Title: Natural Convection Calculation of Waste Package Drift Emplacement REV 00 Document Identifier: CAL-EBS-TH-000001 1. PURPOSE The objective of this calculation is to evaluate the buoyancy-induced natural convection effect on the waste package emplacement in the repository drift. The scope of this calculation is limited to verification of the ANSYS-FLOTRAN solution against the Kuehn and Goldstein correlation (Ref. 3), and evaluation of the natural convection effect in the emplacement drift to support Engineering Barrier System design. The calculation results may be used to support the Licensing Application design activities. The procedure, AP-3.12Q, Calculations (Ref. 1) and Technical Work Plan for: Waste Package Design Description for LA (Ref. 2) are used to develop this document. The information provided by the sketches (Attachments I1 and 111) is that of the potential design of the type of waste package and drip shield considered in this calculation, and all obtained results are valid for these designs only. 2. METHOD Finite element solution is performed using the commercially available ANSYS Version (V) 5.4 finite element code (Ref. 7) and ANSYS V5.6.2-FLOTRAN Computational Fluid Dynamic (CFD) finite element code (Ref. 13). Finite element representations of cylinder-in-cylinder to benchmark with the Kuehn and Goldstein correlation, and the waste package emplacement to evaluate natural convection in the repository drift, are developed and analyzed using the steady-state ANSYS solvers. The control of the electronic management of information was evaluated in accordance with the planned method specified in the technical work plan (Ref. 2). This evaluation determined that current work processes and procedures are adequate for the control of the electronic management of information for this activity. 3. ASSUMPTIONS 3.1 The waste package emplaced in the drift is simulated as a homogeneous inner cylinder with inner and outer shells. The rationale for this assumption is that since the waste package internal temperatures are not of interest for this calculation, smeared material properties for the homogeneous cylinder are applied in the ANSYS representations (see Section 5.3). This assumption is used in Section 5.3. 3.2 The ballast material used in the invert is assumed to have a thermal conductivity of 0.2 Wlm-K. The rationale for selecting this value is that based on the experimental measurements on possible ballast materials (i.e., crushed tuff, overton sand, silica sand, and white marble), the measured values range fiom 0.13 to 0.35 Wlm-K (Ref. 10). Therefore, 0.2 W1m.K is selected for this calculation. This assumption is used in Section 5.3. Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 6 of 29 4. USE OF COMPUTER SOFTWARE AND MODELS 4.1 SOFTWARE APPROVED FOR QUALITY ASSURANCE (QA) WORK The finite element computer code used for this calculation is ANSYS V5.4 (Ref. 7), which is identified by the Computer System Configuration Item (CSCI) identifier 30040 V5.4. ANSYS V5.4 is a qualified commercially available finite element code and is appropriate for the thermal analysis of the waste package as performed in this calculation. Calculations using the ANSYS V5.4 software were executed on a Hewlett-Packard (HP) 9000 Series (Central Processing Unit Name: 'Bloom" and Civilian Radioactive Waste Management System -Management and Operating Contractor [CRWMS-M&O] Tag Number: 700887). The ANSYS V5.4 evaluations performed in this calculation are hlly within the range of the validation performed for ANSYS V5.4. Access to, and use of, the code for this calculation was granted by Software Configuration in accordance with the appropriate procedures. Inputs to ANSYS V5.4 and output files are included as attachments and are described in Section 5 of this document. The finite element computer code also used for this calculation is ANSYS V5.6.2 (FLOTRAN) (Ref. 13), which is identified by the Software Tracking number 10364-5.6.2-00. ANSYS V5.6.2 is a qualified commercially available finite element code and is appropriate for the thermal analysis of the waste package as performed in this calculation. Calculations using the ANSYS V5.6.2 software were executed on a Hewlett-Packard (HP)9000 Series (Central Processing Unit Name: 'Bloom" and Civilian Radioactive Waste Management System -Management and Operating Contractor [CRWMS-M&O] Tag Number: 700887). The ANSYS V5.6.2 evaluations performed in this calculation are hlly within the range of the validation performed for ANSYS V5.6.2. Access to, and use of, the code for this calculation was granted by Software Configuration in accordance with the appropriate procedures. Inputs to ANSYS V5.6.2 and output files are included as attachments and are described in Section 5 of this document. Commercially available software Excel 97, which is exempt from requirements of AP-SI. 1Q (Ref. 6) is used for the calculation in Section 5 and used for plotting results in Section 6. The calculation results can be reproduced and checked by hand. 4.2 MODELS None used. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 7 of 29 5. CALCULATION 5.1 ANSYS-FLOTRAN COMPARISON WITH KUEHN AND GOLDSTEIN CORRELATION To verify the numerical accuracy and assess the capability of the ANSYS-FLOTRAN CFD finite element code, 2-D ANSYS-FLOTRAN representations of concentric and eccentric cylinders are evaluated to compare with the Kuehn and Goldstein correlation (Ref. 3). Since the Kuehn and Goldstein correlation covers a wide range of flow characteristics, including heat transfer by conduction, laminar flow and turbulent flow in concentric and eccentric cylinders, four different cases with different Rayleigh numbers (RaL) and eccentricities are considered (See Table 5-1). The dimensionless parameter, Rayleigh number, which is used to determine the flow regime to be laminar or turbulent, is defined in Equation 5-1 (see Equation 9.23, Ref. 17). va (Equation 5- 1) where: Ti = inner cylinder temperature (OC) To =outer cylinder temperature (OC) g = gravitational acceleration = 9.81 m/s2 p = volumetric thermal expansion coefficient (for ideal gas) = 1/((Ti+To)/2+273.15)(K-') L = characteristic length = gap between inner and outer cylinders = (Do-Di)/2 (m) v = kinematic viscosity of air (m2/s) a = thermal diffusivity of air (m2/s) The boundary conditions for all the cases are constant temperatures at the inner and outer cylinders. Among the four cases, Cases 1 through 3 are solved using the laminar solver for low RaL and Case 4 is solved using the turbulent solver, due to its high R~L. Figure 5-1 schematically shows the geometry used in the ANSYS-FLOTRAN representations. Table 5-1 summarizes the geometric and boundary condition description of the cases analyzed. Figure 5-1. ANSYS-FLOTRAN Geometry This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-000001 REV 00 Paae 8 of 29 Table 5-1. ANSYS-FLOTRAN Cases Case # I Geometric and Boundary Conditions I Rayleigh Number (R~L) The comparison between the ANSYS-FLOTRAN cases and the Kuehn and Goldstein correlation is based on heat transfer rate from the inner cylinder to the outer cylinder, calculated from both ANSYS-FLOTRAN and overall Nusselt number (Nu'Di) correlated in Ref. 3, pages 1130 and 1131, which is provided in Bquations 5-2 through 5-11. The detailed calculation for the four cases analyzed can be found in Attachment IV, Table IV-1, Files #727, #730, #733 and #736 (Files are physically located in Attachment I). The ANSYS-FLOTRAN representation is displayed Figure 5-2. 1/15 Nu Di - (Equation 5-2) Dim,, f5 + NU'^^^ j5] where: Nu'Di= overall Nusselt Number (Equation 5-3) 2 - Nu' 2 1/15 315 ]-5112 ]l5 [o.518hlDi114~+(~) -k(o.lRaDi113Y5] In '7 (Equation 5-4) This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 9 of 29 where: (Equation 5-5) Pr = Prandtl Number - RaDi= Rayleigh number (based on Di) = gp(Ti -T~)D~' (Equation 5-6) va gp(Tb -ToPo3 RaD0= Rayleigh number (based on Do) = va (Equation 5-7) Di = inner cylinder diameter (m) Do= outer cylinder diameter (m) The bulk temperature used in Equations 5-6 and 5-7 can be calculated as follows: Ti NU D~~~ + To NU D,~" = bulk temperature = --(Equation 5-8) NUD~~" +Nu~i~,," (Equation 5-9) (Equation ! Therefore, the heat transfer rate from inner cylinder to outer cylinder is calculated as follows: (Equation 5-1 1) This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 10 of 29 where: h=heat transfer coefficient Ai = inner cylinder surface area (m2) Di = inner cylinder diameter (m) k = thermal conductivity of air (W/m.K) Figure 5-2. ANSYS Representation of Kuehn and Goldstein Benchmark 5.2 NATURAL CONVECTION IN THE EMPLACEMENT DRIFT 5.2.1 Waste Package Emplacement with Drip Shield The post-closure period requires the drip shield to be installed to prevent rock fall. During the post- closure period, ventilation will be shut off. Therefore, the heat transfer mechanism in the drift is radiation f2om the waste package to the drip shield, and the drip shield to the drift wall, natural convection in the fluid region, and conduction in the drip shield and drift rock. To evaluate the impact of natural convection on the waste package emplacement environment, a 2-D one half repository section, including a waste package, a drip shield and a rock layer (5 m into the rock from drift wall) is used for the ANSYS-FLOTRAN CFD calculations. The boundary conditions for the cases are constant temperatures at the 5m-into-rock. Constant heat generation from the waste package is applied. A number of runs have been performed to account for various heat generation rate and temperature boundary conditions. Table 5-2 summarizes the cases analyzed in this calculation. For all the cases analyzed, the waste package is represented as a homogeneous cylinder with waste package shells (see Assumption 3.1). Since the problem involves conjugate heat transfer, and the ANSYS-FLOTRAN CFD solver does not have the capability of calculating radiation, two separate representations are used to solve the problem. One of the representations is built in the ANSYS-only solver, which is used for solving radiation and conduction inside the drift and in the rock. The resulting temperatures at the boundaries are then applied to the second representation, which is built and solved in ANSYS- FLOTRAN, only dealing with the natural convection in the fluid region. The resulting heat fluxes (represents convective heat transfer) on the boundaries are applied to the ANSYS-only representation again to recalculate the radiation and conduction problem. This process repeats for several times until the temperatures and heat fluxes are converged between the two representations. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drifi Emplacement Document Identifier: CAL-EBS-TH-000001 REV 00 Page 11 of 29 Figure 5-3 shows the two representations used in the calculation. Table 5-2. Case Summary for Waste Package Emplacement with Drip Shield Waste Temperature Waste Temperature Load* Case Package Heat Linear Heat Boundary at Case Package Heat Linear Heat Boundary at Name Generation Load* Sm-into-rock Name Generation Sm-into-rock (kWlm) (W) ("C) (W) (kWlm) ("C) drpl9 20 drp9 20 40 drp20 250 0.0475 40 drp5 2000 0.380 drp21 80 drp8 80 drp22 120 drplO 120 drpll 20 drp27 20 dr~"2 40 drpl3 500 0.095 40 dr~28 3000 80 80 drp29 0.570 drp 14 120 drp30 120 drp39 20 drpl5 20 dr~40 750 0.1425 40 drp16 40 drp41 80 drpl7 0.760 80 drp42 120 drpl8 120 drp7 20 drp31 20 drp3 1000 0.190 40 drp32 6000 40 drp6 80 drp33 1.140 80 drp2 120 drp34 120 drp35 20 drp23 20 drp36 1500 0.285 40 drp24 8000 40 drp37 80 drp25 1.520 80 drp38 120 drp26 120 drpl 3540 0.672 60 drp4 450 0.085 110 *Note: linear heat load = waste package heat generation 1 (waste package length + waste package spacing (O.lm, Ref. 5, Table 1-1)). ANSYS only ANSYS-FLOTRAN conduction -convection -radiation Figure 5-3. ANSYS Representations for Waste Package Emplacement with Drip Shield 5.2.2 Waste Package Emplacement without Drip Shield Three cases considering waste package emplacement without drip shield are run for comparing the natural convection behavior in the drift with and without the drip shield. Again, the problem is a This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Tihe: ~afural ~onve&on Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 12 of 29 conjugate heat transfer problem, and the method to calculate the temperature and flow field is the same as that mentioned in Section 5.2.1. The boundary conditions for the cases are constant temperatures at the 5m-into-rock. Constant heat generation from the waste package is applied. Table 5-3 lists the cases analyzed for the calculation. Figure 5-4 displays the mesh configuration for the calculation. Table 5-3. Case Summary for Waste Package Emplacement without Drip Shield Case Name Waste Package Generation (W) Heat Linear Heat Load* (kWlm) Temperature Boundary at Sm-into-rock ("C) ndrpO 3540 0.672 30 ndrpl 3540 0.672 60 ndrp3 1000 0.190 40 *Note: linear heat load = waste package heat generation 1 (waste package length + waste package spacing (O.lm, Ref. 5, Table 1-1)). ANSYS only ANSYS-FLOTRAN anduction -convection Figure 5-4. ANSYS Representations for Waste Package Emplacement without Drip Shield 5.2.3 Waste Package Emplacement Geometric Parameters For the calculations described in Sections 5.2.1 and 5.2.2, the waste package diameter and length are based on the dimensions of a 2 1-PWR waste package (see Attachment 11). The waste package spacing of 0.1 m used to calculate linear heat load is taken from Ref. 5, Table 1-1. The design of the drift invert requires using two layers of materials. The top region is composed of steel beams and ballast material (sand) and the bottom region is composed of only ballast material (see Ref. 20, p. 25 for the design). The sand material is assumed to be filled to the top of the steel invert giving it a height of 0.806 m (Ref. 20, p. 24) from the bottom of the drift. The sand-filled steel invert structure is represented in ANSYS using homogenous thermal properties calculated in Ref. 4. Geometrically, the top region has a depth..of a W 12x65 beam from the surface of the invert. Page 1-28 of Ref. 14 lists the depth of a W12X65 beam as 12.12 inches (0.3078 m). The drip shield design is required during the repository post-closure period The design details and This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 13 of 29 overall dimensions of the drip shield are provided in Attachment 111. In this calculation, the drip shield is simplified as titanium plates with a width of 2.5 12 m, a top radius of the top curvature of 1.285 m, and a thickness of 15 mm. Table 5-4 lists the key dimensions used in this calculation. Table 5-4. Key Dimensions Used in the Calculation I Descri~tion I Dimension I Waste Package Outer Diameter 1I 1.564 m Waste Packaae Lenath 1 5.165 m . . -" " 1 Drift Diameter 1 5.5 m I Waste Packaae Inner Shell Thickness 1 0.050 m I J Waste package Outer Shell Thickness ' 0.020 m Waste P,ackage Spacing 0.1 m Drip Shield Width 2.512 m Dri~ Shield TOD Radius 1.285 m I 1 rib Shield ~hickness I0.015m .I 5.3 THERMAL PROPERTIES The number of digits in the values cited herein may be the result of a calculation or may reflect the results of a units conversion; consequently, it should not be interpreted as an indication of accuracy. Table 5-5 summarizes the waste package, drip shield and rock materials used in the calculation. The source of the materials are described as follows: Table 5-5. Material List I Name I Material I Waste Package Outer Shell Alloy 22 Waste Package Inner Shell 316NG Waste Package Internal homogeneous material Drip Shield Titanium Grade 7 (Attachment Ill) 1 Fluid I Air (Ref. 18., .D. 16 and Ref. 81 Rock , T~t~ll ., , I The drift rock material used in the calculation is Tptpll, since the location of the proposed repository is limited to the TSw2 geologic unit at an elevation of 1072.3 meters (Ref. 18, p. 16), which is located in the Tptpll according to the rock layer stratigraphy (Ref. 8). Table 5-6 lists thermal conductivity and emissivity of the drift rock (Tptpll) taken from Ref. 8 and Ref. 17, page 769 (for rock), respectively. Table 5-6. Thermal Properties of the Drift Rock Thermal Conductivity Emissivity (W1m.K) TslOO°C 1 T>lOO°C This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 14 of 29 To simplify the waste package emplacement representation, the waste package is assumed to be emplaced in the drift as a homogeneous heat-generating cylinder (Assumption 3.1). The effective thermal conductivity for the waste package internal homogeneous cylinder is taken from Ref. 9, Equation 5.1.3-2 for a 21-PWR (pressurized water reactor) waste package. Table 5-7 lists the effective thermal conductivity of the waste package internal cylinder. Table 5-7. Effective Thermal Conductivity of the Waste Package Internal Cylinder Thermal Conductivity (W1m.K) 1.5 Table 5-8 lists the thermal conductivity of Alloy 22, the outer shell material. Values for thermal conductivity are taken fiom Ref. 12, p. 13. The material properties of stainless steel 316 are used for the inner shell material, stainless steel 3 16NG. Stainless steel 3 16NG, which is 3 16 with tightened control on carbon and nitrogen content, has the same mechanical and physical properties as 3 16 (see Ref. 16, page 931 and Ref. 15, SA-240 in Section 11, Table U). Table 5-9 lists the thermal conductivity of stainless steel 3 16NG. Values for thermal conductivity of stainless steel 3 16NG (16Cr-12Ni-2Mo) are taken fiom Ref. 15, Section II, Table TCD. Table 5- 10 lists the emissivity of the outer shell material Alloy 22. The emissivity is taken fiom Ref. 11, p. 10-297 for nickel-chromium alloy. Table 5-8. Thermal Conductivity of Alloy 22 Temperature Thermal Conductivity ("(3 (W1m.K) 48 10.1 100 11.1 200 13.4 300 15.5 400 17.5 500 19.5 600 21.3 Table 5-9 Thermal Conductivity of 316NG This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-000001 REV 00 Page 15 of 29 Table 5-10 Emissivity of Alloy 22 Emissivity Table 5-1 I lists the emissivity of Titanium Grade 7 used as the drip shield material. The emissivity of Titanium Grade 7 is from Ref. 11, Page 10-298, and generalized as that of titanium. Table 5-12 lists the thermal conductivity of Titanium Grade 7. The thermal conductivity is taken from Ref. 15, Section 11, Table TCD. Table 5-1 1. Emissivity of Titanium Grade 7 1 Emissivity 1 Table 5-12. Thermal Conductivity of Titanium Grade 7 Temperature Thermal Thermal Conductivitv Conductivitv Table 5-13 lists the thermal properties of air taken from Reference 17, p. 757. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 16 of 29 Table 5-13. Thermal Properties of Air Temperature Density Specific Heat Kinematic Viscosity Thermal Conductivity (K) (kglm (kJ1kg.K) xlo8 (m21s) x103 (W1m.K) 300 1.1614 1.007 15.89 26.3 350 0.9950 1 .009 20.92 30.0 400 0.871 1 1.014 26.41 33.8 450 0.7740 1.021 32.39 37.3 500 0.6964 1.030 38.79 40.7 550 0.6329 1.040 45.57 43.9 Table 5-14 lists the effective thermal conductivity of the invert top layer (composed of steel beams and ballast material), which is taken from Ref. 4, Tables 6-4,6-8 and 6-12. The thermal conductivity of the invert bottom layer, which is ballast material, is based on Ref. 4, Table 5-7 and Assumption 3.2 and listed in Table 5-1 5. Table 5-14. Effective Thermal Conductivity of the lnvert (top layer) Table 5-15. Thermal Properties of Invert Ballast Material (bottom layer) Dry Bulk Density Specific Heat Thermal Conductivity (kglm3) (J1kg.K) (W1m.K) 1150 948 0.2 5.4 ANSYS FILES This section briefly describes the ANSYS format used to develop the thermal representations. The format of the input file normally includes the following: Describe the file names, problem evaluated, and additional files needed to run the input file, etc. Define parameters and dimensions which are repeatedly used in the representation. Read in additional files, ie., material property files and heat load files needed for the execution. Define element types used in the file. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation -- Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-000001 REV 00 Page 17 of 29 5) Define geometry and generate mesh. 6) Apply the body load (heat output) and boundary conditions and solve the problem. 7) Extract temperature results at desired locations in the representation. All ANSYS files including material properties files (.dat), output files (.out), parameter files (.parm), and post-processing result files (.lis) are stored in a compact disc (Attachment I) and summarized in Attachment IV, Table IV-1. The mesh of the finite element representation is appropriately generated according to standard engineering practice. Thus, the accuracy and representativeness of the results of this thermal calculation is deemed acceptable. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 18 of 29 6. RESULTS This document may be affected by technical product input information that requires confinnation. Any changes to the document that may occur as a result of completing the confirmation activities will be reflected in subsequent revisions. The status of the input information quality may be confirmed by review of the Document Input Reference System database. 6.1 RESULTS FOR ANSYS-FLOTRAN COMPARISON WITH KUEHN AND GOLDSTEIN CORRELATION The heat transfer rate from the inner cylinder to the outer cylinder is compared between the ANSYS-FLOTRAN results and those of the Kuehn and Goldstein correlation. The heat transfer rate from ANSYS-FLOTRAN is obtained based on the average value of heat transfer rate to and from the inner and outer walls (see Attachment IV, Table IV-1, Files #726, #729, #732, and #735 [Files are physically located in Attachment I]), and heat transfer rate based on the Kuehn and Goldstein correlation is calculated in Attachment IV, Table IV-1, Files #727, #730, #733 and #736 [Files are physically located in Attachment I]). Table 6- 1 summarizes result comparison. Table 6-1. Results Comparison between ANSYS-FLOTRAN and Kuehn and Goldstein Heat Transfer Rate Case # Geometry & Boundary R~L Kuehn & ANSYS K&G vs. Conditions Goldstein (W) ON) ANSYS DoIm) 1 0.20 ., , I 1 1 1 1 3 TO(C) 1 80.0 1.08E+O5 17.3 I9 8.9% TI (C) 1, 100.0 I E (m) 1 0.025 1 I I Dnlm) I 5.5 I I I I dl- Table 6-1 shows a good agreement between ANSYS-FLOTRAN results and those of the Kuehn and Goldstein correlation. Case 1 and Case 2, which are both within the laminar regime with concentric geometry, show excellent agreement with the correlation. Case 3 has an eccentric geometry, still within the laminar regime, and shows a slightly higher heat transfer rate from ANSYS than that from Kuehn and Goldstein prediction. Since a limited amount of data of eccentric cases has been obtained for deriving the correlation, the Kuehn and Goldstein correlation may have predicted lower heat transfer rate for eccentric cylinders. This can be observed from the plot shown on page 1132, Fig. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 20 of 29 summarizes the average waste package and drift wall temperatures. The relative importance of natural convection versus radiation in the emplacement drifl is also listed in Table 6-2 by percentage heat removal rate from the waste package through natural convection. Attachment IV, Table IV- 1, File #737 shows the detailed calculation for obtaining the results. Table 6-2. Temperature and Waste Package Heat Removal Rate by Natural Convection spacing (0.lm)). **overall heat transfer coefficient = heat removed by convection I(waste package surface area*(waste package temperature-drift wall temperature) Figures 6-3 and 6-4 display the relationship among waste package heat removal rate by natural convection, waste package surface temperature, and drift wall temperature. The plot shows that for the same waste package surface temperature, the combination of higher waste package heat output This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-000001 REV 00 Page 2 1 of 29 and lower drift wall temperature can increase the natural convection effect. Figure 6-5 shows an alternative way of plotting Figure 6-3. In Figure 6-5, heat removal rate is plotted as a function of linear heat load at constant waste package temperatures. The dash line shows the condition where the temperature at the 5m-into-rock is 20°C, which is probably the limiting case for the emplacement rock. Results in the region above the dash line (temperature at the 5 m-into-rock under 20°C) will be unreasonable for the waste package emplacement environment to achieve. For the heat load range analyzed, the plot implies that the heat removal by natural convection is less than 12%. The manipulation of the results fi-om Figures 6-3 to 6-5 can be found in Attachment IV,Table IV-1, File #738 (File is physically located in Attachment I). If,,,, 0 100 200 300 Waste Package Temperature (C) Figure 6-3. Waste Package Heat Removal By Natural Convection Waste Package Temperature (C) Figure 6-4. Drifl Wall Temperature vs. Waste Package Temperature This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 23 of 29 ANSYS 5.4 WR 16 2001 11:41;49 PLOT NO. 1 NODAL SOLUTION STEP=l SUE =I TIME-1 TEMP SMN =40 SMX =73.256 54.18 58.476 62.171 0 65.866 69.56, 13.256 -D Waste Package Emplacement Model Figure 6-7. Waste Package and Rock Temperature Contours (T5,=400C, Qw=lOOOW) -with Drip Shield ANSYS 5.6.2 WR 9 2001 18:35:29 PLOT NO. 1 FLOW TRACE STEP-2 1 SUB =1 vSUM PouerCraphics EFACET=l AWES-Mat SMX =.I60223 .I24618 ,14242 .I60223 -D Natural Convection Calculation -Fluid Model Figure 6-8. Flow Trace (T5m=40°C, Qw=lOOOW) -with Drip Shield For this particular Case, drp3, the impact of including or ignoring the natural convection in the calculation is also investigated. The temperature comparison at different waste package and drift locations is listed in Table 6-3. Table 6-3 shows that by ignoring natural convection in the calculation, the waste package surface temperatures are over-estimated by 5-7OC. However, the impact on the drift wall temperature is not significant. The temperature results for this comparison can be found in Files #211 and #2 19 (Files are physically located in Attachment I). This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 24 of 29 - TaMe 6-3. Effect of Including Natural Convection in the Calculation Temperature (radiation & Temperature natural (radiation) convection) 6.3 RESULTS FOR WASTE PACKAGE EMPLACEMENT WITHOUT DRIP SHIELD The results of the cases analyzed for the waste package emplacement without drip shield are listed in Table 6-4. The comparison between the Cases with and without drip shield (drpl and ndrpl; and Cases drp3 and ndrp3) shows that without drip shield installed, the heat can be removed more efficiently. This may be explained by comparing the velocity fields in Figures 6-8 and 6-1 1. The waste package emplacement with drip shield divides the cavity into two smaller cells, so that the flow is less turbulent and results in lower convective heat transfer effect. Attachment IV, Table IV-1, File #737 shows the detailed calculation for obtaining the results. Table 6-4. Temperature and Heat Removal Rate by Natural Convection Case Waste Package Linear Heat Temperature Drift Wall Waste Package Heat Removal Overall Heat Name Heat Generation Load* Boundary at Temperature Surface By Natural Transfer (w) (kWlm) Sm-into-rock ("C) Temperature Convection Coefficient** W) W) (%I (wtm2.~) ndrpO 3540 0.672 30 89.5 96.7 8.1 1.55 ndrpl 3540 0.672 60 130.5 135.7 5.5 1.44 ndrp3 1000 0.190 40 56.5 59.6 9.0 1.12 Note: *linear heat load = waste package heat generation I (waste package length + waste package spacing (0.1 m)). **overall heat transfer coefficient = heat removed by convection I (waste package surface area*(waste package temperature-drift wall temperature) This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 25 of 29 ANSYS 5.6 2 JUL 16 2001 09:35.03 PLOT NO. 1 MODAL SOLUTION STEP-2 1 SUB =1 TEMP IAVG) RSYS-0 PouerGraph~cs EPACET=l AVRESmMat SMN =55.981 SMX -61 1 057 I19 57.681 58 256 58 825 59.394 59.962 60.531 a61.1 Figure 6-9. Temperature Contours (T5m=400C, Qw=lOOOW)-without Drip Shield ANSYS 5.4 JUL 16 2001 12:44:12 PLOT NO. 1 noou SOLUTION STEP-1 SUB =1 TIMEol TEMP SMN =40 SMX -70.136 - -D Waste Package Emplacement Model Figure 6-10. Waste Package and Rock Temperature Contours (Ts.=400C. Q,=1000W) -without Drip Shield This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 26 of 29 ANSYS 5.6.2 JUL 16 2001 12;31:25 PLOT NO. 1 FLOW TmE STEF21 SUB =1 VSUM PouerGraphlcs EFACET=l AVRES=k&t SMX s.117566 - . . 2-D Natural Convection Calculation -Fluid Model Figure 6-1 1. Flow Trace (Tsm=40°C, Qwp=lOOOW) -without Drip Shield .. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 27 of 29 7. REFERENCES 1. AP-3.124, REV. 0, ICN 4. Calculations.Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste Management. MOL.20010404.0008. 2. BSC (Bechtel SAIC Company) 200 1. Technical Work Plan for: Waste Package Design Description for LA. TWP-EBS-MD-000004 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20010702.0 152. 3. Kuehn, T.H. and Goldstein, R.J. 1976. "Correlating Equations for Natural Convection Heat Transfer Between Horizontal Circular Cylinders." International Journal of Heat and Mass Transfer, 19, (1 O), 11 27- 1 134. New York, New York: Pergamon Press. TIC: 2384 1 1. 4. CRWMS M&O 2000. Invert Effective Thermal Conductivity Calculation. CAL-WIS-TH- 000004 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.200003 17.0593. 5. Curry, P.M. 2001. Monitored Geologic Repository Project Description Document. TDR- MGR-SE-000004 REV 02 ICN 02. Las Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20010628.0224. , 6. AP-SI.lQ, Rev. 3, ICN 1, ECN 01. Software Management. Washington, D.C.: U.S. Department of Energy, Ofice of Civilian Radioactive Waste Management. ACC: MOL.20010705.0239. 7. CRWMS M&O 1998. ANSYS. V5.4. HP-UX 10.20.30040 5.4. 8. CRWMS M&O 2000. Thermal Modeling Parameters by Stratigraphic Unit. Input Transmittal WP-NEP-99390.T. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000125.0167. 9. CRWMS M&O 1999. Thermal Calculation of the Waste Package with Backfdl. BB0000000- 0 17 17-02 10-0000 1 Rev 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19981214.0073. 10. GS00048335 1030.003. Preliminary Thermal Properties Measured 12/01/99 to 12/02/99 Using the Thennolink Soil Multimeter and Thermal Properties Sensor on Selected Potential Candidate Backfill Materials Used in the Engineered Barrier System. Submittal date: 11/09/2000. 11. Lide, D.R., ed. 1995. CRC Handbook of Chemistry and Physics. 76th Edition. Boca Raton, Florida: CRC Press. TIC: 2 16194. 12. Haynes International. 1988. Hastelloy Alloy C-22. Kokomo, Indiana: Haynes International. TIC: 239938. 13. CRWMS M&O 2000. Software Code: ANSYS. V5.6.2. HP-UX 10.20. 10364-5.6.2-00. 14. AISC (American Institute of Steel Construction) 1989. Manual of Steel Construction, This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 28 of 29 Allowable Stress Design. 9th Edition. Chicago, Illinois: American Institute of Steel Construction. TIC: 205770. 15. ASME (American Society of Mechanical Engineers) 1995. "Materials." Section I1 of 1995 ASME Boiler and Pressure Vessel Code. New York, New York: American Society of Mechanical Engineers. TIC: 245287. 16. ASM International 1987. Corrosion. Volume 13 of Metals Handbook. 9th Edition. Metals Park, Ohio: ASM International. TIC: 209807. 17. Incropera, F.P. and DeWitt, D.P. 1996. Introduction to Heat Transfer. 3rd Edition. New York, New York: John Wiley & Sons. TIC: 24 1057. 18. CRWMS M&O 1998. Repository Ground Support Analysis for Viability Assessment. BCAA00000-0 1 7 17-0200-00004 REV 0 1. Las Vegas, Nevada: CRWMS M&O. ACC: MOL. 199805 12.07 14. 19. CRWMS M&O 1997. Waste Container Cavity Size Determination. BBAA00000-0 17 17- 0200-00026 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL. 19980106.006 1. 20. CRWMS M&O 2000. Invert Configuration and Drip Shield Interface. TDR-EDS-ST-00000 1 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.2000505.0232. This is the background image for an unknown creator of an OCR page with image plus hidden text. Waste Package Project Calculation Title: Natural Convection Calculation of Waste Package Drift Emplacement Document Identifier: CAL-EBS-TH-00000 1 REV 00 Page 29 of 29 8. ATTACHMENTS The attachments to this calculation are summarized in Table 8-1. Table 8-1. Attachments Summary (1 Attachment I Description * Number I II Ill IV Compact disk (CD) (1 of 1 )containing ANSYS V5.4 and V5.6.2 files, and Excel files (see Attachment IV for list of files) Sketch of 21-PWR Waste Package (SK-0175 REV 02 and SK-0191 REV 00) Sketch of Drip Shield (SK-0148 REV 05) File Listing for Attachment I ( Pages (1 NIA 3 2 13 This is the background image for an unknown creator of an OCR page with image plus hidden text. 3 q/r CAI,-EBS-TI1-000001 RI'V 00 Att:\chment IV Page IV-1 FILE SUMMARY The files listcd in Tablc IV-l include thc ANSYS inaterial propcrtics tiles (.dat), output files (.out), parameter files (.parm), print Iilcs (.pfl), and post-processing result files (.lis). Also listed are Excel 97 spreadshcct filcs (.xis). All filcs are physically stored on a compact disc (Attaclimc~itI). Table IV-I. File Summary :ase # /File # IFile Name rpLu ration outout, oarameter files. eat flux a& tehperature lists for aste package and drift iteration output and parameter files This is the background image for an unknown creator of an OCR page with image plus hidden text. 3 BJY CAI.-EBS-7TI-I-000001REV 00 Attachment IV Page IV-2 :ase # - rpl I package heat flux and waste package and drift temperature This is the background image for an unknown creator of an OCR page with image plus hidden text. OFFICE OF CIVILIAN RADIOACTIVE WASTE M SPECIAL INSTRUCTION SHEET Complete Only Applicable Items This is a placeholder page for records that cannot be scanned. 2. Record Date 1 3. Accession Number DL.PQDUOB. 4. Author Nametsl 5. Author Oraanization I 6. TitldDescription NATURAL CONVECTION CALCULATION OF WASTE PACKAGE DRIFT EMPLACEMENT I 9. Document Type 10. Medium DATA CD-ROM I 11. Access Control Code PUB 12. Traceabilitv Designator - DC# 29268 - /Dy8-0 f 13. Comments \I -, THIS IS A SPECIAL PROCESS CD-ROM AS PART OF ATTACHVENT I THIS DATA SUBMITTa TO THE W. RECORDS PROCESSING CENTER IS FOR ARCHIVE PURPOSES ONLY, AND IS NOT AVAILABLE FOR VIEWING OR REPRODUCTION P-17.1U.1 Rev. 04/30/200 This is the background image for an unknown creator of an OCR page with image plus hidden text. 5 "d" CAI,-E13S-TtI-000001 RI;V 00 Attacliment IV Page IV-4 ration output, parameter files. output and parameter files I I 1 1 l~terat~on I I I This is the background image for an unknown creator of an OCR page with image plus hidden text. aste package and drifl ration output, parameter files. aste package and drifl I I 1 literation output and parameter files 1 1 1 1 This is the background image for an unknown creator of an OCR page with image plus hidden text. 7qj i'( Attachment IV Page IV-6 package heat flux and waste package and drift temperature This is the background image for an unknown creator of an OCR page with image plus hidden text. Athchn~entIV Page IV-7 "d" ration output and paramet , . NSYS V5.4 thermal run: 2" ~n~~s/dr~8/dr~~th2.~arm msysldrp8ldrp-fl2.parm ~nsysldrp8lflux~wp.lis ------.- ~nsysldrp8ltemp-wp.lis aste package and drift msysldrp8ltemp-df.lis msysIdrp8/drp-th3.out ~nsvsldrp27ldrp fll .out . . L ~nsysldrp27/dr~~fll.parm iteration output and parameter files 329 8/8/2001 12:56 PM ~nsysldrp27ldrp-th2.out ANSYS V5.4 thermal run: 2"' 43 8/8/2001 12:55 PM 3nsysldrp27ldrp-th2.parm iteration output and parameter files 632 8/8/2001 1255 PM msysldrp27/drp-fl2.out ANSYS V5.6.2 FLOTRAN run: 2" 347 8/8/2001 1256 PM ansys/drp27/drp-fl2.parm iteration output, parameter files. 859 8/8/2001 12:56 PM ~nsysldrp27lflux~wp.lis 'Heat flux and temperature lists for 6 8/8/2001 1255 PM ansysldrp27/temp-wp.lis waste package and drift 6 8/8/2001 12:56 PM 3nsysldrp27/temp-df.lis 5 8/8/2001 12:55 PM ~nsvsldro271dro th3.out . ANSYS V5.4 thermal run: 3m 43 8/8/2001 1255 PM ansys/drp28/drp-f12.~arm-iteration output, parameter files. ansys/drp28/flux-wp.lis Heat flux and temperature lists for 3nsys/drp28/temp-wp.lis aste package and drift This is the background image for an unknown creator of an OCR page with image plus hidden text. Attachment IV Page IV-9 IU 0b ly ion output, parameter files. flux and temperature lists for e package and drift eat flux and temperature lists for aste package and drift This is the background image for an unknown creator of an OCR page with image plus hidden text. CAI .-EI3S-TI-1-000001 RI