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Experimental and analytical study of thermal mixing at reactor conditions
KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.ORCID iD: 0000-0001-8743-7157
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

High-cycle thermal fatigue due to turbulent mixing of streams at distinct temperatures is an interdisciplinary issue affecting safety and life extension of existing reactors together with the design of new reactors. It is challenging to model damage and thermal loads arising from the above mixing.

In order to collect vast data sets for the validation of codes modeling turbulent thermal mixing under reactor conditions, temperatures were sampled at the inner surface of the vertical annular volume between two concentric 316LN stainless steel tubes. This annulus simplifies that between control-rod guide tube and stem in Swedish boiling water reactors (BWRs) Oskarshamn 3 and Forsmark 3. In 2008, several stems there were reported as broken or cracked from thermal fatigue. Cold water entered the annulus at 333 K, at axial level z = 0.15 m. It moved upward and mixed with hot water, which entered the annulus at 549 K, at z = 0.80 m. Pressure read 7.2 MPa. Hot and cold inlet temperatures and pressure match BWR conditions. The thermocouples attached to the inner tube could only acquire inner-surface temperatures at six locations, so the inner tube was translated and rotated about the z-axis to expand the measurement zone.

Mixing inhomogeneity was estimated from such measurements. In the cases examined, the inner-surface temperatures from areas with the highest mixing inhomogeneity show dominant frequencies lower than ten times the inverse of the experiment time.

The uncertainty of this temperature measurement appears to be equal to 1.58 K.

A large eddy simulation (LES) of mixing in the above annulus was conducted. Experimental boundary conditions were applied. The conjugate heat transfer between water and tubes was modeled. The wall-adapting local eddy viscosity (WALE) subgrid model was adopted. A finite element analysis (FEA) of the inner tube was performed using LES pressure and temperature as loads. Cumulative fatigue usage factors (CUFs) were estimated from FEA stress histories. To this end, the rainflow cycle-counting technique was applied. CUFs are highest between z = 0.65 m and z = 0.67 m. Cracking is predicted to initiate after 97 h. LES and experimental inner-surface temperatures agree reasonably well in relation to mean values, ranges, mixing inhomogeneity, and critical oscillation modes in areas sensitive to fatigue. LES inner-surface temperatures from areas with the highest CUFs show dominant frequencies lower than ten times the inverse of the simulation time.

A robust, effective iterative algorithm for reconstructing the transient temperature field in the inner tube from redundant boundary data was implemented and verified. Temperature-dependent properties were included. Initial conditions and over-specified boundary data in the inverse problem were perturbed with Gaussian noise to check the robustness of the solving method to noise.

Abstract [sv]

Termisk högcykelutmattning på grund av turbulent blandning av flöden av olika temperaturer är en tvärvetenskaplig fråga som har bäring på säkerhet, underhåll och livstidsförlängning av kärnkraftverk i drift tillsammans med utvecklingen av nya reaktorer. Det är utmanande att modellera delskador och termiska belastningar som härrör från denna blandning.

För att samla stora datamängder för validering av koder modellerande turbulent termisk blandning vid reaktordriftförhållanden, mättes temperaturer vid den inre ytan av den vertikala annulära (ringformade) kanalen mellan två koncentriska rör i 316LN rostfritt stål. Denna annulära kanal representerar den verkliga geometrin mellan styrstavsledrör och styrstavsförlängare i svenska kokvattenreaktorer (BWR) Oskarshamn 3 och Forsmark 3. Vid dessa reaktorer uppvisade ett antal styrstavsförlängare sprickbildning till följd av termisk utmattning under år 2008. I den annulära kanalen strömmade kallare vattenflöden vid 333 K, vid axiell nivå z = 0.15 m. Flödena rörde sig uppåt och blandades med varmare vattenflöden, vilka strömmade i den annulära kanalen vid 549 K, vid z = 0.80 m. Trycket sattes till 7.2 MPa. 333 K, 549 K och 7.2 MPa överensstämmer med BWR-förhållanden. Termoelement fastlödda vid det inre röret kunde endast mäta innerytans temperatur på sex platser. För att kunna mäta temperaturen i hela blandningsområdet kunde röret roteras från 0° till 360° och förflyttas vertikalt över en sträcka av 387 mm.

Blandningsinhomogenitet uppskattades från sådana mätningar. I de undersökta fallen visar innerytans temperatur från områden där blandningen är som minst homogen dominerande frekvenser som är lägre än tio gånger inversen till experimenttiden.

Osäkerheten i dessa temperaturmätningar visar sig vara 1.58 K.

En storvirvelsimulering (LES) av blandning i den annulära kanalen utfördes. Experimentella randvillkor applicerades. Den konjugerade värmeöverföringen mellan vatten och rör modellerades. De små virvlarna (oupplösta skalor) approximerades med hjälp av en turbulensmodell kallad WALE, som ger rätt asymptotiskt beteende för turbulent viskositet nära väggen. En finitelementanalys (FEA) av det inre röret utfördes med LES-tryck och temperatur som belastningar. Totala delskador uppskattades från FEA-spänning/tid kurvor. För detta ändamål applicerades regndroppsmetoden. De totala delskadorna når sina högsta värden mellan z = 0.65 m och z = 0.67 m. Sprickinitiering förväntas inträffa efter 97 timmar. Innerytans CFD-temperatur är i en rimlig överensstämmelse med experimentella data med avseende på medelvärde, omfång, blandningsinhomogenitet och kritiska svängande modalfunktioner som utgör temperaturtidsserier i områden som är utsatta för utmattning. Innerytans CFD-temperatur från områden med högsta totala delskador visar dominerande frekvenser som är lägre än tio gånger inversen till simuleringstiden.

En robust, effektiv, iterativ algoritm för att beräkna det transienta temperaturfältet i det inre röret utifrån överflödiga randdata implementerades och verifierades. Temperaturberoende egenskaper inkluderades. Initiala förhållanden och överflödiga randdata i det inversa problemet stördes av gaussiskt brus för att undersöka lösningsmetodens robusthet mot brus.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2018. , p. 113
Series
TRITA-SCI-FOU ; 2018:45
Keywords [en]
High-cycle thermal fatigue, Hilbert-Huang transform, large eddy, WALE, rainflow, inverse heat conduction, adjoint conjugate gradient
National Category
Energy Engineering
Research subject
Energy Technology; Physics
Identifiers
URN: urn:nbn:se:kth:diva-236530ISBN: 978-91-7873-001-8 (print)OAI: oai:DiVA.org:kth-236530DiVA, id: diva2:1257426
Public defence
2018-12-06, FB53, AlbaNova University Center, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Funder
Swedish Radiation Safety Authority, 47385
Note

QC 20181022

Available from: 2018-10-22 Created: 2018-10-20 Last updated: 2018-11-13Bibliographically approved
List of papers
1. Experimental investigation of mixing of non-isothermal water streams at BWR operating conditions
Open this publication in new window or tab >>Experimental investigation of mixing of non-isothermal water streams at BWR operating conditions
2017 (English)In: Nuclear Engineering and Design, ISSN 0029-5493, E-ISSN 1872-759X, Vol. 317, p. 158-176Article in journal (Refereed) Published
Abstract [en]

In this experimental investigation, wall surface temperatures have been measured during mixing of three water streams in the annular gap between two coaxial stainless-steel tubes. The inner tube, with an outer diameter of 35 mm and a thickness of 5 mm, holds six K-type, ungrounded thermocouples with a diameter of 0.5 mm, which measured surface temperatures with a sampling rate of either 100 Hz or 1000 Hz. The tube was rotated from 0 to 360° and moved in a range of 387 mm in the axial direction to allow measurements of surface temperatures in the whole mixing region. The outer tube has an inner diameter of 80 mm and a thickness of 10 mm to withstand a water pressure of 9 MPa. A water stream at a temperature of either 333 K or 423 K and a Reynolds number between 1657 and 8410 rose vertically in the annular gap and mixed with two water streams at a temperature of 549 K and a Reynolds number between 3.56E5 and 7.11E5. These two water streams entered the annulus radially on the same axial level, 180° apart. Water pressure was kept at 7.2 MPa. Temperature recordings were performed at five axial and eight azimuthal locations, for each set of boundary conditions. Each recording lasted 120 s to provide reliable data on the variance, intermittency and frequency of the surface temperature time series at hand. Thorough calculations indicate that the uncertainty in the measured temperature is of 1.58 K. The mixing region extends up to 0.2 m downward of the hot inlets. In most cases, measurements indicate non-uniform mixing in the azimuthal direction, because of asymmetries in either geometry or mass flow rates at the hot inlets. Due to the measurement accuracy and a relatively simple geometry, an experimental database has been obtained for validation of computational methods to predict thermal mixing and fatigue. Furthermore, these data can provide new insight into turbulent mixing at BWR operating conditions and, more generally, into mixing coupled to the dynamics, also termed level-2 mixing.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
Wall surface temperature, Temperature measurement, Mixing, Uncertainty analysis, BWR control rods
National Category
Energy Engineering
Identifiers
urn:nbn:se:kth:diva-205197 (URN)10.1016/j.nucengdes.2017.03.034 (DOI)000401117400015 ()2-s2.0-85017113636 (Scopus ID)
Projects
THEMFE
Funder
Swedish Radiation Safety Authority, 47385
Note

QC 20170419

Available from: 2017-04-08 Created: 2017-04-08 Last updated: 2018-10-20Bibliographically approved
2. Analysis of temperature fluctuations caused by mixing of non-isothermal water streams at elevated pressure
Open this publication in new window or tab >>Analysis of temperature fluctuations caused by mixing of non-isothermal water streams at elevated pressure
2017 (English)In: International Journal of Heat and Mass Transfer, ISSN 0017-9310, E-ISSN 1879-2189, Vol. 104, p. 979-992Article in journal (Refereed) Published
Abstract [en]

Temperatures were measured at the inner surface of an annulus between two coaxial tubes, where three water streams mixed. These temperatures were sampled at either 100 Hz or 1000 Hz. The acquisition time was set to 120 s. Two water streams at 549 K, with a Reynolds number between 3.56 × 105 and 7.11 × 105, descended in the annular gap and mixed with a water stream at 333 K or 423 K, with a Reynolds number ranging from 1.27 × 104 to 3.23 × 104. Water pressure was kept at 7.2 MPa. Inner-surface temperatures were collected at eight azimuthal and five axial positions, for each combination of boundary conditions. To better analyze these temperatures and mixing in the vicinity of the wall, scalars estimating the mixing intensity at each measurement position were computed from detrended temperature time series. Fourier and Hilbert–Huang marginal spectra were calculated for the time series giving rise to the highest values of a mixing estimator of choice. The relationship between temperature and velocity was explored by examining the results of an LES simulation using the same boundary conditions as in one of the experimental cases.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
Mixing intensity, Spectral analysis, Thermal mixing
National Category
Energy Engineering
Identifiers
urn:nbn:se:kth:diva-192558 (URN)10.1016/j.ijheatmasstransfer.2016.08.082 (DOI)000387627400087 ()2-s2.0-84990036834 (Scopus ID)
Projects
THEMFE
Funder
Swedish Radiation Safety Authority, 47385
Note

QC 20160927

Available from: 2016-09-14 Created: 2016-09-14 Last updated: 2018-10-20Bibliographically approved
3. An iterative finite-element algorithm for solving two-dimensional nonlinear inverse heat conduction problems
Open this publication in new window or tab >>An iterative finite-element algorithm for solving two-dimensional nonlinear inverse heat conduction problems
2018 (English)In: International Journal of Heat and Mass Transfer, ISSN 0017-9310, E-ISSN 1879-2189, Vol. 126, p. 281-292Article in journal (Refereed) Published
Abstract [en]

It is often useful to determine temperature and heat flux in multidimensional solid domains of arbitrary shape with inaccessible boundaries. In this study, an effective algorithm for solving boundary inverse heat conduction problems (IHCPs) is implemented: transient temperatures on inaccessible boundaries are estimated from redundant simulated measurements on accessible boundaries. A nonlinear heat equation is considered, where some of the material properties are dependent on temperature. The IHCP is reformulated as an optimization problem. The resulting functional is iteratively minimized using a conjugate gradient method together with an adjoint (dual) problem approach. The associated partial differential equations are solved using the finite-element package FEniCS. Tikhonov regularization is introduced to mitigate the ill-posedness of the IHCP. The accuracy of the implemented algorithm is assessed by comparing the solutions to the IHCP with the correct temperature values, on the inaccessible boundaries. The robustness of our method is tested by adding Gaussian noise to the initial conditions and redundant boundary data in the inverse problem formulation. A mesh independence study is performed.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
nonlinear inverse problem, Tikhonov regularization, finite element, FEniCS, adjoint
National Category
Energy Engineering
Identifiers
urn:nbn:se:kth:diva-227719 (URN)10.1016/j.ijheatmasstransfer.2018.04.104 (DOI)000442979300022 ()2-s2.0-85047095749 (Scopus ID)
Funder
Swedish Radiation Safety Authority, 47385
Note

QC 20180530

Available from: 2018-05-12 Created: 2018-05-12 Last updated: 2018-10-20Bibliographically approved
4. Large eddy simulation of thermal mixing with conjugate heat transfer at BWR operating conditions
Open this publication in new window or tab >>Large eddy simulation of thermal mixing with conjugate heat transfer at BWR operating conditions
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Thermal fatigue occurs in most metals under cyclic heat loads and can threaten the structural integrity of metal parts. Detailed knowledge of these loads is of utter importance to prevent such issues. In this study, a large eddy simulation (LES) with wall-adapting local eddy viscosity (WALE) subgrid model is performed to better understand turbulent thermal mixing in an annulus with a pair of opposing cold inlets at a low axial level (z = 0.15 m) and with a pair of opposing hot inlets at a higher axial level (z = 0.80 m). Each inlet pair is 90° from each other in the azimuthal direction. Conjugate heat transfer between fluid and structure is accounted for. The geometry simplifies a control-rod guide tube (CRGT) in a boiling water reactor (BWR). LES results are compared with measurement data. This is one of the first times BWR conditions are met in both experiments and LES: pressure equals 7.2 MPa, while the temperature difference between hot and cold inlets reaches 216 K. LES temperatures at the fluid-structure interface are fairly correlated with their experimental equivalents, with regard to mean values, local variances, and dangerous oscillation modes in fatigue-prone areas (z = 0.65-0.67 m). An elastic analysis of the structure is performed to evaluate stress intensities there. From them, cumulative fatigue usage factors are estimated and used as screening criteria in the subsequent frequency analysis of temperature time series at the fluid-structure interface. Cracks are likely to initiate after 97 h.

National Category
Energy Engineering
Identifiers
urn:nbn:se:kth:diva-236767 (URN)
Funder
Swedish Radiation Safety Authority, 47385
Note

QC 20181022

Available from: 2018-10-22 Created: 2018-10-22 Last updated: 2018-10-22Bibliographically approved

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