Transient Thermal, Hydraulic, And Mechanical Analysis Of A .

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Transient Thermal, Hydraulic, and Mechanical Analysisof a Counter Flow Offset Strip Fin Intermediate Heat Exchangerusing an Effective Porous Media ApproachbyEugenio UrquizaB.S. (Texas A&M University) 2002M.S. (University of California, Berkeley) 2006A dissertation submitted in partial satisfactionof the requirements for the degree ofDoctor of PhilosophyinEngineering-Mechanical Engineeringin theGraduate Divisionof theUniversity of California, BerkeleyCommittee in ChargeProfessor Per F. Peterson, Co-chairProfessor Ralph Greif, Co-chairProfessor Van P. CareyProfessor Tadeusz PatzekFall 2009

Transient Thermal, Hydraulic, and Mechanical Analysisof a Counter Flow Offset Strip Fin Intermediate Heat Exchangerusing an Effective Porous Media Approach 2009by Eugenio Urquiza

AbstractTransient Thermal, Hydraulic, and Mechanical Stress Analysisof a Counter Flow Offset Strip Fin Intermediate Heat Exchangerusing an Effective Porous Media ApproachbyEugenio UrquizaDoctor of Philosophy in Engineering-Mechanical EngineeringUniversity of California, BerkeleyProfessor Per F. Peterson, Co-chairProfessor Ralph Greif, Co-chairThis work presents a comprehensive thermal hydraulic analysis of a compact heatexchanger using offset strip fins.The thermal hydraulics analysis in this work isfollowed by a finite element analysis (FEA) to predict the mechanical stressesexperienced by an intermediate heat exchanger (IHX) during steady-state operation andselected flow transients. In particular, the scenario analyzed involves a gas-to-liquid IHXoperating between high pressure helium and liquid or molten salt.In order to estimate the stresses in compact heat exchangers a comprehensive thermaland hydraulic analysis is needed. Compact heat exchangers require very small flow1

channels and fins to achieve high heat transfer rates and thermal effectiveness. However,studying such small features computationally contributes little to the understanding ofcomponent level phenomena and requires prohibitive computational effort usingcomputational fluid dynamics (CFD).To address this issue, the analysis developed here uses an effective porous media(EPM) approach; this greatly reduces the computation time and produces results with theappropriate resolution [1]. This EPM fluid dynamics and heat transfer computationalcode has been named the Compact Heat Exchanger Explicit Thermal and Hydraulics(CHEETAH) code. CHEETAH solves for the two-dimensional steady-state and transienttemperature and flow distributions in the IHX including the complicating effects oftemperature-dependent fluid thermo-physical properties.Temperature- and pressure-dependent fluid properties are evaluated by CHEETAH and the thermal effectiveness ofthe IHX is also calculated.Furthermore, the temperature distribution can then be imported into a finite elementanalysis (FEA) code for mechanical stress analysis using the EPM methods developedearlier by the University of California, Berkeley, for global and local stress analysis [2].These simulation tools will also allow the heat exchanger design to be improved throughan iterative design process which will lead to a design with a reduced pressure drop,increased thermal effectiveness, and improved mechanical performance as it relates tocreep deformation and transient thermal stresses.2

To my parents, Guillermo and Margarita.i

Table of ContentsNomenclature . viList of Figures . viiiList of Tables . xiiPreface .xiiiIntroduction. xvAcknowledgements. xxiChapter 1·Heat Exchanger Layout,Effective Porous Media (EPM) Approach,and Conservation Equations .11.1Intermediate Heat Exchanger Geometry . 31.2Volume-Averaged Properties . 71.3Phase Fraction. 131.4Media Permeability. 141.5Determining the Effective Permeability . 151.6Fully Developed Flow . 191.7Convection Coefficient. 201.8Surface Area Density. 221.9Effective Conductivity. 221.10Fluid Dynamics. 231.11Fluid Dynamics Equations. 231.12Heat Transfer . 271.13Heat Transfer Equations . 271.14Temperature-Dependent Fluid Properties. 30ii

Chapter 2·Partitioning,Discretization,and Numerical Method .352.1Zoning the IHX. 362.2Diffuser and Reducer Permeability . 392.3Adjustable Flow Distribution . 402.4Specifying the Grid. 442.4.1Rectangular Grid. 452.4.2Staggered Grid. 472.5Fluid Dynamics Discretization . 482.6Heat Transfer Discretization. 512.6.1Control Volume for Liquid Phase in the IHX . 522.6.2Control Volume for Solid Phase in the IHX. 532.6.3Control Volume for Gas Phase in the IHX. 53Chapter 3·Thermal Hydraulic Results .543.1CHEETAH Code Architecture . 543.2Thermal Hydraulic Results with Constant Thermophysical Properties. 563.2.1Liquid Pressure Distribution. 573.2.2Gas Pressure Distribution . 583.2.3Liquid Speed Distribution . 603.2.4Gas Speed Distribution. 613.2.5Steady-State Temperature Distribution . 623.2.6Transient Temperature Distributions. 643.3 Thermal Hydraulic Results with Temperature-Dependent ThermophysicalProperties . 683.3.1Temperature-Dependent Thermophysical Properties . 683.3.2Liquid Pressure Distribution. 723.3.3Gas Pressure Distribution . 743.3.4Liquid Speed Distribution . 763.3.5Gas Speed Distribution. 783.3.6Steady-State Temperature Distribution . 80iii

Chapter 4·Verification of Numerical Method .824.1Verifying Steady-State Temperature Distribution. 824.2Verifying Transient Temperature Distribution . 854.2.1Case 1: Step Change in Temperature of Uniform-Temperature Fluid . 894.2.2Case 2: Step Change in Flow Rate of Single-Phase Fluid. 92Chapter 5·Thermomechanical Stress Analysis .965.1Domain Sub-Structuring with Effective Mechanical Properties . 965.2CHEETAH-ANSYS Communicator Code (CAC code) . 1045.3Steady-State Stress Analysis. 1065.3.1Failure Analysis – Yielding . 1095.3.2Failure Analysis – Creep . 1105.4Effect of Constant and Temperature-Dependent Thermophysical Fluid Properties. 1115.5Transient Stress Analysis. 1145.65.5.1Liquid Salt (Cold) Pump Trip. 1165.5.2Helium (Hot) Pump Trip . 117Fin-scale Stress Analysis . 1205.6.15.75.7Stress Results from the Helium Pump Trip . 1235.7.1Helium Transient (30 seconds). 1235.7.2Helium Transient (60 seconds). 124Stress Results from the Liquid Salt Trip. 1265.7.1Liquid Salt Transient (30 seconds) . 1265.7.2Liquid Salt Transient (60 seconds) . 127Chapter 66.16.2Steady-State (0 seconds). 121·Conclusions and Recommendations .129Recommendations Regarding Example Problem . 1296.1.1System Recommendations. 1296.1.2Hydraulic Recommendations . 1316.1.3Mechanical Recommendations. 132Conclusions . 135iv

References .138Appendix.141AIntermediate Heat Exchanger Sizing Calculations . 141BTable of thermophysical properties for high pressure helium . 156COne-dimensional steady-state temperature distribution using the effectiveness-NTUmethod . 157DEffective Mechanical Properties. 159v

Nomenclaturea'cC12surface area density, m / man empirical constant3hydraulic constant related to the offsetstrip fin geometryJ /(kgK)SttStanton number, dimensionlessthickness of the fins in the offset stripfin arrangement, mTtemperature,uuuDaverage velocity, m / suintinterstitial velocity in the x direction,cpthe specific heat,CFLCourant – Friedrichs – Levy Number,dimensionlessCoDDhSt Pr 2 / 3 orNu /(Re Pr1/ 3 )diameter, mhydraulic diameter, mffFanning friction factor, dimensionlessxwwintFoFourier Number, dimensionlesszgGzhhacceleration due to gravity,Colburn Factor,Kvelocity in the x direction, m / sDarcy velocity in the x direction, m / sm/scoordinate in the flow directionvelocity in the z direction, m / sinterstitial velocity in the z direction,m/scoordinate in the cross-flow directionm / s2Graetz number, dimensionlessfin height, mSubscriptsconvective heat transfer cold fluid2w /(m K)jColburn factor, dimensionlesskeffective conductivity,kfconductivity of the fluid,w /(mK)kleffective permeability, m2Lmm nNuPPePrRelength of flow path, mw /(mK)length of the fins in the offset strip finarrangement, mmass,kgmass flow rate,kg / siteration number (time)Nusselt number, dimensionlesspressure, PaPeclet number, dimensionlessfluidbetween cold fluid and solidcold fluid x directioncold fluid z directionhot fluidbetween hot fluid and solidhot fluid x directionhot fluid z directionsolidbetween solid and cold fluidx directionz directionPrandtl number, dimensionlessReynolds number, dimensionlessvi

Superscript*denotes non-dimensionalGreek Symbolsαthermal diffusivityΔdiscrete changeφphase fractionΦflow potential, Paμdynamic viscosity, Pa*sρdensity, kg / m3Index Variablesijkindex in the x direction (flow direction)index in the y directionindex in the z direction (cross-flowdirection)AbbreviationsAHTR Advanced High-Temperature ReactorCFDComputational Fluid DynamicsCHEETAH Compact Heat Exchanger Thermaland Hydraulic codeEPMEffective Porous MediaFDM Finite Difference MethodFEAFinite Element AnalysisFVAFinite Volume AnalysisIHXIntermediate Heat ExchangerNTUNumber of Transfer UnitsOSFOffset Strip FinPBMR Pebble Bed Modular Reactorvii

List of FiguresIntroduction .xvFigure 0-1Schematic of the Advanced High-Temperature Reactor joined by an intermediateheat transfer loop (shown in red) to an adjoining power or process plant. [Image:Prof. Per F. Peterson - UC Berkeley]. xviiFigure 0-2Photo of a cut-away model of a typical Heatric plate-type compact heatexchanger showing multiple inlet and outlet manifolds and slices across variousplates and flow channels . xviiiFigure 0-3CHEETAH provides thermal hydraulic data that enables the analysis ofcomponent-level (plate-scale) thermal stresses on the composite plate of the IHX(left) and corresponding local (fin-scale) stresses shown on a unit cell (right) .xxChapter 1·Heat Exchanger Layout,Effective Porous Media (EPM) Approach,and Conservation Equations .1Figure 1-1Schematic of gas and liquid plate geometries and flow in the IHX. 4Figure 1-2Solid models of liquid salt and helium plates in the IHX . 5Figure 1-3Temperature contours in the flow direction of the liquid salt in a hightemperature heat exchanger – Ponyavin et al. [7]. 8Figure 1-4Cut-away view through the offset strip fin (OSF) section showing alternatingliquid and gas flow channels. Dark bands at the top of each fin indicate thelocation of diffusion-bonded joints between the plates . 11Figure 1-5The four unit cells characterizing the complex geometry of the compositeplate. 12Figure 1-6Solid phase fraction illustration for unit cell C (67%) . 13Figure 1-7Dynamic viscosity of the liquid salt FLiNaK over temperature range set byfluid inlet temperatures to the IHX . 31Figure 1-8Liquid salt viscosity versus temperature plots from a candidate salt assessmentreport from Oak Ridge National Lab [4]. . 32Figure 1-9Isobaric thermophysical properties for helium at 7MPa from NIST . 34viii

Chapter 2·Partitioning,Discretization,and Numerical Method .35Figure 2-1A schematic of the IHX’s zoning distribution for thermal and hydraulicparameters in the CHEETAH code. 38Figure 2-2Adjustable permeability distributors in the liquid salt inlet and outlet zones . 42Figure 2-3Rectangular grid discretization used in early versions of FVA code. 45Figure 2-4Staggered grid in x-direction illustrating indexing on left side of controlvolume . 47Figure 2-5Staggered grid in x- and z-directions illustrating indexing on left side andbottom of control volume . 47Figure 2-6Continuity in a finite volume analysis for a fluid with constant density . 49Figure 2-7Continuity in a finite volume analysis for a fluid with variable density. 51Figure 2-8Energy balance in the finite volume analysis for a fluid with constant density. 52Figure 2-9Energy balance in the finite volume analysis for the solid exchanging heat withseparate fluids and conducting heat from its surroundings. 53Figure 2-10 Energy balance in the finite volume analysis for a fluid with variable density . 53Chapter 3·Thermal Hydraulic Results .54Figure 3-1Five modules executed sequentially comprise the CHEETAH code. 55Figure 3-2The steady-state liquid salt pressure distribution through the composite plateof the IHX . 57Figure 3-3The steady-state helium pressure distribution through the composite plate ofthe IHX . 59Figure 3-4Flow speed distribution of liquid salt through the composite plate of the IHX. 60Figure 3-5Flow speed distribution of gas through the composite plate of th

Transient Thermal, Hydraulic, and Mechanical Analysis . This work presents a comprehensive thermal hydraulic analysis of a compact heat exchanger using offset strip fins. The thermal hydraulics analysis in this work is . Figure 0-2 Photo of a cut-away model of a typical Heatric plate-type compact heat

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