Arbeiter, F.

Ruck, S.

KITopen

KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz AssociationINSTITUTE OF NEUTRON PHYSICS AND REACTOR TECHNOLOGYwww.kit.eduDES AND URANS DOWNSTREAM OF A HEATEDBACKWARD-FACING STEPS. Ruck, F. Arbeiter First Thermal and Fluids Engineering Summer Conference, August 2015, New YorkInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)2 12th August 2015 Dr. Sebastian RuckIntroductionValidated “tool” for an accurate thermohydraulic prediction of heated, turbulent flow to develop new designs of thermally high loaded cooling channels with structured or rib-roughened walls.Cooling the plasma-faced 1st wall of fusion reactor( ~700-1000°C, ~0.75 MW/m2) MotivationComputational Fluid Dynamics Not limited to global performance estimations  Capturing transient 3d-effects Thermal and fluid fields are resolved simultaneouslyCFD is very sensitive to the numerical method and turbulence treatmentExperimental Methods PIV, LDA measurements, Infrared Camera Thermocouple and pressure tabsInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)3 12th August 2015 Dr. Sebastian RuckMethodsReynolds-Averaged-Navier-Stokes (RANS) + isotropic EVMInaccurate flow and heat transfer prediction [Acharya 1993, Ooi 2002]Large Eddy Simulations (LES) Accurate flow and heat transfer prediction [Labbé 2013,Tafti 2005]Limited for engineering applications by its demanding grid requirementsHybrid RANS/LESDetached Eddy Simulations (DES) for high-Reynolds number, massively separated flows [Spalart, 1997]Only a few studies of internal turbulent flows with heat transfer Accurate thermohydraulic predictions for heated, rib-roughened channel flow [Viswanathan 2005; 2006]) at moderate Re=2E4.Numerical MethodsValidation of DES for boundary conditions of plasma-faced 1st wall of fusion reactorsInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)4 12th August 2015 Dr. Sebastian RuckBoundary ConditionsPlasma-Faced 1st Wall  10E3<ReDh<150E3; ReDh,Operating=1,05E5Asymmetrically heated cooling channels15 x 15 mm with 2 mm round edges, rib-pitch-to-rib-height-ratio of p/e=10, rib-height-to-hyd.-diameter-ratio of e/Dh=0.0638High pressure 8-MPa-helium gas1st Step - Validation with Heated Backward Facing Step FlowNumerous experimental [Vogel 1984; Adams 1984] and numerical [Keating 2001] benchmark data for Reh=2.8E4 are presentScaling flow conditions from benchmark to a 4h x 4h channel, step height h = 3.8 mm, 8-MPa-helium gas, Reh=2.8E4  ReDh=1.12E5No experimental data at the operating conditionsExperiments were designed, installed and will be carried out soonInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)5 12th August 2015 Dr. Sebastian RuckMethodsSimulation OverviewComputational Domain27 h x 4 h x 4 h: 181 x 78 x 108, expansion ratio of 1.25Local grid refinement behind the step to generate a focus region 2.8 Mio CellsBoundary ConditionsConstant heat flux density at the lower bottom wallFluid with ideal gas conditionsInflow ConditionsPeriodic flow simulationsReh=2.8E4  ReDh=1.12E5Institute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)6 12th August 2015 Dr. Sebastian RuckMethodsNumerical approachDelayed DES and URANSk-ε-realizable-model and k-ω-SST-modelSegregated Solver / Fluent V.15Convective terms: QUICK & UW SchemeMomentum Equation: DES BCD; URANS: QUICKDiffusion terms: 2nd CD SchemePressure: 2nd SchemeTemporal: Bounded 2nd Imp. SchemeSimulation timeAfter received a fully developed flow field, the simulation were run 10 flow-throughs for DES and 3 flow-throughs for URANS ResultsSpatial average: 10 spanwise positionsTemporal average: 10 flow-throughs for DES, 3 flow-throughs for URANS Simulation OverviewInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)7 12th August 2015 Dr. Sebastian RuckFlow FieldFree shear layer are formed by flow separation at the edge of the step Reattachment XR≈6hSpanwise limitation of computational domainRecirculation and redeveloping regionsFlow structures caused by the flow separation either impact on the bottom wall or flow further downstreamImpingement ones move upstream or downstreamCooling EffectTransporting colder fluid from the core flow toward the heated wallReducing the viscous sublayer and heat transfer is enhancedMaximum occur in the vicinity of reattachmentDESInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)8 12th August 2015 Dr. Sebastian RuckFlow FieldDESFree shear layer are formed by flow separation at the edge of the step Reattachment XR≈6hSpanwise limitation of computational domainRecirculation and redeveloping regionsFlow structures caused by the flow separation either impact on the bottom wall or flow further downstreamImpingement ones move upstream or downstreamCooling EffectTransporting colder fluid from the core flow toward the heated wallReducing the viscous sublayer and heat transfer is enhancedMaximum occurs in the vicinity of reattachmentInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)9 12th August 2015 Dr. Sebastian RuckFlow FieldDESFree shear layer are formed by flow separation at the edge of the step Reattachment XR≈6hSpanwise limitation of computational domainRecirculation and redeveloping regionsFlow structures caused by the flow separation either impact on the bottom wall or flow further downstreamImpingement ones move upstream or downstreamCooling EffectTransporting colder fluid from the core flow toward the heated wallReducing the viscous sublayer and heat transfer is enhancedMaximum occurs in the vicinity of reattachmentInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)10 12th August 2015 Dr. Sebastian RuckLocal Heat TransferAcceptable agreement with experimentsDifference upstream of reattachmentInsufficient spatial averageDrifting downstream of reattachmentCorrelates with the end of the focus regionDESClose to the step, URANS results differ from experiments Except the minimum and maximum values, k-ω-SST agrees wellk-ε-reali. differs enormously60% for peaksURANSInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)11 12th August 2015 Dr. Sebastian RuckTemperature DistributionsTemperature gradients at the near wall region are similar for DES and URANS and start to differ with increasing wall distanceInfluence of turbulence heat transfer increaseExcept very close to the step, DES results are in good agreement with experiments and URANS results differDES & URANSHigh gradients across the free shear layer for URANS Underprediction of turbulent mixing Correlates with an underprediction of turbulent flux Yield higher surface temperaturesInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)12 12th August 2015 Dr. Sebastian RuckTurbulent Heat FluxDES show similar trends to LES resultsPeaks in the free shear layer and wall boundary layerHigh turbulent mixingDESAssociated with turbulent large-scale eddies Gradients decrease further downstream and vanish with flow reattachmentDownstream of reattachment heat transfer occurs mostly at the bottom wallInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)13 12th August 2015 Dr. Sebastian RuckTurbulent FluctuationsDES results show good agree with experimentsDistribution are well predicted (by the DES(k-ω-SST))Peak values are overpredicted (by the DES(k-ε-reali.))Maximum is reached upstream of reattachmentURMS>WRMS,VRMSuRMS , vRMS and wRMSInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)14 12th August 2015 Dr. Sebastian RuckSummaryTransient flow field was well reproduced by DESTemperature levels and heat transfer at the bottom wall were accurately determined by DESSignificant turbulent heat transfer occurs across the shear layer and is triggered by turbulent large-scale flow structures. It is well resolved by DES.OverviewResults of the 1st Step - Validation with Heated Backward Facing Step Flow: DES is promising approach for thermohydraulic prediction of turbulent flows. Ongoing research focus on an extended validation for high Reynolds number flow in heated, rib-roughened channels at boundary conditions of plasma-faced 1st wall of fusion reactorsKIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz AssociationINSTITUTE OF NEUTRON PHYSICS AND REACTOR TECHNOLOGYwww.kit.eduDES AND URANS DOWNSTREAM OF A HEATEDBACKWARD-FACING STEPS. Ruck, F. Arbeiter First Thermal and Fluids Engineering Summer Conference, August 2015, New YorkInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)16 12th August 2015 Dr. Sebastian RuckAppendixIt is a non-zonal approach providing a single smooth velocity field. Uniform turbulence model taking the (integral) turbulence length scale and the spatial grid density into accountDetached Eddy Simulationregions where the maximum spatial grid density is much smaller than the flow turbulence length scale: LES moderegions where the maximum spatial grid density is greater than the flow turbulence length scale: RANS mode Subdivision of the computational domain into regions of LES (separated flow regions) and RANS (boundary layers, near wall region) quality. Institute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)17 12th August 2015 Dr. Sebastian RuckMethodsUniform turbulence model concept taking the (integral) turbulence length scale and the spatial grid density into account regions where ∆max൏ ܥ ∙ ݈௧: DES functions in LES moderegions where ∆max൐ ܥ ∙ ݈௧: DES functions in RANS modeIntroducing a gird dependent length-scale into the destruction term2E-EVM: Destruction term of the k-equation [Strelets, 2001]k-ε-realizable-model ݈௧௞ ൌ௞య/మఌ;	k-ω-SST-model ݈௧௞ ൌ௞భ/మఉ∗∙ఠRANS Mode ߥ௧ ൌ ܥఓ ∙௞మఌ; ߥ௧ ൌ௞ఠ∙ଵ୫ୟ୶	ሾభഀ∗,ೄ∙ಷమೌభ∙ഘሿLES Mode ߥௌீௌ ൌ ܥ௞ ∙ ݇ௌீௌଵ/ଶ ∙ ∆Detached Eddy Simulationܦ෩௞ ൌ ߩ ∙݇ଷ/ଶ݈௧௞ → ܦ஽ாௌ ൌ ߩ ∙݇ଷ/ଶ݈௧஽ாௌ ݈௧஽ாௌ ൌ min	ሾ݈௧௞, ܥ஽ாௌ௞ ∙ ∆௠௔௫]݈௧஽஽ாௌ ൌ ݈௧௞ െ ஽݂஽ாௌ ∙ max	ሾ0, ݈௧௞ െ ܥ஽ாௌ௞ ∙ ∆௠௔௫]Institute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)18 12th August 2015 Dr. Sebastian RuckAppendixFavre-averaging (RANS) or -filtering (LES) the governing flow equations and decomposing flow quantities into resolved and unresolved ones introduces turbulence closure terms [Garnier, 2009][Hirsch, 1988].Momentum equation: Reynolds stresses ߬௜௝௧ 	or subgrid-scale stresses ߬௜௝ௌீௌEnergy equation: Reynolds heat flux ܳ௜௝ௌீௌ	and subgrid-scale heat flux ܳ௜௝௧Boussinesq hypothesis: deviatoric portion of the stresses are related by the eddy-viscosity to the mean and resolved strain-rate tensor respectively (RANS: ߥ௧, LES: ߥௌீௌ) Heat fluxes are approximated by correlating the energy flux of the unresolved and modelled scales with the gradients of the resolved or mean temperatures and a turbulent thermal conductivity (RANS: ߢ௧~	ߥ௧ ∙ ܲݎ௧ିଵ, LES: ߢௌீௌ~ߥௌீௌ ∙ ܲݎௌீௌ							ିଵ)Detached Eddy SimulationInstitute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)19 12th August 2015 Dr. Sebastian RuckAppendixFavre-averaged flow equationsMomentum equationEnergy euquationDetached Eddy Simulation߲߲ݐߩ ∙ ݑ෤௜ ൅߲߲ݔ௝ߩ ∙ ݑ෤௜ ∙ ݑ෤௝ ൌ ݂௜ െ߲݌߲ݔ௜൅߲߲ݔ௝߬̃௜௝௠௢௟ ൅߲߲ݔ௝߬௜௝௧ܳ௝௧ ൌ െߩ ∙ ݑᇱᇱ௜ ∙ ݄ᇱᇱ 			 → 			ܳ௝௧ ൌ െߩ ∙ ߥ௧ ∙ ܥ௣ܲݎ௧∙߲ ෨߲ܶݔ௝߲߲ݐߩ ∙ ෨݄ ൅߲߲ݔ௝ߩ ∙ ݑ෤௝ ∙ ෨݄ ൅߲ݍ෤௝߲ݔ௝െ߲݌߲ݐെ ݑ෤௝ ∙߲݌߲ݔ௝െ Φ෩ ൌ െ߲߲ݔ௝ܳ௝௧ ൅ ݑ௝ᇱᇱ ∙߲݌߲ݔ௝߬௜௝௧ ൌ െߩ ∙ ݑᇱᇱ௜ ∙ ݑᇱᇱ௝			→ 			߬௜௝௧ ൌ 2 ∙ ߩ ∙ ߥ௧ ∙ ሚܵ௜௝ െ13∙ ሚܵ௞௞ ∙ ߜ௜௝ െ23∙ ߩ ∙ ෨݇ ∙ ߜ௜௝Institute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)20 12th August 2015 Dr. Sebastian RuckAppendixFavre-filtered flow equationsMomentum equationEnergy equationDetached Eddy Simulation߲߲ݐߩ ∙ ݑ෤௜ ൅߲߲ݔ௝ߩ ∙ ݑ෤௜ ∙ ݑ෤௝ ൌ ݂௜ െ߲݌߲ݔ௜൅߲߲ݔ௝߬̃௜௝௠௢௟ െ߲߲ݔ௝߬௜௝ௌீௌ߬௜௝ௌீௌ ൌ ߩ ∙ ݑ௜ ∙ ݑ௝෧ െ ݑ෤௜ ∙ ݑ෤௝ 			→			߬௜௝ௌீௌൌ െ2 ∙ ߩ ∙ ߥௌீௌ ∙ ሚܵ௜௝ െ13∙ ሚܵ௞௞ ∙ ߜ௜௝ ൅13∙ ߬௞௞ௌீௌ ∙ ߜ௜௝߲߲ݐߩ ∙ ෨݄ ൅߲߲ݔ௝ߩ ∙ ݑ෤௝ ∙ ෨݄ ൅߲ݍ෤௝߲ݔ௝െ߲݌߲ݐെ ݑ෤௝ ∙߲݌߲ݔ௝െ Φ෩ ൌ െܥ௣ ∙߲߲ݔ௝ܳ௝ௌீௌܳ௝ௌீௌ ൌ ߩ ∙ ܶ ∙ ݑ௝෫ െ ෨ܶ ∙ ݑ෤௝ 			→			ܳ௝ௌீௌൌ െߩ ∙ ߥௌீௌܲݎௌீௌ∙߲ ෨߲ܶݔ௝Institute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)21 12th August 2015 Dr. Sebastian RuckAppendixFavre-filtered flow equationsMomentum equationEnergy equationDetached Eddy Simulation߲߲ݐߩ ∙ ݑ෤௜ ൅߲߲ݔ௝ߩ ∙ ݑ෤௜ ∙ ݑ෤௝ ൌ ݂௜ െ߲݌߲ݔ௜൅߲߲ݔ௝߬̃௜௝௠௢௟ െ߲߲ݔ௝߬௜௝ௌீௌ߬௜௝ௌீௌ ൌ ߩ ∙ ݑ௜ ∙ ݑ௝෧ െ ݑ෤௜ ∙ ݑ෤௝ 			→			߬௜௝ௌீௌൌ െ2 ∙ ߩ ∙ ߥௌீௌ ∙ ሚܵ௜௝ െ13∙ ሚܵ௞௞ ∙ ߜ௜௝ ൅13∙ ߬௞௞ௌீௌ ∙ ߜ௜௝߲߲ݐߩ ∙ ෨݄ ൅߲߲ݔ௝ߩ ∙ ݑ෤௝ ∙ ෨݄ ൅߲ݍ෤௝߲ݔ௝െ߲݌߲ݐെ ݑ෤௝ ∙߲݌߲ݔ௝െ Φ෩ ൌ െܥ௣ ∙߲߲ݔ௝ܳ௝ௌீௌܳ௝ௌீௌ ൌ ߩ ∙ ܶ ∙ ݑ௝෫ െ ෨ܶ ∙ ݑ෤௝ 			→			ܳ௝ௌீௌൌ െߩ ∙ ߥௌீௌܲݎௌீௌ∙߲ ෨߲ܶݔ௝Institute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)22 12th August 2015 Dr. Sebastian RuckAppendixk-equationDestruction termk-ε-realizable-model [Ansys]k-ω-SST-model [Strelets, 2001] [Menter, 1994]Detached Eddy Simulation߲߲ݐߩ ∙ ݇ ൅߲߲ݔ௜ߩ ∙ ݇ ∙ ݑ෤௜ ൌ߲߲ݔ௝ߤ ൅ ߪ௞ ∙ ߩ ∙ ߥ௧ ∙߲߲݇ݔ௝൅ ෨ܲ௞ ൅ ܦ௞ ൅ ܵ௞݈௧௅ாௌ ൌ ܥ஽ாௌ௞ ∙ ∆௠௔௫݈௧௞ ൌ݇ଵ/ଶߚ∗ ∙ ݈߱௧௞ ൌ݇ଷ/ଶߝܦ௞ ൌ ߩ ∙݇ଷ/ଶ݈௧→ ܦ஽ாௌ ൌ ߩ ∙݇ଷ/ଶ݈௧஽ாௌ ݈௧஽ாௌ ൌ min	ሾ݈௧௞, ݈௧௅ாௌሿܥ஽ாௌ௞ ൌ 0.61ܥ஽ாௌ௞ ൌ 1 െ ܨଵ ∙ ܥ஽ாௌ௞ିఌ ൅ ܨଵ ∙ ܥ஽ாௌ௞ିఠ; ܥ஽ாௌ௞ିఌ ൌ 0.61; ܥ஽ாௌ௞ିఠ ൌ 0.78Institute of Neutron Physics and Reactor TechnologyMeasurement Technology and Experimental Methods (MET)23 12th August 2015 Dr. Sebastian RuckAppendixRANS modeTwo-equation k-ω-SST model, k-ε-realizable-model ߥ௧ ൌ௞ఠ∙ଵ୫ୟ୶	ሾభഀ∗,ೄ∙ಷమೌభ∙ഘሿ; ߥ௧ ൌ ܥఓ ∙௞మఌ;LES modeTurbulent kinetic energy is considered as subgrid-scale kinetic energy ݇		 → 		 ݇ௌீௌDynamic Kinetic Energy Subgrid-Scale Model [Kim, Menon, 1997] [Kim, 2004]ߥௌீௌ ൌ ܥ௞ ∙ ݇ௌீௌଵ/ଶ ∙ ∆߬௜௝ௌீௌ ൌ െ2 ∙ ߩ ∙ ܥ௞ ∙ ݇ௌீௌଵ/ଶ ∙ ∆ ∙ ሚܵ௜௝ ൅ଶଷ∙ ߩ ∙ ݇ௌீௌ ∙ ߜ௜௝∆ൌ ܸሾ∆ݔ, ∆ݕ, ∆ݖሿଵ/ଷMotivation

Des and urans downstream of a heated backward facing step

https://publikationen.bibliothek.kit.edu/230102678/3816938

Des and urans downstream of a heated backward facing step

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