[PPT] - Investigation of the Fatigue Cracking and Leakage Rate potential of PowerPoint Presentation

SLIDE 1

Background Elements of Investigation Numerical Simulations Results

Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend Tube Bundles subjected to Flow-Induced Vibrations

University of Guelph Fluid-Structure Interaction Laboratory Canadian Nuclear Safety Commission Marwan Hassan, Jovica Riznic and Salim Elbouzidi

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 1/80

SLIDE 2

Background Elements of Investigation Numerical Simulations Results

Outline

1 Background 2 Elements of Investigation 3 Numerical Simulations 4 Results

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 2/80

SLIDE 3

Background Elements of Investigation Numerical Simulations Results

SG Mechanical Problems

SG Problems

Many failures due to corrosion FIV related failures

Fretting Wear at Supports Cracking Tube-to-Tube Impact

SG Support Functional architecture

Hydraulically invisible Ensure stability Clearance

Affects fretting wear Should be kept small

   Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 3/80

SLIDE 4

Background Elements of Investigation Numerical Simulations Results

Clearance Enlargement

Cause: Tube Degradation

Fretting wear damage Should be accounted for at the design stage

Support Degradation

Tube support plate corrosion Loss of support effectiveness May affect stability May accelerate wear at other supports

 

5 10 15 20 25 30 10 20 30 40 50 60 70 80 90 100

90% 80% 70% 60% 50% 40%

Time [y] < Percentage of wall loss [tw %] Support S2A, probability of exceeding tw%

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 4/80

SLIDE 5

Background Elements of Investigation Numerical Simulations Results

Background

Tube/support Example : Bruce Boilers 7 Tube support plates (TSPs) 3 U-bend supports. TSPs are 25.4 mm thick carbon steel plates.

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 5/80

SLIDE 6

Background Elements of Investigation Numerical Simulations Results

Bruce Unit 8 FAC damage to the tube support plate Minor to complete loss of ligaments (H07) Loss of tube support = ⇒ risk of instability Counter measures: 2 pairs of flat bars in the U-bend 1 Comb support at H07

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 6/80

SLIDE 7

Background Elements of Investigation Numerical Simulations Results

Objectives

The main objective is to independently evaluate the integrity

f steam generator tubes as plants age and degradation
proceeds. Special attention will be paid to the consequence of

support loss in the straight portion of the tube in terms of fatigue cracking rate of the tube bundle.

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 7/80

SLIDE 8

Background Elements of Investigation Numerical Simulations Results

Outline

1 Background 2 Elements of Investigation 3 Numerical Simulations 4 Results

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 8/80

SLIDE 9

Background Elements of Investigation Numerical Simulations Results

Elements of Investigation

Structural Modelling (FEA)

Tube Loose supports (impact+friction)

Fluid Excitation Modelling

Turbulence Fluidelastic

Tube Cracking and Leakage

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 9/80

SLIDE 10

Background Elements of Investigation Numerical Simulations Results

Structural Modelling (FEA)

[M] n ·· w

+ [C]

n · w

+ [K] {w} = {fT} + {fa} + {ffei} + {fc)}

{fc)} Contact Forces {fa} Add Mass Effect {fT} Turbulence Forces {ffei} Fluidelastic Forces

 

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 10/80

SLIDE 11

Background Elements of Investigation Numerical Simulations Results

Support Types

Support Types Drilled-Hole Support Scallop-Bar Support Broached-Hole Support Lattice-Bar Support

 

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 11/80

SLIDE 12

Background Elements of Investigation Numerical Simulations Results

Forces due to support contact

Tube support contact by adding massless bars attached to: Contact Stiffness Contact damper

   

δni = yni − Cri Fci = Fsi + Fdi Fsi = − (Kciδni) ˆ eni Fdi = −sign ⇣ ˙ δni ⌘ (1.5α |Fsi|) ˆ eni

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 12/80

SLIDE 13

Background Elements of Investigation Numerical Simulations Results

Fluid Excitation

Turbulence Random excitation Small amplitude response (< 2% tube diameter) Determines the long-term wear Turbulence Bounding Spectrum = ⇒ Equivalent Random Distributed force Fluidelastic Forces (FEI) FEI under the spotlight for the last 40 years. Extensive research provided a progressive understanding:

Empirical Models. Semi-Analytical.

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 13/80

SLIDE 14

Background Elements of Investigation Numerical Simulations Results

Fluidelastic Instability (FEI)

Self exciting mechanism Critical flow velocity Reduced critical velocity Ucr = Uc

fd

Mass-damping parameter MDP = mδ

ρd2

Uc = Critical flow velocity f = Tube frequency m =Tube mass per unit length δ = Logarithmic decrement ρ = Flow density Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 14/80

SLIDE 15

Background Elements of Investigation Numerical Simulations Results

Fluidelastic Instability Force Model

Based on the original model of Weaver et al. Flow-cell 1-D flow Flow perturbation A(s, t) = A0 + a(s, t) U(s, t) = U0 + u(s, t) P(s, t) = P0 + p(s, t) Time Lag FL(t) = R ss

sa [Pi1 − Pi2] cos β∂s

FD(t) = R ss

sa [Pi1 − Pi2] sin β∂s

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 15/80

SLIDE 16

Background Elements of Investigation Numerical Simulations Results

U-bend Fluid Force Model

Flow is divided into a number of layers Each layer is associated with a tube finite element. Layer = two flow channels. For layer i we have Uoi and ρoi. The flow is defined by

ˆ uLi Lift ˆ uDi Drag

                

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 16/80

SLIDE 17

Background Elements of Investigation Numerical Simulations Results

Tube Cracking and Leakage

             

   

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 17/80

SLIDE 18

Background Elements of Investigation Numerical Simulations Results

 

 





      

     

    Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 18/80

SLIDE 19

Background Elements of Investigation Numerical Simulations Results

Fatigue Crack Growth

Inconel 600 Crack Growth Model (Kozluk 1989) da dN = 2.39 E 2√ 1 − R ⇥ ∆K −

25.9 × 106E
×
e0.66R⇤2

Calculate Crack Growth Rate Determine Stress Cycles

Rainflow counting

Determine Crack Length

vs. Time

Block Method

           

 

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 19/80

SLIDE 20

Background Elements of Investigation Numerical Simulations Results

Crack Opening Displacement (COD)

GE/EPRI Method Zahoor (1989) δ = δelastic + δplastic Paris-Tada Model NUREG





40 60 80 100 120 140 160 180 200 220 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10

−3

Bending Stress [MPa] Crack Opening Displacement [m]

Paris−Tada Model Zahoor E.P. Model Zahoor E. Model Experimental Data Points

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 20/80

SLIDE 21

Background Elements of Investigation Numerical Simulations Results

Leak Rate Modelling

Leak Rate Modelling Flow through Non-Circular Ducts Single Phase Approx (Upper Bound, Friedel, 1990) Equilibrium Expansion (Lower Bound, Feburie, 1993) * ANL Model *French LB Model

                

   

  

           

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 21/80

SLIDE 22

Background Elements of Investigation Numerical Simulations Results

Outline

1 Background 2 Elements of Investigation 3 Numerical Simulations 4 Results

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 22/80

SLIDE 23

Background Elements of Investigation Numerical Simulations Results

Tube Configuration

Bundle: Parallel triangle P/D=1.6 Flow Distribution

External flow density: variable External flow velocity: variable

Support config

3 scallop bars (S1,S2,S3) 14 broached holes C01:C07 and H01-H07

Tube:

Diameter 13 mm Thickness 1.2 mm

              

     Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 23/80

SLIDE 24

Background Elements of Investigation Numerical Simulations Results

Models

Simulations were conducted using INDAP code Linear Models

Natural frequencies Mode shapes Determine the stability threshold

Nonlinear Models

Response Impact force Work rates

Three Configurations Configuration 1 (original) Configuration 2 (total loss) Configuration 3 (remedies)

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 24/80

SLIDE 25

Background Elements of Investigation Numerical Simulations Results

Outline

1 Background 2 Elements of Investigation 3 Numerical Simulations 4 Results

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 25/80

SLIDE 26

Background Elements of Investigation Numerical Simulations Results

Linear - Configuration 1

   

1st in-plan (37.3 Hz) 2nd in-plan (42.3 Hz) 1st out-of-plan (56.1 Hz) 2nd out-of-plan (81.6 Hz) Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 26/80

SLIDE 27

Background Elements of Investigation Numerical Simulations Results

Linear - Configuration 2

   

1st in-plan (28.3 Hz) 2nd in-plan (37.3 Hz) 1st out-of-plan (55.5 Hz) 2nd out-of-plan (80.3 Hz) Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 27/80

SLIDE 28

Background Elements of Investigation Numerical Simulations Results

Stability Threshold

velocity ratio = Flow Velocity Rate Velocity

0.5 1 1.5 10 20 30 40 50

Velocity ratio Lift Displacement [%d] Config 01

10

−2

10

−1

10 10

1

10

2

10

3

10

−1

10 10

1

10

2

m δ / ρ d2 Ucr / fn d simulation

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 28/80

SLIDE 29

Background Elements of Investigation Numerical Simulations Results

NL Configurations

   

       

     

Configuration 1

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 29/80

SLIDE 30

Background Elements of Investigation Numerical Simulations Results

NL Configurations cont.

      

       

    

Configuration 3

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 30/80

SLIDE 31

Background Elements of Investigation Numerical Simulations Results

Effect of Scallop bar S1

      

   

    

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 31/80

SLIDE 32

Background Elements of Investigation Numerical Simulations Results

RMS Tube Displacement

20 40 60 80 100 0.02 0.04 0.06 0.08 0.1 0.12 Node Number RMS Response y/do Config03a , Turbulence + FEI, Cr

b=0.2 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Node Number RMS Response y/do Config03a , Turbulence + FEI, Cr

b=0.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 0.02 0.04 0.06 0.08 0.1 0.12 Node Number RMS Response y/do Config03a , Turbulence + FEI, Cr

b=0.7 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Node Number RMS Response y/do Config03a , Turbulence + FEI, Cr

b=0.9 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 32/80

SLIDE 33

Background Elements of Investigation Numerical Simulations Results

RMS Bending Stresses

20 40 60 80 100 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 x 10

6

Node Number RMS stress [Pa] Config03a , Turbulence, Cr

b=0.2 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 1 1.5 2 2.5 3 3.5 4 x 10

6

Node Number RMS stress [Pa] Config03a , Turbulence, Cr

b=0.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10

6

Node Number RMS stress [Pa] Config03a , Turbulence, Cr

b=0.7 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 x 10

6

Node Number RMS stress [Pa] Config03a , Turbulence, Cr

b=0.9 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 33/80

SLIDE 34

Background Elements of Investigation Numerical Simulations Results

SCC Crack Configuration

Crack ratio Crack size Aspect ratio Crack (a/t) (a) [mm] (2L/a) angle [deg] 45% 0.54 5.76 30 50% 0.60 5.18 30 55% 0.66 4.71 30 60% 0.72 4.32 30 65% 0.78 3.99 30 70% 0.84 3.70 30 75% 0.90 3.46 30

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 34/80

SLIDE 35

Background Elements of Investigation Numerical Simulations Results

SCC Crack Growth Predictions

Configuration 03a, a/tw = 45%, θ = 30

2 4 6 8 10 12 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03a, FEI+Turb, Loc 03, SSC, C

rb=0.2 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03a, FEI+Turb, Loc 03, SSC, C

rb=0.5 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.5 1 1.5 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03a, FEI+Turb, Loc 03, SSC, C

rb=1 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.05 0.1 0.15 0.2 0.25 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03a, FEI+Turb, Loc 03, SSC, C

rb=1.5 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 35/80

SLIDE 36

Background Elements of Investigation Numerical Simulations Results

TWC Crack Growth Predictions

Configuration 03a, a0 = 1.5 mm

2 4 6 8 10 12 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03a, FEI+Turb, Loc 03, TWC, C

rb=0.2 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.5 1 1.5 2 2.5 3 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03a, FEI+Turb, Loc 03, TWC, C

rb=0.5 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.05 0.1 0.15 0.2 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03a, FEI+Turb, Loc 03, TWC, C

rb=1 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.01 0.02 0.03 0.04 0.05 0.06 0.07 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03a, FEI+Turb, Loc 03, TWC, C

rb=1.3 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 36/80

SLIDE 37

Background Elements of Investigation Numerical Simulations Results

TWC Leakage Conditions

Internal pressure Pi = 9.31 MPa. External pressure Po = 4.43 MPa. Internal temperature Ti = 303.2C. External temperature To = 243.0C. Two-phase mixture model.

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 37/80

SLIDE 38

Background Elements of Investigation Numerical Simulations Results

TWC Leakage Rate Predictions

Configuration 03a

2 4 6 8 10 12 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time [years] Leakage Rate [kg/s] Config03aFEI+Turb, Location 03, Leakage rate, C

rb=0.2 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.5 1 1.5 2 2.5 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time [years] Leakage Rate [kg/s] Config03aFEI+Turb, Location 03, Leakage rate, C

rb=0.5 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.05 0.1 0.15 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time [years] Leakage Rate [kg/s] Config03aFEI+Turb, Location 03, Leakage rate, C

rb=1 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 0.01 0.02 0.03 0.04 0.05 0.06 0.07 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03a, FEI+Turb, Loc 03, TWC, C

rb=1.3 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 38/80

SLIDE 39

Background Elements of Investigation Numerical Simulations Results

Effect of Scallop bar S2

      

   

    

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 39/80

SLIDE 40

Background Elements of Investigation Numerical Simulations Results

RMS Tube Displacement

20 40 60 80 100 0.02 0.04 0.06 0.08 0.1 0.12 Node Number RMS Response y/do Config03b , Turbulence + FEI, Cr

b=0.2 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 0.02 0.04 0.06 0.08 0.1 0.12 Node Number RMS Response y/do Config03b , Turbulence + FEI, Cr

b=0.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Node Number RMS Response y/do Config03b , Turbulence + FEI, Cr

b=0.7 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 0.02 0.04 0.06 0.08 0.1 0.12 Node Number RMS Response y/do Config03b , Turbulence + FEI, Cr

b=0.9 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 40/80

SLIDE 41

Background Elements of Investigation Numerical Simulations Results

RMS Bending Stresses

20 40 60 80 100 1 2 3 4 5 6 7 8 x 10

6

Node Number RMS stress [Pa] Config03b , Turbulence, Cr

b=0.2 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 1 2 3 4 5 6 7 8 9 x 10

6

Node Number RMS stress [Pa] Config03b , Turbulence, Cr

b=0.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 1 2 3 4 5 6 7 8 x 10

6

Node Number RMS stress [Pa] Config03b , Turbulence, Cr

b=0.7 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 20 40 60 80 100 1 2 3 4 5 6 7 8 x 10

6

Node Number RMS stress [Pa] Config03b , Turbulence, Cr

b=0.9 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 41/80

SLIDE 42

Background Elements of Investigation Numerical Simulations Results

SCC Crack Growth Predictions

Configuration 03b, a/tw = 45%, θ = 30

2 4 6 8 10 12 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03b, FEI+Turb, Loc 03, SSC, C

rb=0.2 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03b, FEI+Turb, Loc 03, SSC, C

rb=0.5 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03b, FEI+Turb, Loc 03, SSC, C

rb=1 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [years] a/tw Config03b, FEI+Turb, Loc 03, SSC, C

rb=1.5 mm, ao/tw %= 45

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 42/80

SLIDE 43

Background Elements of Investigation Numerical Simulations Results

TWC Crack Growth Predictions

Configuration 03b, a0 = 1.5 mm

2 4 6 8 10 12 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03b, FEI+Turb, Loc 03, TWC, C

rb=0.2 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03b, FEI+Turb, Loc 03, TWC, C

rb=0.5 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03b, FEI+Turb, Loc 03, TWC, C

rb=1 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [years] Half Crack Length [mm] Config03b, FEI+Turb, Loc 03, TWC, C

rb=1.3 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 43/80

SLIDE 44

Background Elements of Investigation Numerical Simulations Results

TWC Leakage Rate Predictions

Configuration 03b

2 4 6 8 10 12 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time [years] Leakage Rate [kg/s] Config03bFEI+Turb, Location 03, Leakage rate, C

rb=0.2 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time [years] Leakage Rate [kg/s] Config03bFEI+Turb, Location 03, Leakage rate, C

rb=0.5 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 10 12 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time [years] Leakage Rate [kg/s] Config03bFEI+Turb, Location 03, Leakage rate, C

rb=1 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm 2 4 6 8 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time [years] Leakage Rate [kg/s] Config03bFEI+Turb, Location 03, Leakage rate, C

rb=1.3 mm, ao= 1.5 mm

0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.5 mm 0.6 mm 0.7 mm 0.8 mm 0.9 mm 1.0 mm 1.1 mm 1.2 mm 1.3 mm 1.4 mm 1.5 mm

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 44/80

SLIDE 45

Background Elements of Investigation Numerical Simulations Results

Probabilistic Evaluation

The deterministic simulation is useful in providing a basic understanding of the effect of the clearance Controlling clearance value is difficult Almost impossible to keep tubes centred There is very complex interaction of supports Investigate all possible combinations a very large number

f simulations is required

The solution is to employ a probabilistic techniques

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 45/80

SLIDE 46

Background Elements of Investigation Numerical Simulations Results

Probabilistic Evaluation



  



         



 

               

 

   

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 46/80

SLIDE 47

Background Elements of Investigation Numerical Simulations Results

Input Distributions

Variable Distribution µ Range SCC, a0/tw Uniform 0.60 0.45 − 0.75 SCC, 2L/a Uniform 7.5 3 − 12 TWC, a0 Uniform 2.5 mm 1.5 − 3.5 mm

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 50 100 150 200 250 300 350

Crack depth ratio (a/t) Number of occurences

Distribution of SCC crack depth ratios

1 1.5 2 2.5 3 3.5 4 50 100 150 200 250 300 350

Initial crack length a0 [mm] Number of occurences

Distribution of TWC initial crack lengths

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 47/80

SLIDE 48

Background Elements of Investigation Numerical Simulations Results

Support Clearance Distribution

Support Distribution µ σ H01 - H06 Gaussian 0.25 − 4.15 mm⇤ 0.1 mm C01 - C07 Gaussian 0.25 − 0.55 mm⇤ 0.1 mm Flat bars Gaussian 0.21 mm 0.02 mm S1-S3 Gaussian 0.3 mm 0.1 mm

∗ Clearance linearly varied along leg

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 50 100 150 200 250 300

Support Clearance [mm] Number of occurences

Broached Hole H07 Support Clearance Distribution

−0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 50 100 150 200 250 300

Support Clearance [mm] Number of occurences

Scallop Bar Support Clearance Distribution

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 48/80

SLIDE 49

Background Elements of Investigation Numerical Simulations Results

SCC Results

Location 3.

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Final crack growth. 1000 cases. SCC, Location 3

Initial Crack Ratio a/t Final Crack Ratio a/t

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 49/80

SLIDE 50

Background Elements of Investigation Numerical Simulations Results

TWC - Final Crack Length

1.5 2 2.5 3 3.5 1 2 3 4 5 6 7

Final crack growth. 1000 cases. TWC, Location 1

Initial Crack Length [mm] Final Crack Length [mm]

1.5 2 2.5 3 3.5 1 2 3 4 5 6 7 8 9

Final crack growth. 1000 cases. TWC, Location 2

Initial Crack Length [mm] Final Crack Length [mm]

1.5 2 2.5 3 3.5 1 2 3 4 5 6 7 8 9 10

Final crack growth. 1000 cases. TWC, Location 3

Initial Crack Length [mm] Final Crack Length [mm]

1.5 2 2.5 3 3.5 2 4 6 8 10 12

Final crack growth. 1000 cases. TWC, Location 4

Initial Crack Length [mm] Final Crack Length [mm]

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 50/80

SLIDE 51

Background Elements of Investigation Numerical Simulations Results

TWC - Crack Growth vs. Initial Crack

1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 3 3.5 4

a0 [mm] ∆ a [mm]

∆ a vs. a01000 cases. TWC, location 1

1.5 2 2.5 3 3.5 1 2 3 4 5 6

a0 [mm] ∆ a [mm]

∆ a vs. a01000 cases. TWC, location 2

1.5 2 2.5 3 3.5 1 2 3 4 5 6 7

a0 [mm] ∆ a [mm]

∆ a vs. a01000 cases. TWC, location 3

1.5 2 2.5 3 3.5 1 2 3 4 5 6 7 8 9

a0 [mm] ∆ a [mm]

∆ a vs. a01000 cases. TWC, location 4

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 51/80

SLIDE 52

Background Elements of Investigation Numerical Simulations Results

TWC - Tube Crack Life

1.5 2 2.5 3 3.5 2 4 6 8 10 12 14

Initial Crack Length [mm] Life [years]

Crack life. 1000 cases. TWC, Location 1

1.5 2 2.5 3 3.5 2 4 6 8 10 12 14

Initial Crack Length [mm] Life [years]

Crack life. 1000 cases. TWC, Location 2

1.5 2 2.5 3 3.5 2 4 6 8 10 12 14

Initial Crack Length [mm] Life [years]

Crack life. 1000 cases. TWC, Location 3

1.5 2 2.5 3 3.5 2 4 6 8 10 12 14

Initial Crack Length [mm] Life [years]

Crack life. 1000 cases. TWC, Location 4

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 52/80

SLIDE 53

Background Elements of Investigation Numerical Simulations Results

TWC - Tube Crack Life Probabilities

1.5 2 2.5 3 3.5 0.2 0.4 0.6 0.8 1

Initial Crack Length a0 [mm] Probability

Probability of tube life exceeding thresholds. TWC, Location 1

Life exceeds 3 years Life exceeds 5 years Life exceeds 8 years Life exceeds 12 years           

     

        

                1.5 2 2.5 3 3.5 0.2 0.4 0.6 0.8 1

Initial Crack Length a0 [mm] Probability

Probability of tube life exceeding thresholds. TWC, Location 3

Life exceeds 3 years Life exceeds 5 years Life exceeds 8 years Life exceeds 12 years 1.5 2 2.5 3 3.5 0.2 0.4 0.6 0.8 1

Initial Crack Length a0 [mm] Probability

Probability of tube life exceeding thresholds. TWC, Location 4

Life exceeds 3 years Life exceeds 5 years Life exceeds 8 years Life exceeds 12 years

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 53/80

SLIDE 54

Background Elements of Investigation Numerical Simulations Results

TWC - Leakage Rate vs. Initial Crack

1.5 2 2.5 3 3.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10

−6

Leakage. 2000 cases. TWC, Location 1

Initial Crack Length [mm] Leakage Rate [kg/sec]

1.5 2 2.5 3 3.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10

−6

Leakage. 2000 cases. TWC, Location 2

Initial Crack Length [mm] Leakage Rate [kg/sec]

1.5 2 2.5 3 3.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10

−6

Leakage. 2000 cases. TWC, Location 3

Initial Crack Length [mm] Leakage Rate [kg/sec]

1.5 2 2.5 3 3.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10

−6

Leakage. 2000 cases. TWC, Location 4

Initial Crack Length [mm] Leakage Rate [kg/sec]

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 54/80

SLIDE 55

Background Elements of Investigation Numerical Simulations Results

TWC - Tube Leakage Rate Probabilities

1.5 2 2.5 3 3.5 0.2 0.4 0.6 0.8 1

Initial Crack Length a0 [mm] Probability

Probability of leakage rate exceeding thresholds. TWC, Location 1

Leakage Rate exceeds 0.1 mg/sec Leakage Rate exceeds 0.3 mg/sec Leakage Rate exceeds 0.5 mg/sec Leakage Rate exceeds 0.8 mg/sec 1.5 2 2.5 3 3.5 0.2 0.4 0.6 0.8 1

Initial Crack Length a0 [mm] Probability

Probability of leakage rate exceeding thresholds. TWC, Location 2

Leakage Rate exceeds 0.1 mg/sec Leakage Rate exceeds 0.3 mg/sec Leakage Rate exceeds 0.5 mg/sec Leakage Rate exceeds 0.8 mg/sec 1.5 2 2.5 3 3.5 0.2 0.4 0.6 0.8 1

Initial Crack Length a0 [mm] Probability

Probability of leakage rate exceeding thresholds. TWC, Location 3

Leakage Rate exceeds 0.1 mg/sec Leakage Rate exceeds 0.3 mg/sec Leakage Rate exceeds 0.5 mg/sec Leakage Rate exceeds 0.8 mg/sec 1.5 2 2.5 3 3.5 0.2 0.4 0.6 0.8 1

Initial Crack Length a0 [mm] Probability

Probability of leakage rate exceeding thresholds. TWC, Location 4

Leakage Rate exceeds 0.1 mg/sec Leakage Rate exceeds 0.3 mg/sec Leakage Rate exceeds 0.5 mg/sec Leakage Rate exceeds 0.8 mg/sec

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 55/80

SLIDE 56

Background Elements of Investigation Numerical Simulations Results

Summary

Both deterministic and probabilistic evaluation were conducted Clearance is an important factor that affects life. SCC - no risk TWC - no risk if If the support clearance in the U-Bend region ≤ 0.2 mm Degradation of Scallop Bars 1 or 3 did not result in a dramatic effect. Degradation of the scallop bars at the apex of the U-Bend proves to be critical for the system. The variability of combination of the clearances is very important - Probabilistic evaluation would be more realistic

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 56/80

SLIDE 57

Background Elements of Investigation Numerical Simulations Results

Questions and Comments

Marwan Hassan, Jovica Riznic and Salim Elbouzidi — Investigation of the Fatigue Cracking and Leakage Rate potential of U-Bend T 57/80