length’, i.e. criterion at row 20.
The scaling factors which give origin or are consistent with the design factors in Table 1 shall be classified as the ‘primary scaling parameters’, as discussed in Section 2.2.6. The following remarks apply (i.e. in addition to the notes provided in the last column of the table):
This is the end of Section 2.2.1 and the end of the quoted material.
The cited References associated with the Camp NRTS work follow. I have not included the others cited in the above excerpt. The two papers that appeared in Nuclear Science and Engineering are available, but cost 30 bucks each. The ANS has a very hard paywall, as does the ASME.
Ybarrondo, L.Y., Griffith, P., Fabic, S., McPherson, G.O., 1974. Examination of LOFT Scaling, In: Proceedings of the ASME Winter Meeting, New York, USA.
Nahavandi, A.N., Castellana, S., Moradkhaniav, E.N., 1982. Scaling laws for modeling nuclear reactor systems, Nuclear Science and Engineering, Vol. 72.
Larson, T.K., Anderson, J.L., Shimeck, D.J., 1982. Scaling criteria and assessment of Semiscale Mod 3 scaling for Small Break LOCA transients, In: Proceedings of the ANS-NRC Meet of Basic Thermal-hydraulic Mechanisms in LWR Analysis, Bethesda, USA.
Karwat, H. 1983. Problems of scaling and extrapolation of experimental results in the area of fluid-dynamics and associated heat transfer related to Reactor Safety, CEC Study Contract, ECI-930-B7221-82-D, Bruxelles (B).
Kiang, R.L., 1985. Scaling criteria for nuclear reactor thermal-hydraulics, Nuclear Science and Engineering, Vol. 89 (3), pp. 207–216.
Larson, T.K., Anderson, J.L., Shimeck, D.J., 1982. Scaling criteria and assessment of Semiscale Mod 3 scaling for Small Break LOCA transients In: Proceedings of the ANS-NRC Meet of Basic Thermal-hydraulic Mechanisms in LWR Analysis, Bethesda, USA.
The Table of Contents of the 1998 Special Issue of Nuclear Engineering and Design. mentioned in the excerpt are here. NRTS results are the subject of this paper:
S. Banerjee, M.G. Ortiz, T.K. Larson, D.L. Reeder, Scaling in the safety of next generation reactors, Nuclear Engineering and Design, Volume 186, Issues 1–2, 1 November 1998, Pages 111-133, ISSN 0029-5493, https://doi.org/10.1016/S0029-5493(98)00219-2.
The Abstracts for all the papers are here.