THERMAL MODELING OF PACKAGES FOR NORMAL CONDITIONS OF TRANSPORT WITH INSOLATION THERMAL MODELING OF PACKAGES FOR NORMAL CONDITIONS OF TRANSPORT WITH INSOLATION t Tehnial Programs and Servies/Engineering Analysis Martin Marietta Energy Systems, In., Central Engineering Servies Oak Ridge, Tennessee ABSTRACT As part of the Safety Analysis Report for Pakaging (SARP)for eah speial nulear materials pakage, experimental tests or an analysis must be performed to determine the temperature distribution throughout the pakage when exposed to normal onditions of transport. These normal onditions inlude two ases one with insolation and one without insolation. Insolation (total solar heat load) values to be used in the analyses are given in 1 CFR 71.71; however, the manner in whih the insolation is to be applied is not speified. Several approahes an be taken: 1) perform a steadystate analysis assuming the insolation is applied ontinuously, 2) perform a transient analysis assuming the inident insolation is represented by a step funtion (i.e., insolation is applied and then not applied in 12hour yles), or ) perform a transient analysis the inident insolation is represented by a more omplex funtion involving variables suh as time of day. The purpose of this paper is to present these various approahes and examine the effet they have on pakage temperature distributions. The DC1 shipping pakage with the 288 an was used for the analyses to represent a typial thinwalled Celotexbased shipping pakage. The results of the study indiate that the method used in applying the insolation has a signifiant effet on the outermost portions of the pakage. Maximum outer ontainer temperatures were found to vary by as muh as 19."C depending on whih insolation method was used. Typially, internal pakage temperatures are more ritial in this type of analysis. Sine the total insolation over any 24hour period is the same for all ases, internal pakage temperatures (seondary ontainment vessel, primary ontainment vessel, ontent, et.) are relatively unaffeted by the way in whih the insolation is applied. Internal pakage temperatures vary no more than 2 C for the three insolation methods investigated. DESCRIPTION OF THE SHIPPING PACKAGE USED FOR THE ANALYSES The DC1 shipping pakage, whih is transported in a vertial position, inludes a stainless steel drum whih serves as the outer ontainer and a stainless steel seondary ontainment vessel. The spae between the outer ontainer and the seondary ontainment vessel is filled with alternating staked rings and disks of Celotex fiberboard insulating material and plywood. The primary ontainment vessel is loated inside the seondary ontainment vessel. Both polyurethane and monothane foams are used as paking materials. A sketh of the DC1 pakage with the 288 an is shown in Fig. 1. DESCRIPTION OF THE ANALYTICAL MODEL PATRAN. was used to reate a fmite element model of the DC1 shipping pakage. An axisymmetri (rz) model was onstruted as shown in Fig. 2. Six materials were used in the model. The thermal properties used in the analysis are presented in Table 1. Where available, temperature dependent thermal ondutivities and speifi heats were used. Densities were assumed to be onstant for all materials. P/T IERMAL 2.6 was used to perform the heat transfer analyses. As speified in 1 CFR71.71 (1 CFR71, 1987), heat transfer between the pakage exterior and the environment ours by three mehanisms: 1) insolation (heat flux due to solar radiation), 2) radiant exhange with the surroundings at 8 C t Prepared by MARTIN MARIFITA ENERGY SYSTEMS, INC. managing the Oak Ridge K25 Siie Oak Ridge National Laboratory Oak Ridge Y12 Plant under Contrat DEACO584OR2 14 for the U.S. DEPARTMENT OF ENERGY The U.S. Governmentretainsanonexlusive, ro yaliyfree liense topublish or reprodue the published form of this ontribuiion, or allow others to do so, for U.S. Government purposes. DISTRIBUTiON OF THE CIXUImJ'i E U t W g E D 1 w. C. Anderson and M. R. Feldman
KATERIAL KEY SPAINLESSSTEEL CELOTM PLWOOD (FIR) ALUMINUM (881TB) POLYURETHAHE MONOTHANE KONCNRED NODES A OUTER CONTAINER TOP CENTER B SECONDARY CONTAINMENT VESSEL IUNG C PRIMARY CONTAINMENT YESSEL ORING D 288CANISTERTOPCEHTER Note : AU dimensions are in inhes. FIG. 1 DC1SHIPPING CONTAINER SCHEMATIC (11K), and )natural onvetion to still ambient air at 8 C. The inident solar radiation applied in the model is speified in 1 CFR 71.71. The manner in whih this insolation is to be applied, however, is not speified. Several approahes an be taken and eah will be disussed in later setions. The heat transfer due to radiant exhange with the environment (q \,J is alulated as ep = emissivity of pakage surfae, = emissivity of surroundings, Ap = surfae area of the pakage, A, = surfae area of the surroundings. E, u = StefanBolamann onstant, T, = surfae temperature (absolute), To = ambient temperature (absolute), F, = overall interhange fator. The overall interhange fator is alulated as (Siege1 and Howell, 1981) Sine the area of the surroundings is muh larger than the surfae area of the pakage, F, =. The natural onvetive heat transfer to air (q,,,,,~,j alulated as () is
FIG. 2 DC1 FINITE ELEMENT MODEL R a = g p ATL va it = onvetive heat transfer oeffiient. g = aeleration of gravity, P = oeffiient of thermal expansion, AT = temperature differene, Y = kinemati visosity, The heat transfer oeffiient over the top surfae of the pakage is alulated as @/THERMAL, 1991) CY (5) k L > = thermal diffusivity [k/hj. The values of the onstants C, and C, in Eq. 5 are given in Table 2. The heat transfer oeffiient over the sides of the pakage an be estimated as @/THERMAL. 1991) = thermal ondutivity of air, = harateristi length (ratio of surfae area to perimeter = D/4 for a irular surfae). The Rayleigh number is defined as Pr = PrandtI number = VICY.
TABLE 1 MATERIAL PROPERTIES USED IN THE ANALYSES Temperature W) Thermal Condutivity (WlmK) Density (kg/m) Speifi Heat (JkzK) Stainless Steel 2 4 6 12.6 14.9 16.6 19.8 79 42 477 515 557 Celotex 298 59 419 499 55 1.5.59.6.65.51 27 128 156 1745 246 26.12 545 1215.5 264 17.2929 125 167.6 2698 87.5 Material Plywood (Fir) I ~~ 27.15 27.2 5 7 4 47 5 57 6 26 27 24 24 27 22 The values of the onstants C, through C, are given in Table 2. Properties for air were taken from Inropera and DeWitt (1985). Heat transfer through the solid materials ours solely by ondution. As seen from Fig. 1, several air gaps exist in the pakage. It is assumed that heat is transferred aross these gaps by radiant exhange. PNIEWFACTOR was used to alulate the view fators in all enlosures. The initial temperature of the pakage was assumed to be 8 C (11 K). The following insolation data are provided in 1 CFR 71.71 (1 CFR 71, 1987): Flat surfaes transported horizontally Base Other surfaes Curved surfaes.87.5 916.89 98.88 129.94 speified in the regulations. Several approahes an be taken: 1) perform a steadystate analysis assuming the insolation is applied ontinuously, 2) perform a transient analysis assuming the inident insolation is represented by a step funtion (ix., insolation is applied and then not applied in 12hour yles), or ) perform a transient analysis the inident insolation is represented by a more omplex funtion involving variables suh as time of day. Eah of these methodologies is disussed in detail below. METHODS OF APPLYING INSOLATION Form and loation of surfae.22 ~ Polyurethane Aluminum (661T6) Emissivity Steadvstate approah The following inident solar heat flux values an be alulated by distributing the heat speified in 1 CFR 71.71 evenly throughout a 24hour period: Total Insolation for a 12hour period (al/m2) Form and loation of surfae None 8. 4. Flat surfaes transported horizontally Base Other surfaes Curved surfaes The manner in whih this insolation is to be applied is not 4 Inident solar heat flux (w/m2) None 88. 194.
TABLE 2 NATURAL CONVECTION CORRELATION COEFFICIENTS Coeffiient Rayleigh Number Range Cl 2.6E+4 < Ra 1.OE+7 < Ra < 1.OE+7 <.OEf1.54.15 2 2.6E+4 < Ra 1.OE+7 < Ra < 1.OE+7 <.OEf1.25 11 Ra < l.oe+9 Ra > 1.OE+9.68.825 4 Ra < l.oe+9 Ra > l.oe+9.67.87 CS Ra < 1.OE+9 Ra > l.oe+9.25 1/6 '6 Ra < l.oe+9 Ra > l.oe+9 419 8/27 7 Ra < l.oe+9 Ra > l.oe+9 1 2 Form and loation The values presented above represent inident heat flux (q",oolnr.i). Sine the exterior surfae of the pakage is not a perfet absorber, the insolation atually absorbed by the pakage surfae (q",ohrj is alulated as Value of surfae Flat surfaes transported horizontally Base Other surfaes Curved surfaes Inident solar heat flux Wlm2) None 775. 88. As with the steadystate solution, these values should be orreted for the drum absorptivity (see Eq. 8). The heat fluxes are represented as step funtions as shown in Fig. (Le., the heat fluxes are applied and not applied in alternating 12hour periods). ad = absorptivity of the drum. The heat fluxes alulated by Eq. 8 an be applied ontinuously to obtain a steadystate temperature distribution for the shipping pakage. This method provides the fastest and most simple solution. Sinusoidal funtion approah A third approah for the appliation of the solar heat flux is to represent the insolation as sinusoidal funtions whih vary throughout the day Step funtion approah The following inident solar heat flux values an be alulated by distributing the heat speified in 1 CFR 71.71 evenly throughout a 12hour period: 5
7 14 12 ru h 5 Sinusoidal Funtion E \ % \ 1 fn 6 eo Step Funtion 6 5 4 x i 8 r B VI PE 6 4 2 2 1 FIG. INCIDENT SOLAR HEAT FLUX AS A FUNCTION OF TIME q'',olar,r= inident solar heat flux (W/mz), ( hours). Data used in the onstrution of these urves represent every 6 hours, with the exeption of days 1 and 14 data were taken every hour. It was determined that a "quasisteadystate" temperature distribution had been reahed at the onlusion of 1 days. At this time, values of the temperature differene between suessive days at Node 2417, whih represents the top enter of the 288 anister, had dropped below.1"c. This indiates that the interior of the DC1 pakage had been fully heatsoaked after approximately 1 days. It should be noted that Node 2417 is representative of that portion of the pakage whih requires the longest amount of time to reah "quasisteadystate". Although the temperatures vary throughout the day, the temperatures are the same (within O.l C) from one day to the next (Le., the temperature at any loation at 12:OO PM on day 1 is the same as the temperature at 1 2 9 PM on day 14). Figure 4 shows the temperature history of the top enter of the DC1 outer ontainer for eah of the three insolation ases onsidered. The top enter of the outer ontainer represents the maximum temperature in the pakage. The "quasisteadystate" maximum temperatures ahieved at this loation are approximately 51.25, 61.25 and 7.55"C for the steadystate, step funtion and sinusoidal methods, respetively. As expeted, the maximum temperature predited by the sinusoidal method is approximately 9."C higher than that predited by the step funtion method sine the solar heat flux is 57% higher 6 hours after sunrise. These results indiate that loations near the pakage surfae are signifiantly affeted by the method in whih the insolation is applied. These differenes in external surfae temperatures and durations of elevated temperatures will affet q5 = total insolation for a 12hour period (MJ/mz) from 1 CFR 71.71, t = time (hours). The insolation is defmed by Eq. 9 for 12n 5 t 5 12(n + 1) n =, 2, 4... and the insolation equals zero for 12n 5 t 5 12(n + 1) n = 1,, 5... This sinusoidal representation of the heat fluxes is shown graphially in Fig.. It should be noted that the peak solar heat fluxes alulated by Eq. 9, whih our 6 hours after sunrise, are approximately 122 and 68 W/mz for the top and side surfaes, respetively. These maximum heat fluxes are approximately 57 % higher than those used in the step funtion model. The total insolation inident on the pakage over a 24hour period is equal for eah of the three methods desribed above. In other words, the area under eah of the three urves in Fig. is the same. DISCUSSION OF RESULTS Temperatures at seleted loations in the DC1 pakage are shown graphially as a funtion of time in Figs. 47 for eah of the three insolation ases. Day 1 is assumed to begin at sunrise 6 J. C. Anderson and M. R. Feldrnan
I SteadyState Funtion S i n u s o i d a l Step I 7. 65 s A e 6. 55. 5. 45. 4. FIG.4 OUTER CONTAINER TOP CENTER TEMPERATURE AS A FUNCTION OF TIME he heat lost by the pakage and, onsequently, internal pakage primary ontainment vessel. temperatures. Figure 5 shows the temperature history of the seondary ontainment vessel Oring loation. The "quasisteadystate" maximum temperatures ahieved at this loation are 47.55,48.5 and 47.45"C for the steadystate, step funtion and sinusoidal methods, respetively. The step funtion and sinusoidal methods predit temperatures whih are within 1.1"C of one another throughout the entire transient. These results indiate that internal pakage temperatures are relatively unaffeted by the method in whih the insolation is applied. The small temperature differenes are present beause the amount of heat lost by the pakage to the surroundings is different for the three ases onsidered. Due to the high external temperatures predited by the sinusoidal method, more heat is lost to the environment and, therefore, lower temperatures are ahieved at internal loations. Observation of Fig. 5 shows that the insolation yle is still felt somewhat at the seondary ontainment vessel sine a definite temperature variation is present throughout the day. Figures 6 and 7 show the temperature history of the primary ontainment vessel Oring loation and the top enter of the 288 anister, respetively. These two temperature profiles are nearly idential. The "quasisteadystate" maximum temperatures ahieved at these loations are 47.25,47.45 and 46.45"C for the steadystate, step funtion and sinusoidal methods, respetively. All three methods predit temperatures whih are within 1.O"C of one another after a "quasisteadystate'' ondition has been reahed. Figures 6 and 7 indiate that the daily flutuation in heat flux is nearly damped out ompletely at loations around the CONCLUSIONS The results of this study indiate that the method used in applying the insolation has a signifiant effet on the temperatures of the outermost portions of the pakage. Maximum outer ontainer temperatures were found to vary by as muh as 19."C depending on whih insolation method was used. The sinusoidal method predits outer ontainer temperatures whih are higher than those predited by the step funtion method, whih are, in turn, higher than those predited by the steadystate solution. However, sine the total insolation over any 24hour period is the same for all ases, internal pakage temperatures (seondary ontainmentvessel, primary ontainment vessel, ontent, et.) are relatively unaffeted by the way in whih the insolation is applied. Temperatures at the seondary ontainment boundary and further into the pakage vary no more than 2 C for the three insolation methods investigated. As mentioned previously, these small temperature differenes are present due to the differenes in the amount of heat lost by the pakage to the surroundings resulting from differenes in external surfae temperatures. 7
SteadyState 5. Step Funtlon S ~ n u s o l d a l 4 7 =e 44. = e xe 4t. 8. 5. 1 2 4 5 6 7 8 9!! 1 1 2 1 1 4 Tlme (days) FIG. 6 PRIMARY CONTAINMENT VESSEL ORINGTEMPERATURE AS A FUNCTION OF TIME SteadyStale 5. +Step Funtion Sinusoidal I 47. e B I 41. 8. 5. 1 2 4 5 6 7 8 Tlme (days) 9 1 1 1 1 2 1 1 4 FIG. 7 ZSS CANISTER TOP CENTER TEMPERATURE AS A FUNCTION OF TIME J. C. Anderson and M. R. Feldrnan