Scaling Analysis as a part of Verification and Validation of Computational Fluid Dynamics and Thermal-Hydraulics software in Nuclear Industry

Transcription

1 Scaling Analysis as a part of Verification and Validation of Computational Fluid Dynamics and Thermal-Hydraulics software in Nuclear Industry M. Dzodzo 1), A. Ruggles 2), B. Woods 3), U. Rohatgi 4), N. Dinh 5), S. Bajorek 6), G. Zigh 6), H. Lee 7), Y. Hassan 8), R. Schultz 9), C. Freitas 10) 1) Westinghouse Electric Company, 2) The University of Tennessee, 3) Oregon State University, 4) Brookhaven National Laboratory, 5) North Carolina State University, 6) United States Nuclear Regulatory Commission, 7) Bettis Atomic Power Laboratory, 8) Texas A&M University, 9) Idaho National Laboratory, 10) Southwest Research Institute 1

2 Evaluation Model Development and Assessment Process - EMDAP Six Basic Principles (Elements) of Evaluation Model Development and Assessment Process (EMDAP) are presented in Transient and Accident Analysis Methods (USNRC, Regulatory Guide 1.203, 2005). Scaling Analysis is a part of EMDAP and Transient and Accident Analysis Methods. Added Element 5 Follow an Appropriate Quality Assurance Protocol Quality assurance standards (as in Appendix B to 10 CFR Part 50) Peer review by independent experts Element 6 Provide comprehensive, accurate, up-to-date documentation Needed for a credible NRC review Needed for the peer review Develop and keep current documentation about the changes in the importance determination 2

3 Role of Scaling Analysis in V&V of TH and CFD software in Nuclear Industry The entire plant (full scale) under transient accident conditions data is not available to assess the evaluation model and this lack of data for direct comparison is the main difference between V&V 20 and V&V 30 Standards Some Separate Effects Tests (SET) can be designed for almost full scale and with minimal scale distortions. V&V 30 Standard uses Scaling Analysis to guide selection and design of experiments used to generate validation data for Evaluation Models. 3

4 Status of development of Scaling Analysis document supporting V&V 30 Standard Table of Content Introduction - Scaling Uses and Context for Nuclear Power System Evaluation Model Validation Data Development Scaling History and Types Volumetric Scaling Approach Overview and Comparison of H2TS and FSA References APPENDIX A - EXAMPLES OF H2TS APPLICATIONS A.1 FOR INTEGRAL TEST FACILITITIES A.2 FOR SEPARATE TEST FACILITIES APPENDIX B EXAMPLES OF FSA APPLICATIONS B.1 FOR INTEGRAL TEST FACILITITIES B.2 FOR SEPARATE TEST FACILITIES APPENDIX C EXAMPLES OF THREE WAY SCALING APPENDIX D EXAMPLES OF OTHER SCALING METHODS APPENDIX E - NEW TRENDS 4

5 EMDAP Element 1 Step 4: Identify and Rank Key Phenomena and Processes Sensitivity studies can help determine the relative influence of phenomena identified early in the PIRT. 1.The scenario is divided into operationally characteristic time periods (time sequences) in which the dominant process and phenomena (if we know them!) remain almost constant and there is no change in system configuration (due to the operator action, or automatic valve actuation, start or stop of pumps, etc.). 2.The processes and phenomena are identified for each component of the system and for each time period, to differentiate cause from effect. 3.Starting with the first time period the potentially significant processes are identified, component by component. 4.The procedure is repeated sequentially, from time period to time period (until the end of the scenario). We might need to go back (to 1.) and introduce additional characteristic time periods and/or rearrange them and repeat 2, 3 and 4. 5

6 EMDAP Element 1 Step 4: Identify and Rank Key Phenomena and Processes Initial phases of the PIRT process usually rely on expert opinion, which can be subjective. An Example: Portion of the PIRT for Non-LOCA Heat-up Transients System Modules Phenomena Loss of Normal Feedwater Flow State of knowledge RCS Core Fuel Heat Transfer L Decay Heat H Pressurizer Thermal-hydraulics H (high impact on the figure of merit) Coolant Pumps Natural Circulation L Critical Flow L Structural heat absorption and loss Steam System Steam Generator Primary side TH H L Secondary side TH Separator behavior M (medium impact on the figure of merit) L (low impact on the figure of merit) 6

7 EMDAP Element 2 Develop Assessment Base Steps: 5. Specify objectives for assessment base 1. Separate effects experiments needed to develop and assess empirical correlations and other closure models 2. Integral systems tests to assess system interactions and global code capability 3. Benchmarks with other codes 4. Plant transient data (if available) 5. Simple test problems to illustrate fundamental calculational device capability 6. Perform scaling analysis and identify similarity criteria 7. Identify existing data and/or perform IETs and SETs to complete data base 8. Evaluate effects of IET distortions and SET scale-up capability 9. Determine experimental uncertainties 7

8 EMDAP Element 2, Step 6 - Possible Scaling Analysis Approaches The Hierarchical, Two-Tiered Scaling (H2TS) Analysis Methodology (see Zuber, 1991), and (Zuber et al., 1998) Fractional Scaling Analysis (FSA) (see Zuber et al., 2005) as an update could be applied for EMDAP as well. The H2TS and FSA methodologies use concepts from the hierarchical theory presented by Mesarovic et al., 1970, two-tiered approach, and the concept of time-scale modeling used to analyze large power systems (presented in Chow, 1986, Kline 1986). Chow T. H., editor, Time Scale Modeling of Dynamic Networks and Applications to Power Systems, Springer Verlag, New York, 1986 Kline S.T., Similitude and Approximation Theory, Springer, New York, 1986 Mesarovic M. D., Macko D., and Takahara Y., Theory of Hierarchical Multilevel Systems, Academic Press, New York, 1970 Zuber N. Appendix D: A Hierarchical, Two-Tired Scaling Analysis, An Integrated Structure and Scaling Methodology for Severe Accident Technical Issue Resolution, U. S. Nuclear Regulatory Commission, Washington, D.C , NUREG/CR-5809, November 1991 Zuber N., et al., An Integrated Structure and Scaling Methodology for Severe Accident Technical Issue Resolution: Development of Methodology, Nuclear Engineering and Design, 186, pp. 1-21, 1998 Zuber N., Wulff W., Rohatgi U. S., Catton I., Application of Fractional Scaling Analysis (FSA) to Loss of Coolant Accidents (LOCA), Part 1: Methodology Development, The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), Paper 153, Popes Palace Conference Center Avignon, France, October 2-6,

9 Flow Diagram for a Hierarchical, Two-Tiered Scaling (H2TS) Stage 1 Stage 2 Stage 3 Stage 4 SYSTEM DECOMPOSITION SCALE INDENTIFICATION TOP-DOWN SYSTEM SCALING ANALYSIS BOTTOM-UP PROCESS SCALING ANALYSIS PROVIDE: System hierarchy IDENTIFY for each time sequence: Characteristic: Constituents PROVIDE HIERARCHY FOR: Volumetric concentrations Area PROVIDE: Conservation equations DERIVE: Scaling groups and characteristic time ratios PERFORM: Detailed scaling analysis for important processes DERIVE AND VALIDATE: Scaling groups Phases Geometries concentrations ESTABLISH: Scaling hierarchy Processes Process time scales IDENTIFY: Important processes to be addressed in bottom-up process scaling analyses 9

10 10 Concept of Time Scale Modeling Dimensionless Groups in terms of Time Ratios Example: heat transfer to a fluid flowing through a pipe of length L, and diameter L. Ratio of the heat transferred from the surface to the enthalpy inflow into the pipe is: h π L L ( Ts Tb ) π L L ( Ts Tb ) q" AT VCV Π = = St = = ω τ 2 2 CV L L ρ H VCV Q ρ V c p Tb π Tb π 4 4 The characteristic frequency specifies how many times per second the enthalpy contained in the control volume ρ H V CV is being changed due to a heat transfer at the pipe surface q" A T (particular transfer process). The characteristic time ratio Π is the total change during the residence time τ CV. If the LOCA integral test facility operates at prototypical pressure with the same fluid and residence time the power to volume scaling criterion is: q " A / V = q" A / V [ T CV ] [ T CV ] m p

11 Example 2: Volumetric Scaling Advantages of the Volumetric Scaling Approach: Full Height Provides prototypical distance between heat sources and heat sinks centers to properly simulate natural convection effects Both, single phase and two phase natural convection loops can be simulated simultaneously Prototype and model fluid velocities and residence times in the loops are the same Horizontal inter-phase areas (transfer area concentrations) are properly scaled Prototypical Pressure and Temperature Distortions due to the different fluid properties are not present (Scaling Analysis does not generate additional terms related to property distortions) and Interpretation of the results is easier SPES3 facility layout (Figure 3 in A. Achili, et al., SPES3 Facility RELAP5 Sensitivity Analyses on the Containment System for Design Review, Hindawi Publishing Corporation, Volume 2012, Article ID , 19 pages) 11

12 Example 2: Volumetric Scaling Disadvantages of the Volumetric Scaling Approach: Area of the Side Walls decreases only 100 times as volumes) A A p m SideWalls = D D p m H H = V V V p / V m p m =, for example: 10 times (not D D 2 p 2 m = 100 = 10 Resulting in 10 times larger Transfer Area Concentrations for heat transfer (energy exchange) and wall friction (momentum exchange). Some flow regimes can not be simulated due to the elongated/narrow domains (flow paths). Some components (like heat exchangers) might be represented with limited number of tubes (not adequate to address side/bundle effects). 12

13 Features of Hierarchically Organized Systems Hierarchy can be established from the differences in spatial, temporal and energetic scales. Processes can be grouped into classes with similar scales. The sufficiently distinct classes can be decoupled, resulting in a hierarchical organization. Levels in a hierarchy are isolated from each other (because they operate at different scales). A lower level in the hierarchy communicates only its average to the higher level (less detailed information is needed at higher levels). Larger characteristic spatial scales are associated with characteristic longer time scales. Each lower level provides more detailed information (specificity). 13

14 System Decomposition and Hierarchy System decomposition Hierarchy for processes Hierarchy for length, time and volumetric concentration SYSTEM (S) S (S) Nuclear Power Plant SUBSYSTEM (SS) SS 1 SS k (SS 1,, SS k ) (Reactor Vessel, Steam Generators, Pressurizer, Pumps, Containment, etc.) MODULES (M) M 1 M k (M 1,, M k ) (Core, Lower Plenum, Downcomer, Upper Plenum, etc.) CONSTITUENTS (C) C 1 C k (C 1,, C k ) (Water, Steel, Nitrogen, etc.) PHASES (P) g f s (g,f,s) (Gas, Fluid Liquid, Solid) GEOMETRICAL CONFIGURATIONS (GC) G 1 G k (G 1,.., G k ) (Bulk Liquid, Bulk Gas, Liquid Film, Drops, Bubbles, etc.) FIELDS (F) M MM E (M,MM,E) (Mass, Momentum, Energy) PROCESSES P 1 P k (P 1,., P k ) (Convection, Conduction, Condensation, etc.) 14

15 Top-Down Approach - Scaling Hierarchy The control volume balance equation for constituent i is dviψ i dt [ Qψ ] m 1 ( = i i ± jik Aik ) + Si k = 1 where ψ = ρ, ρv, ρu i for mass, momentum, energy After substituting variables in dimensionless form as: V + i = V i + / Vi o, ψ i =ψ i / ψ i,, o,... Q i, oψ i, o and normalizing the equation with the convective term ( ) V dv ψ + + i i i, oψ i, o = Qi, oψ i, o i i ik, o ik, o ik ik i, o i / dt k = 1 the dimensionless form is: + dvi ψ τ i dt + i [ ] m Q ψ ± ( j A ) j A + S S ( Q ψ ) m 1 [ ] Q ψ ± ( Π j A ) + Π S = i i ik ik ik si i k = 1 i, o i, o 15

16 Top-Down Approach - Scaling Hierarchy where the residence time of constituent i in volume V i is: τ i = and each specific time ratio for a transfer process between constituents i and k is composed of a specific frequency and residence time of constituent i in volume V i. Π ik = j ik,0 Q i,0 A ψ ik,0 i,0 = j V Q ik,0 V i,0 i,0 i,0 A ψ ik,0 i,0 V Q i,0 i,0 = ω Time ratios provide a metric for evaluating the relevance of a particular process on the response of constituent i. Thus, all processes can be ranked according to their importance on the system. Top-down system approach provides a method for establishing a scaling hierarchy. S ik τ i 16

17 Bottom-UP Approach The bottom-up approach is performed only for the processes which were identified as being important to the behavior of the system in the case of IET, or component (or module) in the case of SET. Thus, the bottom-up analysis is focused on the specific process and quantification of flux and geometrical terms present in non-dimensional groups. According to Zuber, 1991, the bottom-up approach has three important objectives: To discern the mechanisms that govern the flux and geometrical terms, To establish and validate functional relations for calculating these terms, and To demonstrate that these fractional relations (or models) can be applied to a full scale system. For example, the applicability of correlations for heat and mass transfer present in the evaluation model need to be confirmed for both, plant and model conditions. The detailed analysis of governing mechanisms ensures that processes important to system response are adequately addressed. 17

18 Two-Tiered Scaling Approach The top-down approach scales the behavior of the whole system and establishes important processes. In the bottom-up approach, the effects of the important specific process are investigated and quantified at the lower levels. Top-Down or System Approach provides Efficiency; Bottom-Up or Process Approach provides Sufficiency of the Scaling Analysis. 18

19 Top-Down Approach - Effects of Scale Distortions Time ratios represent the total change of a conserved property in the control volume, during the residence time, caused by the relevant transfer process. Time ratios are used to establish a hierarchy and ranking for various processes to be tested. If time ratio is small ( Π << 1) only small quantity of the corresponding property would be transferred in the limited available time. As a consequence the specific process would not be important to the overall transient. If time ratio is large ( Π >>1) the specific process has a high transfer rate of the conserved property during the residence time period. The larger the time ratio the more important is the transfer process. The characteristic time ratio must be preserved for the prototype and the model Π = Π ). The effect of a distortion in the model can be estimated from ( m p D = Π m Π Π p p To quantify the distortion the time ratios for the model and prototype need to be calculated. 19

20 Fractional Scaling Analysis (FSA) Fractional Scaling Analysis (FSA) (see Zuber, 2001 and Zuber et al., 2005) could be applied for EMDAP as well. FSA methodology is based on two concepts: Fractional Scaling provide a synthesis of experimental data to generate quantitative criteria for assessing the effects of various design and operating parameters. Hierarchy is applied at three levels: System, Component, Process. Zuber N., The Effects of Complexity, of Simplicity and of Scaling in Thermal Hydraulics, Nuclear Engineering and Design, 204, 1-27, 2001 Zuber N., Wulff W., Rohatgi U. S., Catton I., Application of Fractional Scaling Analysis (FSA) to Loss of Coolant Accidents (LOCA), Part 1: Methodology Development, The 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), Paper 153, Popes Palace Conference Center Avignon, France, October 2-6,

21 Fractional Change / Effect Metric State Variable U Mechanics Ecology/Biology Economy Momentum Energy Population/ Capital Biomass Agent of Change Force Power Reproductive du Φ = ϕ Force dt Fractional Rate of Change Φ ω = U mv F Mechanical Impedance F mv E ϕ E Specific Growth Rate Economic Force Interest Rate Fractional change/ Effect Metrics Φ Ω = δt U o F δ t mv ϕ t E δ Specific Growth Return on Investment 21

22 FSA Activities at each level Process Level: Synthesis of parameters governing the process is achieved via the effect metric Ω. Component Level: Synthesis is performed on processes via effect metrics Ω. The effect of each process on a state variable is quantified by the corresponding effect metric Ω, and by ordering them by their magnitude the Hierarchy of Processes is generated. Component Process Effect Metrics A Ω... Ω1 Ω 2 3 Ω n This level identifies important processes that must be addresses in codes and experiments; Establishes priorities for modeling and/or design; Identifies the effect of scale distortions; Provides a quantitative PIRT at the component level 22

23 FSA Activities at each level System Level: Synthesis is performed on system components via System Matrix (rows are for the components, columns are for their processes). System Matrix is different for different Time Sequences! 23

24 Hierarchy of Processes: Distortion Quantification Distortion of each process can be evaluated as in Wulff, 2005** for each time sequence: D i = Ω Ω i, MODEL i, PROTOTYPE As in Wulff, 1998* 3 regions are identified: 1. If 1/2<D<2 the phenomenon is well scaled i = 1φ l,1φ v, 2φ, N 2. If 1/3<D<1/2 or 2<D<3 the phenomenon presents a distortion of the first grade 3. If D<1/3 or D>3 the phenomenon presents a distortion of the second grade If D<0 the phenomenon is completely distorted: OMEGA has different sign in the prototype (plant) and model (test Facility) The distortion acceptability criteria might be different in some cases due to the different normalization of the Effect Metrics. * NUREG/CR-5541, System Scaling for the Westinghouse AP600 PWR and related facilities, January 1998 ** Zuber N., Wulff W., Rohatgi U. S., Catton I., Application of Fractional Scaling Analysis (FSA) to Loss of Coolant Accidents (LOCA), Part 1: Methodology Development, The 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), Paper 153, Popes Palace Conference Center Avignon, France, October 2-6,