Role of Scaling in Validation

Transcription

1 Role of Scaling in Validation U.S. (Kumar) Rohatgi ASME V&V Conference Las Vegas May 13-15,

2 Outline Introduction and Concepts Scaling methods General comments; scale distortions Extrapolation 2

3 Complex System-Pressurized Water Reactor 3

4 Safety Requirements Reactor could under go variety of transients, Loss Coolant accident, ATWS, Instabilities etc Safety Systems have to maintain integrity of barriers to release of radioactive material Peak Clad temperature below 2200F or surrogate criteria of water inventory in the core Conservative approach-best estimate approach 4

5 Knowledge Base 5

6 What are System codes Computer Codes are developed to simulate steady and transient condition of the systems Codes consist of Conservation Equations (Formulations) Constitutive relationships; Intrinsic and Extrinsic Nuclear system codes have over 100 constitutive relationships- Wall and phasic interfacial transfer Component models (black box approach, pump etc) Discretization (PDE to Algebraic) and numerical method, nodalization 6

7 Validation Validation is tests of code s capability to predict phenomena Validation is specific to code, plant and transient Validation provides two answers; 1) Code applicability (existence and accuracy of models) to simulate prototype and, 2) Quantification of uncertainty in code models ; for input for total uncertainty in plant simulation. 7

8 Hierarchal approach of decomposition of the problem prototype/ Facility Component 1 Component 2 Component n Processes 1,2,------m Processes 1,2,------m Processes 1,2,------m 8

9 Hierarchal approach of decomposition of the problem Decompose Problem to levels with lowest level where measurements are possible Rank components and processes at each level based on sensitivity study, expert opinion, or scaling methods Look for tests for high ranking phenomena and components 9

10 Validation Process-Frozen Code 10

11 Contributors to Uncertainty in Prediction Geometrical Representation Boundary and initial conditions Intrinsic Constitutive relationships-properties Extrinsic constitutive relationships such as interfacial and wall transfer of mass, momentum and energy (Flow regimes etc) Numerical representation and methods User Effects 11

12 Applicability of Validation Tests to Prototype Prototype and Transient Data Prototype prediction Frozen Computer codes Scalability, Applicability of tests to Prototype Validation Tests Comparison of predictions and Test Data 12

13 Scale Effect There are many parameters for scale effects. In some cases the Validation space may match or exceed application space 13

14 Counter Part Tests 14

15 Scaling Contributions Quantitative PIRT-prioritizes the effort Ensures that tests are similar to application (plant and transient) Designing new test facilities Counterpart tests Reviewing existing tests for different application Estimation of Scale distortion Coupling for multiphysics system 15

16 Scaling Methods 16

17 Type of similarity Types of similarity between two objects and processes. Geometric similarity linear dimensions are proportional. Kinematic similarity includes proportional time scales, i.e., velocity, acceleration. Dynamic similarity includes force scale similarity, i.e., Reynolds number (inertial/viscous), Froude number Thermal similarity-nusselt, Biot, Prandtl 17

18 Scaling Methods Buckingham Π Theorem (1914) Reductionist Approach; o Nahavandi (Nul. Science and Technology,1979) o Ishii, Kataoka (NED,81, 1984) o Kiang- (NED,89,1985) Global Approach; o H2TS method (Zuber, App D, NUREG/CR-5809) o FSA (Zuber, Wulff, Catton et al, NED, 237,2007) o Three Steps Method(Ishii et. al.ned,186,1998) 18

19 Reductionist Approach Balance equations (PDE) valid at a point and time in space, with BC/IC provide unique solution Non-dimensionalized equations generate set of scaling groups representing all the phenomena represented in the balance equations Nahavandi approach was based on local balance equations (PDE) Kiang, Ishii et al.used equations integrated over area; One dimensional equations accounting for wall momentum and heat transfer terms 19

20 Non-Dim Equations 20

21 Scaling Groups (Kiang, 1985) RRRRRRRRRRRRRRRRRRRR nnnnnn RR = gggg TT 00ll 00 uu FFFFFFFFFFFFFFFF nnnnnn FF = ffff dd + KK HHHHHHHH SSSSSSSSSSSS nnnnnn QQ = qq ll 00 ρρρρ pp uu 00 TT 00 MMMMMM SSSSSSSSSSSSSS nnnnnn SSSS = ρρρρ pp uu 00 dd LLLLLLLLLLLLLL CCCCCCCCCCCCCCCCCCCC nnnnnn LLLL = hh22 ll 00 ρρ ss CC pppp kk ss uu 00 TTTTTTTTTTTTTT mmmmmmmm rrrrrrrrrr = aa ssssρρ ss CC ss aa ii ρρρρ pp 21

22 Facility Dimensions Comparison of scaling groups will provide dimensions for test facility (for same fluid/pressure). Time preserving, requires same height, same velocity and power to volume matching Linear scaling will require time and velocity reduction and higher power/volume 22

23 Additional Scaling Groups Two-Phase 23

24 Comments Reductionist approach leads to many groups some at process level (wall heat transfer, friction factor etc) and at component level. It does address the physics. It is difficult to identify the importance of groups in term of effect on figure of merit and identify which one to preserve. It is difficult to match all groups, leading invariably to scale distortions 24

25 Global Approach Scaling based on Integral Analysis o o o o o o Holistic Approach; Deals with Transients on three levels: Systems, Components and Processes, Finite volumes, use ODEs. (integrated over space) Includes directly boundary and initial conditions, i.e., all Agents of Change at surface or in volume Addresses the Aggregate Effect of all Agents of Change on State Variables or Safety Parameters. H2TS and Fractional Scaling Analyses 25

26 Hierarchal Two Tier Scaling H2TS-(Zuber, App-D, NUREG/CR 5809) Complex system is decomposed in components, constituents, geometry and phases to make it tractable. A nested hierarchical system is generated based on volume fraction, length scale and time scale. Lower levels have smaller spatial and temporal scales. There impact decreases on upper levels. The exchange at the interface has different impact on two interacting entities. The scaling groups are ratio of specific time (process dependent) and residence time 26

27 System Decomposition 27

28 Two Area Concentrations 28

29 Basic Idea Find residence time in specific control volume Identify property of interest-mass, energy etc Identify the phenomena affecting the property and find time it will take to change total property due to this phenomenon (Reverse of frequency) Non-dim group is product of residence time and frequency-higher Freq. higher the effect. 29

30 Fractional Scaling Analyses It is global (holistic) approach that starts from fractional analysis and with decomposition from system to component and component to processes as needed. Integral form of balance equations are written (integrated over volume) to include boundary conditions. The fractional change of state variables results from action on the volume of interest. The contribution to fractional change leads to scaling groups and order of importance. 30

31 Fractional Scaling Analyses ω agg = ω i, a lg ebr i 31

32 FSA System Level Scaling Fractional Rate of Change and Fractional Change p* 1 for selected ω agg of system Fractional Change for ω i < ω agg 0 ω i > ω agg ω agg 1 ω i < ω agg t* = ω agg t 32

33 FSA The impact of an agent of change is evaluated through effect metric, Ω i ; (Fractional Change) Ω ii = ωω ii tt rrrrrr Ω = ii Ω ii = ii ωω ii tt rrrrrr For similarity of two facilities with ref times t ref1 and t ref2 Ω jj 1 = ωω jj 1 tt rrrrrr,1 Ω jj 2 = ωω jj 2 tt rrrrrr,2 The scale distortion is defined as Ω bb = Ω b 1 Ω bb 2 33

34 FSA System Level Scaling Agent of Change Hierarchy: PIRT Fractional Change Rate Agent 1 Agent 2 Agent 3 Agent j,... Agent n ω 1 > ω 2 > ω 3 > ω j > ω n Effect Metric (Fractional Change) Agent 1 Agent 2 Agent 3 Agent j,... Agent n Ω 1 > Ω 2 > Ω 3 > Ω j > Ω n 34

35 Scale Distortion ( Column) FSA System Level Agent a Agent b... Agent m Facility 1 (Ω a ) 1 (Ω b ) 1... (Ω m ) 1 Facility 2 (Ω a ) 2 (Ω b ) 2... (Ω m ) 2 Quantitative Assessment of Scale Distortion provides directly the difference In fractional change of a state variable or safety parameter during selected time: ( ) ( ) Ω = Ω Ω b b 1 b 2 35

36 FSA System Level Scaling for System Depressurization APPLICATIONS Hierarchy & Scale Distortion of Depressurizing Agents of Change Large-Break LOCAs ω is in %/s Net Break Flow Net Heating of Two- Phase Mixture Net Heating (Cooling) of Liquid Pumping Power Noncondensable Gases ω bk ω ω PPP ω N2 Q 2φ ω Q 1φ LOFT N.A. Semiscale N.A. 36

37 FSA System Level Scaling -Comments 1. Transfer processes have been identified, quantified and prioritized in the order of their impact on system pressure changes (depressurization during LOCA with six agent of change). 2. Scale distortion on the basis of differences between individual Change Metrics, ΔΩ have been shown 3. Break flow was dominant agent of change 4. Synthesis of different break sizes and facilities have been shown. 37

38 Scale Distortions All small size facilities have to compromise on preserving scaling groups. Facilities based on constant power/volume approach, inherently has larger surface area /volume, leading to heat losses and internal heat addition. Flow regimes differences can influence the phenomenon such as break in horizontal pipe in SBLOCA, ECC-Bypass phenomenon in LBLOCA and other phase changes and interactions 38

39 Scale Distortion Flow regimes are size/geometry dependent Vapor fraction is function of interfacial area and heat/momentum transfers Bubbles and drops have their own length scales-weber number; Interfacial rate processes have own time scales Entrance length-momentum and heat transfer Boiling Heat transfer and two phase pressure drop characteristics have multi-valued functions and scale distortion can move system to different regimes. 39

40 Examples of Scale Distortions 40

41 Viscous Pipe Flow: Entrance and Fully Developed The entrance region in a pipe flow is quite complex (1) to (2): The fluid enters the pipe with nearly uniform flow. The viscous effects create a boundary layer that merges. When they merge the flow is fully developed. There are estimates for determining the entrance length for pipe flows: and 41

42 Horizontal Flow 42

43 Horizontal Stratification- LOFT(28 cm) and Semiscale (3.4 cm) 43

44 Vertical Flow 44

45 Vertical Flow Regime 45

46 Boiling Heat Transfer 46

47 Extrapolation 47

48 Application of Validation results to Plant Extrapolation is an educated guess. There are three approaches Counterpart tests; extrapolation based on scaling differences or Counterpart Tests; Bounding values CFD analyses for extrapolation 48

49 Extrapolation- Vol ratio;d Auria et. al. 49

50 Statistical Approach-Counterpart Tests Estimate Accuracy for each facility (j) (different scale) based on many runs(i) MMMMMMMM aaaaaaaaaaaaaaaa oooooooo cccccccccccccccccccccc; aa = mm 1 aa jj PP jj mm If accuracy is trending towards 1.0 and conservative; take value from largest facility Counterpart Test average could be weighted by size and other distortions. There are suggestion that accuracy statement from counterpart IET could be used for prototype. 50

51 Use of CFD Use of codes for evaluating scale distortion and extrapolation is to be treated carefully. Code has to be validated for similar phenomenon. Model the tests with highest volume ratio and model prototype. The difference in scaled quantity will indicate scale distortion. This can be used as a bias. 51

52 General Rules Sol Levy commented that engineering judgement is important. He suggested that for reactor applications, tests that are 1/3 or higher in size will capture the phenomenon without much distortion. The internal scales of two phase topology is generally much smaller then channel sizes. 52

53 Scale Distortions-Pumps Pumps with same specific speed Flow with same cavitation number Head for smaller pump degrades more Pump at higher pressure will degrade less than at lower pressure where phasic density ratio is larger 53

54 Pump Performance-CE(1/5), CREARE(1/20) 54

55 Downcomer Flow 55

56 ECC Bypass 56

57 Downcomer-Flow ECC Inj 57

58 MHI Adv Accumulator

59 CFD Application

60 BWR-LaSalle Instability Event (March 1988) GE-Calc-TRAC-G- Max-Ampl-0.9 BNL-Calc-Plant Analyr Max-Ampl-12 60

61 Choked Flow Area Scaling Area(a 0 ) R =1/100 Velocity (v 0 ) R =1/2 Time (t 0 ) R =1/2 Mass flow rate scaling mm R = (ρva) R = 1/200 Area ratio 1/100, Velocity ratio, v R =1/2 At choking point, velocity ratio v R = 1 (same pressure) Therefore area ratio a R at choking points has to be 1/200, (in stead of 1/100) 61

62 Summary Global Scaling makes problem tractable-spatial and temporal decomposition (Phases) Develop ranking of phenomena based on Global scaling; High ranking should have least distortion and more validation Estimate scale distortions for each period. Counterpart Tests are essential for extrapolation Validated CFD could be used for estimating distortion 62

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65 Validation-USNRC

66 Scaling Issue Does the test represent the application-scales it for full range of conditions What are scale distortions What are consequences 66

67 Buckingham π Theorem Comments Buckingham π Theorem provides a minimum set to represent test data It does not provide actual correlations that will come from tests and analysis. It is good for synthesis of data Good example is Moody diagram for friction factors 67

68 Volume Fraction Hierarchy 68

69 Hierarchy of Phasic Interfacial area 69

70 Characteristic Frequency jj ii AA cccccc ψψψψ cccc = αα CC αα cccc αα cccccc ωω cccccc = ωω ii jj ii AA cccccc ψψψψ cc = αα cccc αα cccccc ωω cccccc jj ii AA cccccc ψψψψ cccc = αα cccccc ωω cccccc jj ii AA cccccc = jj ii AA cccccc = ωω ψψψψ cccccc ψψ VV cccccc cccccc 70

71 Residence Time Hierarchy 71

72 FSA System Level Scaling for System Depressurization APPLICATIONS) Data Synthesis for Small-Break LOCA Two Facilities: LOFT and Semiscale Four Break Sizes: 0.1% - 10% Measured Depressurization History Observe the spread of data; Present practice in NPP Safety Analysis; One calculation and one experiment for each test run. Pressure (bar) LOFT 0.1% sbloca Semiscale 2.5% sbloca Semiscale 5% sbloca Semiscale 10% sbloca Time (s) 72

73 Applications FSA System Level Scaling for System Depressurization Data Synthesis for Small-Break LOCA Two Facilities: LOFT and Semiscale Four Break Sizes: 0.1% - 10% Scaled Depressurization History Fractional Pressure, p* LOFT, 0.1% sbloca (8,000s) Semiscale, 5% sbloca (1,400s) Semiscale, 10% sbloca (600s) Semiscale, 2.5% sbloca (1,400s) Fractional Change Metric Ω 73

74 R=Y meas / Y cal Extrapolation Distortion Increasing Distortion Decreasing 1.00E E E E E+00 74

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76 SBLOCA 76

77 Summary H2TS approach shows that time ratio can provide scaling groups The impact of lower level phenomena decreases as we move up the hierarchy Distortion can be estimated by comparing facility and prototype scaling groups. These scaling groups can also be obtained from integral balance equations. 77

78 FSA System Level Scaling Scale Distortion & Time time need not to be preserved. Given: Experimental Pressure Histories 1.0 Time t of Effect Metric Ω = ωt is selected as characteristic response times t 1, t 2 which produce the same fractional change in both facilities. Fractional Pressure p* Facility 1 Facility 2 Fractional Change 0.0 t Time t t2 78